Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Suppose he combines those two teams into a parlay at 13:5. If each bet has 55 percent chance to win and the two bets are independent,
there is a 30.25 percent chance that the parlay will win. Getting 13:5 on the winner is a return of 8.9 percent on Frank’s bet. If Frank is able to find another independent 55 percenter to combine with the first two in a three-team parlay at 6:1, all three teams will win

CURRENT SUMMARY:
Suppose he combines those two teams into a parlay at 13:5. If each bet has 55 percent chance to win and the two bets are independent,
there is a 30.25 percent chance that the parlay will win.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Thus Frank earns a higher rate of return on parlays than on straight bets. But parlays are also more risky: Frank wins 55 percent of his
straight bets but only 30 percent of his two-teamers and 16.6 percent of his three-teamers. One reason for Frank or any other winning handicapper to consider parlays is to get money down on a high-expected-value situation. For
example, if you want to bet a particular game to go over and the sportsbook has a $300 max on that bet, you might be able to parlay the over with
something else for $500 without your bet affecting the line. Parlays With Odd Odds

Suppose you want to parlay teams listed on the board at terms other than -110. Can you do it? Of course you can; the sportsbooks have
figured out a way for you to make that bet. The first step in figuring o

CURRENT SUMMARY:
Thus Frank earns a higher rate of return on parlays than on straight bets. But parlays are also more risky: Frank wins 55 percent of his
straight bets but only 30 percent of his two-teamers and 16.6 percent of his three-teamers.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
For underdogs that’s easy: just move the decimal point two places to the left and add in the bet. For example, for a team being offered at
+160, a winning wager of $1 would result in cashing a ticket for $2.60. A $10 parlay of two dogs, say +140 and +160, should result in a ticket of
$10 x 2.40 x 2.60 = $62.40 if both dogs win. For favorites, the math is particularly easy to do for certain numbers, such as -200. A winning wager of $1 at terms of -200 would result in
cashing a ticket of $1.50. The math is easy enough to do for other favorites, and the results are shown in table 6. This is the table that sportsbooks
should use to calculate payoffs for parlays involving favorites. For example, a $10 parlay of -120 and -150 favorites should result in a ticket of $10
x $1.833 x 1.667 = $30.56 i

CURRENT SUMMARY:
For underdogs that’s easy: just move the decimal point two places to the left and add in the bet. For example, for a team being offered at
+160, a winning wager of $1 would result in cashing a ticket for $2.60.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge car


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
That yields the payoff per
dollar wagered on the parlay. Suppose you want to bet a $5 parlay of two baseball teams, one of which is being offered at -160 while the other is +170. For the -160 team,
table 6 shows that the $1 payoff is $1.625. For the +170 team, the $1 payoff is $2.70. If your $5 parlay wins, the payoff should be $5 x 1.625 x 2.70
= $13.81. You probably won’t be paid the odd penny. Probably your payoff will be rounded down. Individual sportsbooks may use slight variations of table 6. For example, the conversion number for a team going off at -130 should be 1.769,
but a sportsbook might round up to 1.770. The conversion number for -135 should be 1.741, but a sportsbook might round down to 1.740. In summary, when you parlay a group of teams that are going off at other than -11

CURRENT SUMMARY:
That yields the payoff per
dollar wagered on the parlay. Suppose you want to bet a $5 parlay of two baseball teams, one of which is being offered at -160 while the other is +170.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge car


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Parlay Cards
Parlay cards are not the same thing as off-the-board parlays. On parlay cards, the customer chooses from only those selections listed on the
cards. Those selections may or may not be listed on the board as being available for straight bets. Ties on parlay cards are handled according to the fine print on the parlay card. “Ties lose” is most common. Some cards specify that ties win. Payoffs are made according to the schedule listed on the card. The advantages of betting parlay cards are sometimes you can bet better numbers than are shown on the board, and sometimes you can bet
things that are not shown on the board, such as points scored by particular players. For several years I have been visiting Las Vegas just prior to the Super Bowl, and one of the things I have enjoyed doin

CURRENT SUMMARY:
Parlay Cards
Parlay cards are not the same thing as off-the-board parlays. On parlay cards, the customer chooses from only those selections listed on the
cards.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, let's tackle this step by step. The user is asking me to refine a knowledge card about sports betting, specifically focusing on parlay cards. They provided a excerpt and a current summary, an


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
For several years I have been visiting Las Vegas just prior to the Super Bowl, and one of the things I have enjoyed doing is walking from
sportsbook to sportsbook evaluating parlay cards and prop sheets. One reason to bet a parlay card is if you can make correlated selections. (Correlation is covered later in this chapter.) Another reason to bet a
parlay card is if you can find enough bets that you would love to make individually if they were listed on the board. Correlation Example
An interesting card I found at Santa Fe in Las Vegas in 1996 allowed me to select either team for first field goal, shortest field goal, or longest
field goal. That was an obvious correlation situation, because the first field goal could turn out to be the shortest or the longest. I made two parlay
bets:
1. Dal

CURRENT SUMMARY:
For several years I have been visiting Las Vegas just prior to the Super Bowl, and one of the things I have enjoyed doing is walking from
sportsbook to sportsbook evaluating parlay cards and prop sheets. One reason to bet a parlay card is if you can make correlated selections.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Pittsburgh to kick first, shortest, and longest field goal. The result: Dallas kicked the first field goal, and also had shortest and longest until the fourth quarter. Then Pittsburgh, behind two scores at
20-7, kicked a long field goal that left it still two scores behind. So both my parlays lost. Example of Good Selections
As an example of bets that might make a parlay card worthwhile, here are three items I selected on a parlay card at the Rio in Las Vegas for
the 2001 Super Bowl. I was able to combine Baltimore most penalty yards, Baltimore to kick the first field goal, and the total to go under 34 in a
parlay paying 6 for 1. During the season, Baltimore had suffered considerably more penalty yards than had the Giants. Baltimore had been
averaging 2.2 field goals per game, compared to

CURRENT SUMMARY:
Pittsburgh to kick first, shortest, and longest field goal. The result: Dallas kicked the first field goal, and also had shortest and longest until the fourth quarter.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The shakiest selection of the three was total to go under 34, but the total all
over town was 32 or 32.5 so under 34 looked worthwhile. Baltimore kicked the first field goal, and had 70 penalty yards to 27 for the Giants. But the final score was Baltimore 34, New York Giants 7,
so the under 34 was a loser. I lost $100 instead of winning $500. Disadvantages of Parlay Cards
The disadvantage of betting parlay cards is the payoff schedule: usually it is horrible. You might, for example, see a parlay card with a payoff
schedule similar to the third column of table 5, but specifying that ties lose. Or you might see a payoff schedule that looks like the third column of table 5 but all the numbers are “for 1” instead of “to 1.” For 1 means the
listed price includes the bet that is returned to you.

CURRENT SUMMARY:
The shakiest selection of the three was total to go under 34, but the total all
over town was 32 or 32.5 so under 34 looked worthwhile. Baltimore kicked the first field goal, and had 70 penalty yards to 27 for the Giants.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, let's tackle this. The user provided a detailed conversation history where they were refining a knowledge card. They've given me a new excerpt and a current summary, and I need to improve the


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Summary of Parlay Cards
In general, parlay cards are for suckers. But they are fun, and if you search hard enough you will find some good ones. Correlated Parlays
A time to consider betting a parlay is when you can take advantage of correlation. Correlation means the outcomes of two bets are linked
somehow; if one bet wins the other is likely to win, and if one bet loses the other is likely to lose. Two related terms that need to be defined are correlation and covariance. Correlation is the property of two outcomes being linked. Covariance is the mathematical measure that describes the degree of correlation. Lack of correlation is covariance of zero. A perfect correlation
has covariance of 1.0. A perfect negative correlation also has covariance of 1.0. A good example of bets that are corre

CURRENT SUMMARY:
Summary of Parlay Cards
In general, parlay cards are for suckers. But they are fun, and if you search hard enough you will find some good ones.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The team that is ahead at halftime is more
likely to win the game than is the team behind at halftime. Sportsbooks are aware of that correlation, and will not let you parlay halftimes and
totals of the same game. What you need are correlations that you are allowed to bet. There is zero correlation when two games are independent. When Tampa Bay plays at St. Louis and Tennessee plays at Jacksonville, you
probably have no reason to parlay St. Louis and Jacksonville because the results of those two games are uncorrelated. The probability of St. Louis covering the spread is the same whether Jacksonville wins or loses. One situation that can cause correlation is when there is a single random variable that is overly important in deciding the outcome of two
bets. A caution: Don’t use the word “cor

CURRENT SUMMARY:
The team that is ahead at halftime is more
likely to win the game than is the team behind at halftime. Sportsbooks are aware of that correlation, and will not let you parlay halftimes and
totals of the same game.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user has given me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge car


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Sportsbooks generally do not knowingly accept correlated parlays. Example: Storm
For example, suppose a big storm is predicted to move into an area in which two outdoor games are being played, but nobody knows
whether the storm will arrive early enough to affect the games. Also suppose that if the storm hits, it most likely will affect both games; it would be
unlikely for the storm to hit one game and not the other. Further suppose that you have a good idea of how a big storm is likely to affect each
game. That suggests making correlated parlays. How you bet each game depends on how you expect a storm to affect it. Perhaps you think that a
storm will hold down the score in one game, and will favor one team in the other game. You might want to parlay the under in the first game and
the appr

CURRENT SUMMARY:
Sportsbooks generally do not knowingly accept correlated parlays. Example: Storm
For example, suppose a big storm is predicted to move into an area in which two outdoor games are being played, but nobody knows
whether the storm will arrive early enough to affect the games.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Louis (14-3) against Tampa Bay (12-5) for the conference championship on 23 January 2000. Louis brings the NFL’s
best offense to the game, and Tampa Bay brings the conference’s best defense. Half of Las Vegas’s sportsbooks have St. Louis favored by 13.5,
and the other half have 14. The total also varies from book to book, ranging from 45 to 46.5. I think the St. Louis/Tampa Bay game is a correlation situation because the uncertainty in St. Louis’s score seems higher than the uncertainty
in Tampa Bay’s score. In the first seventeen games this season, Tampa Bay generally scored 13-24 points, and St. Louis typically allowed 10-24
points, so Tampa Bay probably will score in the 10-24 range. Louis’s score, on the other hand, is more uncertain. Louis generally scored more than 30 points and has

CURRENT SUMMARY:
Louis (14-3) against Tampa Bay (12-5) for the conference championship on 23 January 2000. Louis brings the NFL’s
best offense to the game, and Tampa Bay brings the conference’s best defense.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
But Tampa Bay’s defense is not typical. Tampa Bay
generally held its opponents to 17 points or less, and often held them to 10. If Tampa Bay were playing a typical opponent, we’d predict 10 to 17
points for that opponent. Louis of course is not a typical opponent; it is a scoring machine. Will Tampa Bay hold St. Louis to 17 points, or will
St. Louis break 30? The greater uncertainty as to the number of points to be scored by St. Louis is what gives rise to correlation. The big uncertainty in the game is whether Tampa Bay’s stingy defense can stop St. Tampa Bay seems incapable of mounting
offensive fireworks of its own, so it seems reasonable to expect Tampa Bay to stay within two touchdowns only if its defense stops St. Louis’s
offense. If Tampa Bay’s defense does stop St. Louis’s offense,

CURRENT SUMMARY:
But Tampa Bay’s defense is not typical. Tampa Bay
generally held its opponents to 17 points or less, and often held them to 10.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Louis’s offense proves overwhelming, St. Louis should cover the spread. Louis’s defense probably won’t stop

Tampa Bay from scoring its usual 10-24 points, so if St. Louis covers the spread the final total probably will go over. There seems to be much more uncertainty over how many points St. Louis will score than over how many points Tampa Bay will score. Both
the winner against the spread and whether the final total goes over or under seem to depend much more on how many points St. Louis scores
than on how many points Tampa Bay scores. That is the feature that makes this game an example of a correlation situation: A single random
variable appears to be important in deciding the outcome of two bets. Louis covers the spread, it is easier to visualize a high-scoring game
than a low-scoring

CURRENT SUMMARY:
Louis’s offense proves overwhelming, St. Louis should cover the spread.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Louis covers the spread, it is easier to visualize a high-scoring game
than a low-scoring game because Tampa Bay seems likely to get some points on the board. If Tampa Bay wins against the spread, it is easier to
imagine a low-scoring game than to imagine Tampa Bay scoring a lot of points. There are four possible side/total parlays, and one of them must win. Of the four, Tampa Bay/over seems particularly unlikely to win. I think
the probability of Tampa Bay covering the spread while the total goes over is no more than .05. Assigning a probability of .05 to TB/over means
assigning a probability of .95 to the sum of the other three parlays: TB/under, SL/over, and SL/under. The break-even point when a parlay pays
13:5 is .28. It’s possible that all three of those parlays are positive-EV bets,

CURRENT SUMMARY:
Louis covers the spread, it is easier to visualize a high-scoring game
than a low-scoring game because Tampa Bay seems likely to get some points on the board. If Tampa Bay wins against the spread, it is easier to
imagine a low-scoring game than to imagine Tampa Bay scoring a lot of points.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
If the total probability of those three
parlays is .95, the three-parlay combo has an EV of 14%. I think the SL/under parlay is weak, and I am trying do better than 14% by making only
the other two parlays. These are the two parlays I made on the game:
St. Louis and over
Tampa Bay and under
Caution: This analysis is my opinion, and could be wrong. Some experts think that the amount of correlation in this game was not enough to
make good bets of the parlays. As I visited various sportsbooks in Las Vegas looking for good numbers to make those parlays, one of the sportsbooks I visited was the
Frontier. It had Tampa Bay +14 and the total at 46.5, which was the second-highest total I found combined with Tampa Bay +14. I tried to put $500
on Tampa Bay and the under, but the Frontier would accept

CURRENT SUMMARY:
If the total probability of those three
parlays is .95, the three-parlay combo has an EV of 14%. I think the SL/under parlay is weak, and I am trying do better than 14% by making only
the other two parlays.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The supervisor actually used the word “covariance”
when explaining why he would not let me bet more than $100. When I posted that on BJ21.com, Frank B responded with:
I’ve had the same experience with that guy. The Frontier went independent awhile back and are very cautious of any type of action. They would only take $100 bets on many mainstream sporting events this year. When I went to bet a couple of correlated parlays there, the
writer called for approval. The manager started yelling about correlated parlays and limited me to $20 bets. The sportsbook manager there
will check any parlays he sees that match up the fav/over or dog/under when a large point spread is involved. He was getting hit all year with
parlays on the Cleveland Browns’ opponents and the OVER and the Browns/UNDER. The B

CURRENT SUMMARY:
The supervisor actually used the word “covariance”
when explaining why he would not let me bet more than $100. When I posted that on BJ21.com, Frank B responded with:
I’ve had the same experience with that guy.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
In another post, Frank adds:
There is an extensive track record of certain combinations of side/total lines showing a profit when parlayed. I would not call the St. Louis game one in which the two outcomes would be correlated much. For the most part, you want to deal with the lower totals. Big point
spread and a low total. I do not have figures in front of me to cite but there is a formula that has shown a respectable profit over quite a period
of time. Final score of the game: St. Louis 11, Tampa Bay 6. Tampa Bay covered the spread and the under won. Correlation Involving Playoff Hopes
Parlays are harder to evaluate than they are to spot. Here is one I considered one Sunday in late 2000: Indianapolis will make the playoffs
only if it beats Minnesota while Baltimore beats the Jets. The Bal

CURRENT SUMMARY:
In another post, Frank adds:
There is an extensive track record of certain combinations of side/total lines showing a profit when parlayed. I would not call the St.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The Baltimore-Jets game will be over (or almost over) before the Indianapolis-Minnesota
game starts. It’s possible that Indianapolis will play harder if Baltimore beats the Jets than if Baltimore loses to the Jets. That suggests parlaying
Indianapolis and Baltimore, and also parlaying Minnesota and the Jets. Caution: there are capable sports bettors who insist that the degree to which pro athletes “play harder” is too small to overcome the vig
inherent in a parlay. But just because correlation exists does not mean the amount of correlation is high enough to justify making the parlay. You should evaluate
each parlay individually. You might decide, for example, that it’s worth betting on Indianapolis to throw in the towel if their playoff hopes disappear
just before they take on Minnesota, b

CURRENT SUMMARY:
The Baltimore-Jets game will be over (or almost over) before the Indianapolis-Minnesota
game starts. It’s possible that Indianapolis will play harder if Baltimore beats the Jets than if Baltimore loses to the Jets.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
You might decide, for example, that it’s worth betting on Indianapolis to throw in the towel if their playoff hopes disappear
just before they take on Minnesota, but not worth betting on Indianapolis to rise to a higher level if Baltimore beats the Jets. You can also bring in the Miami-New England game, which also will be concluded before the Indianapolis-Minnesota game starts; If New
England beats Miami and Baltimore beats the Jets and Indianapolis beats Minnesota, then Indianapolis is the AFC East champion. I did not
parlay New England, Baltimore, and Indianapolis because I thought the correlation was not high enough to make the bet attractive at the odds I
expected to find in Las Vegas. But if you can find a sportsbook that pays 7:1 on three-team parlays, then such a parlay might justif

CURRENT SUMMARY:
You might decide, for example, that it’s worth betting on Indianapolis to throw in the towel if their playoff hopes disappear
just before they take on Minnesota, but not worth betting on Indianapolis to rise to a higher level if Baltimore beats the Jets. You can also bring in the Miami-New England game, which also will be concluded before the Indianapolis-Minnesota game starts; If New
England beat

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Many casinos offer proposition or prop bets for big events such as Super Bowls. Prop bets are limited only by the imagination of the
linesmakers. Prop bets can be on anything. Sportsbooks set up prop bets to attract more dollars of action and to bring in bettors who just want to peruse large numbers of bets. It seems
to work. This chapter explains how to evaluate certain prop bets: those involving events that occur one at a time, such as field goals. Three-Step Process
Evaluating a prop bet is a three-step process. The first step is to make a prediction of what is likely to happen. The second step is to assign
probabilities to both sides of the prop. The third step is to quantify your edge so that you can decide whether to place a bet. Step 1: Prediction
To predict the likely outcome, look

CURRENT SUMMARY:
Many casinos offer proposition or prop bets for big events such as Super Bowls. Prop bets are limited only by the imagination of the
linesmakers.

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Look at anything you can think of that might affect the prop. The linesmaker who thought up the prop probably thinks up several prop bets per
hour. If you devote enough time to analyzing enough props, you surely can find props where your prediction differs from the line posted in the
sportsbook. You are looking for props where the number of occurrences you expect is different from the number of outcomes specified in the prop. For
example if a prop allows you to bet over or under 2.5 of something or other, and you think the average number of that something ought to be 1.5,
then you can move on to step 2. Your prediction represents an average value, and the actual number of occurrences during the game may be greater or less than your
prediction. Technically what you are looking for is the me

CURRENT SUMMARY:
Look at anything you can think of that might affect the prop. The linesmaker who thought up the prop probably thinks up several prop bets per
hour.

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Summary: <1-2 sentences capturing the main point about sports betting>
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Stop 2: Assign Probabilities
Completing step 1 means you have a prediction, a number of something or others that you think will occur. You also have the description of
the prop. Now you must figure out the probability that each side of the prop will win. That’s what this chapter is all about. If, for example, you predict 1.5 and the prop allows you to bet over or under 2.5, step 2 is figuring out how likely the under 2.5 is to win. It’s all
mathematics. For this example, the answer is 81 percent. Under 2.5 means 0 or 1 or 2, and those happen 81 percent of the time when the
average is 1.5. Over 2.5 happens only 19 percent of the time. This arithmetic may seem like magic, but by the time you devour this chapter you will be able to perform such magic yourself. Step 3: Quantify Your Edge
Compl

CURRENT SUMMARY:
Stop 2: Assign Probabilities
Completing step 1 means you have a prediction, a number of something or others that you think will occur. You also have the description of
the prop.

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- <concise bullet 2>
- <concise bullet 3>
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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
You can compare that to the terms of the prop to determine
whether you have an edge, and if so what your edge is. Think of step 3 as shopping for value. It’s the same process you would use to evaluate any financial investment. You know how much money
you will be laying out, you know how much you will be collecting if you win, and in step 2 you have figured out how likely you are to win. Multiply the amount you will collect if you win by the probability of winning. That gives you the expected value of the payoff. Then compare that expected value with the amount you will be investing. If the expected value of the payoff is higher, you have an edge. If
the expected value of the payoff is the same as the bet, you will break even on average. If the expected value of the payoff is less than the

CURRENT SUMMARY:
You can compare that to the terms of the prop to determine
whether you have an edge, and if so what your edge is. Think of step 3 as shopping for value.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
If the expected value of the payoff is less than the amount
of the bet, do not make the bet unless you want to enrich the sportsbook. Example: Backing a Favorite
Suppose for example that you have identified a prop that you think will win 81 percent of the time. Suppose the terms on that bet are -190. Do
you have an edge, and if so what is it? The break-even point comes when you invest $81 to receive $100, which is a win of $19. To find the break-even terms, divide $81 by $19,
multiply by 100, and put a minus sign in front of it: -426. Think of the -426 as being a price tag: $426. The value of a $100 win is $426, but the sportsbook is offering to sell you that $100 win for only
$190. The smart shopper in you smiles at paying $190 for something worth $426. If the terms of the bet specified s

CURRENT SUMMARY:
If the expected value of the payoff is less than the amount
of the bet, do not make the bet unless you want to enrich the sportsbook. Example: Backing a Favorite
Suppose for example that you have identified a prop that you think will win 81 percent of the time.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
So what is your edge in percent? You pay $190, and that buys you an 81 percent chance of cashing a ticket for $290. The expected value of
the ticket you will be cashing is 81 percent times $290, or $235. On average you will be winning $235 minus $190, or $45. Simple division
computes your rate of return when you can earn $45 on an investment of $190: it’s almost 24 percent. Example: Backing a Dog
Suppose the terms on that bet are +125. There is no need to change any of the other details. You can still assume the bet has an 81 percent
chance of winning. So what is your edge in percent when you can make the bet at +125? It’s the same logic as above. You pay $100, and that buys you an 81 percent chance of cashing a ticket for $225. The expected value of the ticket you will be cashing is 81

p

CURRENT SUMMARY:
So what is your edge in percent? You pay $190, and that buys you an 81 percent chance of cashing a ticket for $290.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
A prop like that might be worth betting. In deciding whether to bet that prop and which side of it to take, there are two steps you will have to
take. Step one is analyzing data from games already played to see what has occurred in the past. The next step is to use your best judgment to estimate the expected number of quarterback sacks that will be allowed in the upcoming game. Think of it as estimating the average number of quarterback sacks that would occur if the game were played over and over a large number of
times. There might be reasons why you will expect more or fewer sacks than have typically happened in the past. This book will help you with the rest of the analysis after you have come up with the number that you think best represents expected or
average quarterback sacks. Suppo

CURRENT SUMMARY:
A prop like that might be worth betting. In deciding whether to bet that prop and which side of it to take, there are two steps you will have to
take.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Suppose you arrive at 4.7 as the mean number of sacks per game total for the two teams. Once you have settled on a mean number of
occurrences, mathematics takes over because there is a particular distribution of outcomes that applies. In other words, once you have told me that you expect an average of 4.7 somethings to happen during the game, I can tell you the probability
that the actual number will be 0, 1, 2, etc. Thus once you tell me 4.7 quarterback sacks, I can tell you precisely how likely it is that the number of quarterback sacks will be over 5,
under 5, or exactly 5. The material of this chapter applies to more than just quarterback sacks. It applies to any wager involving how many of one countable
variable. The last part of this chapter applies to any wager involving how many of

CURRENT SUMMARY:
Suppose you arrive at 4.7 as the mean number of sacks per game total for the two teams. Once you have settled on a mean number of
occurrences, mathematics takes over because there is a particular distribution of outcomes that applies.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The last part of this chapter applies to any wager involving how many of one countable variable versus how many of another countable
variable. Poisson Distribution
The mathematical distribution that describes the probabilities of each possible number of quarterback sacks is called the Poisson
distribution. Thanks to the work of an early 19th century French mathematician named Simeon Denis Poisson, you can start with the number you select
as the expected value and determine the probability of each possible outcome. Thus you can calculate how likely you are to win if you take one
side of the prop, and how likely you are to win if you take the other side of the prop. The two properties necessary for the Poisson distribution to apply to the number of events are: 1. The variable must be somethi

CURRENT SUMMARY:
The last part of this chapter applies to any wager involving how many of one countable variable versus how many of another countable
variable. Poisson Distribution
The mathematical distribution that describes the probabilities of each possible number of quarterback sacks is called the Poisson
distribution.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The probability of occurrence of an event is small, while the number of chances to achieve the event is large. Quarterback sacks follow a Poisson distribution because a) sacks occur one at a time, and b) there is a small chance of a quarterback sack
on any given play, but there are many plays in the game. Yards lost on quarterback sacks do not follow a Poisson distribution, because the yards occur in bunches instead of one at a time. Number of scores follows a Poisson distribution, but number of points scored is Poisson only if each score is worth one point. Number of penalties is Poisson, but not number of penalty yards since penalties vary in the number of yards assessed. The binomial distribution applies when there is a single event that can have either of two possible results — such as

CURRENT SUMMARY:
The probability of occurrence of an event is small, while the number of chances to achieve the event is large. Quarterback sacks follow a Poisson distribution because a) sacks occur one at a time, and b) there is a small chance of a quarterback sack
on any given play, but there are many plays in the game.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The
binomial distribution also applies when that event is repeated over and over. When one of the results is rare and there are a large number of repetitions, the binomial distribution begins to resemble the Poisson
distribution. Thus you can think of the Poisson as what the binomial distribution becomes when there are a large number of possible occurrences
of a rare event. What really gets interesting are props involving two Poisson distributions. There have been props comparing, say, missed free throws by a
particular basketball player and number of completions by a particular quarterback. The last part of this chapter applies to props like this. The easiest way to understand Poisson analysis is with examples. The Math
The old-fashioned way of solving problems like this is to find a stat

CURRENT SUMMARY:
The
binomial distribution also applies when that event is repeated over and over. When one of the results is rare and there are a large number of repetitions, the binomial distribution begins to resemble the Poisson
distribution.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The Math
The old-fashioned way of solving problems like this is to find a statistics text book, open it up to the tables of Poisson probabilities in the
appendix, and find the number you need. That’s easy to do if you happen to have a statistics book close at hand, and if you understand statistics
well enough to be confident you are grabbing the correct number out of the correct table. The way to solve problems like this without a statistics book is to use a spreadsheet, such as Excel. Excel gives the Poisson distribution
directly, and all you have to do is plug in three things:
1) the number of events of interest (5 in the example of quarterback sacks)
2) the average (4.7 in this example)
3) whether you want exactly 5 sacks, or 5 or fewer sacks. In this example you want the cumulative amo

CURRENT SUMMARY:
The Math
The old-fashioned way of solving problems like this is to find a statistics text book, open it up to the tables of Poisson probabilities in the
appendix, and find the number you need. That’s easy to do if you happen to have a statistics book close at hand, and if you understand statistics
well enough to be confident you are grabbing the correct number out of the correct table.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
I have used Excel to create appendixes A and B. They list the probabilities of events for Poisson distributions. If you wish, you can use Excel
to recreate any number in appendixes A and B. Appendix A has tables showing the probability of any exact number of events, and you would use it to find the probability of exactly 5
quarterback sacks. Appendix B has tables showing the cumulative probability, and you would use it to find the probability of 5 or fewer
quarterback sacks. You also can use Excel to analyze situations not specifically included in appendix A or B. For example, suppose you estimate 4.75 sacks per
game; appendix A gives you numbers for 4.7 and 4.8 but does not mention 4.75. You can interpolate between numbers in appendix A to come up
with an approximate answer, or you can us

CURRENT SUMMARY:
I have used Excel to create appendixes A and B. They list the probabilities of events for Poisson distributions.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
You can interpolate between numbers in appendix A to come up
with an approximate answer, or you can use Excel and come up with a more accurate answer. Likewise, if you need the distribution of something that occurs more frequently than the maximum listed in appendix A, Excel will give you the
answers you need. Our web site, BJ21.com, has a Links page with a link called Sports: Prop Tools, which includes an expansion of the material in appendixes A
and B. The numbers in the tables in appendix A may not add up to exactly 1.00 due to rounding. Back to the prop: “Total QB Sacks by: Both Teams. OVER EV; UNDER -120.” Find the applicable part of appendix A, the columns
that apply to the average QB sacks expected, which is 4.7. Find the row corresponding to five sacks. You should find the number 1

CURRENT SUMMARY:
You can interpolate between numbers in appendix A to come up
with an approximate answer, or you can use Excel and come up with a more accurate answer. Likewise, if you need the distribution of something that occurs more frequently than the maximum listed in appendix A, Excel will give you the
answers you need.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
That’s the probability in percent of five or fewer sacks. Subtract 67 percent from 100 percent to get the probability of more than five sacks. Appendix A says there is 17 percent probability of exactly five sacks. Appendix B says there is 33 percent probability of more than five sacks,
and 49 or 50 percent probability of fewer than five sacks. (A more precise figure on fewer than five sacks is 49.46 percent, which is rounded to 49
percent if you look at the row of appendix B corresponding to four sacks, but gets rounded to 50 percent if you look at the row corresponding to
five sacks. Either number is close enough for your purposes.)
Since you get your money back on pushes, you need be concerned only with the ratio of losses to wins. If that ratio is less than 1.0, you flip it
over and add

CURRENT SUMMARY:
That’s the probability in percent of five or fewer sacks. Subtract 67 percent from 100 percent to get the probability of more than five sacks.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
A bet on over five sacks would win 33 percent of the time, push 17 percent of the time, and lose 50 percent of the time. Looking at losses over
wins, you need 50/33 or +150 to break even on the over. Thus you certainly would not want to bet over five sacks at even money; your loss rate
would be 17 percent. A bet on under five sacks would win 50 percent of the time, push 17 percent of the time, and lose 33 percent of the time. The ratio of losses to
wins is 33/50, which is less than one. Flipping it over and adding a minus sign gives -50/33 or -150 to break even. You can make that bet for just 120. So if your 4.7 estimate is correct, you have an edge on under five sacks. Assuming the estimate of 4.7 expected sacks is correct, your $120 ticket has a 50% chance of turning into $220, a 17% cha

CURRENT SUMMARY:
A bet on over five sacks would win 33 percent of the time, push 17 percent of the time, and lose 50 percent of the time. Looking at losses over
wins, you need 50/33 or +150 to break even on the over.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user gave me a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card for


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
So the player advantage is 10.4/120 or 8.7
percent. Recap
Appendix A and B apply to proposition bets where events are counted in increments of one, such as number of quarterback sacks, number of
runs in baseball, number of eagles in a golf tournament, or number of free throws missed by a basketball superstar. Sample Usage of Appendix A
Find the part of appendix A that describes the distribution when the expected number of events is four. What is the probability of exactly four
events, what is the probability of three, and what is the probability of five? The applicable part of appendix A is reproduced above. The 20 in the 4 row means that the probability of getting exactly four events when 4.0
are expected is 20 percent. The probability of getting three events is 20 percent, and the probab

CURRENT SUMMARY:
So the player advantage is 10.4/120 or 8.7
percent. Recap
Appendix A and B apply to proposition bets where events are counted in increments of one, such as number of quarterback sacks, number of
runs in baseball, number of eagles in a golf tournament, or number of free throws missed by a basketball superstar.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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First, the user provided a specific excerpt that


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
How Many vs. How Many

Sometimes sportsbooks offer proposition bets that pit one variable against another. These bets can represent profitable opportunities to the
sharp bettor. An example of one such bet is:
Team to Make Most Field Goals in Game:
Baltimore Ravens -1/2 EV, or
New York Giants +1/2 -120
One of the props available for betting in Super Bowl XXXV was which team would kick more field goals, with the tie going to the New York
Giants. The line on the prop varied from sportsbook to sportsbook, and at one place was BAL even, Giants -120. If Baltimore kicked more field
goals, a $100 bet on Baltimore turned into $200. If the New York Giants kicked as many or more field goals than did Baltimore, a $120 bet on the
Giants turned into $220. Analyzing the Bet
The first part of analyzing a

CURRENT SUMMARY:
How Many vs. How Many

Sometimes sportsbooks offer proposition bets that pit one variable against another.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
You must look at the statistics for each team and decide for yourself how many
field goals each team is likely to kick in the upcoming game. You must come up with numbers representing a sort of average performance by
each team. I looked at the regular-season totals for each team and discovered that Baltimore on average kicked 2.2 field goals per game, and the New
York Giants kicked 1.2 per game. I saw no reason why either team should kick more or fewer field goals than that during the Super Bowl, so I
used 2.2 for Baltimore and 1.2 for the New York Giants. One caution: The betting advice you will get out of this chapter is only as valuable as the numbers you come up with for frequencies of
events. If the 2.2 and 1.2 field goals are good predictions of what is going to happen, then the anal

CURRENT SUMMARY:
You must look at the statistics for each team and decide for yourself how many
field goals each team is likely to kick in the upcoming game. You must come up with numbers representing a sort of average performance by
each team.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
have been able to win money using the material in this chapter; you should be able to do it too. You might have looked at the data and formed a different opinion of how many field goals to expect from each team, and that’s fine. You still
have to use your best judgment to come up with the average number of times the two events will happen, but after you have your two estimates
the rest is simply mathematics — no more judgment required. Before proceeding with the chapter, decide for yourself if you would have made the field goal bet presented above. Assume that the 2.2 and

CURRENT SUMMARY:
have been able to win money using the material in this chapter; you should be able to do it too. You might have looked at the data and formed a different opinion of how many field goals to expect from each team, and that’s fine.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
to kick as many as or more field goals than Baltimore? Do you think it is a close decision, or do you think your choice stands head and shoulders
over the opposing bet? The Math
Before you had quick computers in your homes and offices, and spreadsheets to do lightning-fast calculations, the way you solved problems
like this was to find the probabilities in a table in the appendix of a statistics book, multiply the numbers by hand, and then add them up to find the
probabilities of the various joint events. That’s a tedious, time-consuming job, and it’s easy to make a mistake. Once again, Excel is at your service. Excel does not solve this problem directly, but it gives you the numbers that you need to multiply
together and add up. Excel is quick and easy and accurate, but the procedure is c

CURRENT SUMMARY:
to kick as many as or more field goals than Baltimore? Do you think it is a close decision, or do you think your choice stands head and shoulders
over the opposing bet?

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Excel is quick and easy and accurate, but the procedure is complicated and mistakes are likely. I have used Excel to calculate the results for the range of numbers you are likely to encounter in prop bets in casinos, and have presented
those results as appendix C. It’s possible for you to use Excel to verify all the numbers in appendix C, but it’s tedious and time-consuming. You can interpolate between two rows or two columns of appendix C, but extrapolating beyond the given numbers is risky. It’s possible to
use Excel to generate numbers beyond the range given in appendix C, and one easily could expand that table to fill a hundred pages. If you need
Poisson probabilities beyond the range of numbers in appendix C, go to the Links page of our web site, BJ21.com, and click on Sports: Prop
To

CURRENT SUMMARY:
Excel is quick and easy and accurate, but the procedure is complicated and mistakes are likely. I have used Excel to calculate the results for the range of numbers you are likely to encounter in prop bets in casinos, and have presented
those results as appendix C.

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Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
If you need
Poisson probabilities beyond the range of numbers in appendix C, go to the Links page of our web site, BJ21.com, and click on Sports: Prop
Tools. The Math: An Example
Obviously, kicking an average of 2.2 field goals per game does not mean kicking exactly 2.2 field goals in every game. 2.2 is an average,
total field goals divided by total games. A similar statistic is the average American family having 2.2 children. I certainly hope that not too many
families have exactly 2.2 children! For an average of 2.2 field goals per game, appendix A yields:
For an average of 1.2 field goals per game, appendix A yields:

The totals might not sum to exactly 100 percent due to rounding. The next step is to multiply the numbers in the first list by the appropriate numbers in the second list t

CURRENT SUMMARY:
If you need
Poisson probabilities beyond the range of numbers in appendix C, go to the Links page of our web site, BJ21.com, and click on Sports: Prop
Tools. The Math: An Example
Obviously, kicking an average of 2.2 field goals per game does not mean kicking exactly 2.2 field goals in every game.

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Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Okay, so I'm trying to understand this sports betting thing. The user provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge card fo


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The next step is to multiply the numbers in the first list by the appropriate numbers in the second list to figure out the probability of Baltimore
kicking more field goals, the Giants kicking more field goals, and each team kicking the same number of field goals. The probability of neither team kicking a field goal is 11 percent times 30 percent, or 3.3 percent. They could also tie with one field goal
apiece (24 percent times 36 percent), two field goals apiece (27 percent times 22 percent), three field goals apiece (20 percent times 9 percent),
four field goals apiece (11 percent times 3 percent), or five field goals apiece (5 percent times 1 percent). Add those up and you get 20 percent
chance of a tie in the number of field goals kicked. You don’t need to do all this work yourself; it

CURRENT SUMMARY:
The next step is to multiply the numbers in the first list by the appropriate numbers in the second list to figure out the probability of Baltimore
kicking more field goals, the Giants kicking more field goals, and each team kicking the same number of field goals. The probability of neither team kicking a field goal is 11 percent times 30 percent, or 3.3 percent.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Using Appendix C
Appendix C applies to the situation of comparing the numbers of occurrences of two variables. The table describes them as “Variable A” and
“Variable B.” It does not matter whether A or B occurs first in time; either variable could be Variable A. Find the part of appendix C that contains a column heading matching the number you expect of one variable and a row that matches the
number you expect of the other variable. You might have to interpolate between two rows or between two column headers. Under each column header are three columns of numbers. Thus for the variables of interest you will find a set of three numbers in appendix
C. The first number is the probability that there will be more of Variable A. The second number is the probability that there will be more of Vari

CURRENT SUMMARY:
Using Appendix C
Appendix C applies to the situation of comparing the numbers of occurrences of two variables. The table describes them as “Variable A” and
“Variable B.” It does not matter whether A or B occurs first in time; either variable could be Variable A.

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Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Answer to the Field-Goal Example
Find the part of appendix C that applies to 2.2 for one team and 1.2 for the other. You should find three numbers: 60, 20, and 20. Those
numbers are percentages, 60 percent, 20 percent, and 20 percent. The third number is probability of a tie, and was calculated exactly as
explained above. The 60 percent is the probability that the actual number of occurrences of the variable expected to occur 2.2 times will exceed the actual
number of occurrences of the variable expected to occur 1.2 times. You can verify that if you enjoy arithmetic. The probability that Baltimore wins
the field-goal battle 1-0 is 24 percent times 30 percent. The probability that Baltimore wins the field-goal battle 2-0 is 27 percent times 30 percent,
etc. Again, appendix C has the final

CURRENT SUMMARY:
Answer to the Field-Goal Example
Find the part of appendix C that applies to 2.2 for one team and 1.2 for the other. You should find three numbers: 60, 20, and 20.

Provide an improved knowledge card in this exact format:
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Alright, so I'm trying to understand this sports betting thing. The user has provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Assuming 2.2 field goals for Baltimore and 1.2 for the Giants, appendix C tells you that the probability that Baltimore will kick more field goals
is 60 percent. The probability that the Giants will kick more is 20 percent, and the probability of a tie is 20 percent, for a win-or-tie total of 40
percent. A bet on Baltimore to kick the most field goals would win 60 percent of the time and lose 40 percent of the time, since ties go to the Giants. You need 40/60 or -60/40 or -150 to break even on that bet. Thus you certainly would smile when you see the bet offered at even money. At even
money, the player edge is 20 percent. One book offered Baltimore to kick most field goals at +120, a player edge of 32 percent. I jumped all over
that one, and was certainly pleased when Baltimore kicked the

CURRENT SUMMARY:
Assuming 2.2 field goals for Baltimore and 1.2 for the Giants, appendix C tells you that the probability that Baltimore will kick more field goals
is 60 percent. The probability that the Giants will kick more is 20 percent, and the probability of a tie is 20 percent, for a win-or-tie total of 40
percent.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

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Alright, so I'm trying to understand this sports betting thing. The user has provided a bunch of excerpts and wants me to extract the most important information and present it in a specific knowledge


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
You need 60/40 +150 to break
even. Since you are offered -120, you would decline. Of course you knew you would decline as soon as you saw that the bet on Baltimore is
worthwhile; you could not find both bets worthwhile at the same time. Minus or Plus Events
Sometimes you find props matching the number of times one thing will occur with one less than the number of times something else will
occur. It might have been reasonable, for example, for some sportsbook to offer bets on Baltimore Ravens field goals minus one versus New York
Giant field goals during Super Bowl XXXV. Had that prop been offered, the numbers in appendix C are approximations that would be close
enough for your purposes. Suppose the expected number of Ravens field goals is 2.2 and the expected number of Giants field goals i

CURRENT SUMMARY:
You need 60/40 +150 to break
even. Since you are offered -120, you would decline.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user has given me a few excerpts and wants me to extract the most important information and present it in a specific knowledge card for


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
For 1.2 versus 1.2, appendix C yields 36 percent chance of each side winning and 28
percent chance of a tie. For 2.2 versus 2.2, appendix C yields 40 percent chance of each side winning and 20 percent chance of a tie. Exact
calculations show that Ravens minus one has 38 percent chance of winning, Giants have 40 percent chance of winning, and there is 22 percent
chance of the Ravens ending up with exactly one field goal more than the Giants. So appendix C gives a fair approximation for plus or minus one
field goal. Some props involve plus or minus two or more events. Appendix C yields good-enough approximations for them also. The approximations are better for larger numbers of expected events. For example, you expect Variable A to occur 7.6 times and Variable B 6.4, and the prop is for the

CURRENT SUMMARY:
For 1.2 versus 1.2, appendix C yields 36 percent chance of each side winning and 28
percent chance of a tie. For 2.2 versus 2.2, appendix C yields 40 percent chance of each side winning and 20 percent chance of a tie.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

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Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Or you can find 7.6 versus 7.4, which is 47, 43, 10. Exact calculations yield 47, 43,
11, which does not sum to 100 percent due to rounding. For Higher Numbers
For numbers of events higher than are shown on appendix C, here is an approximation. Ties get rarer and rarer. Ignoring ties and looking at
just wins and losses, the difference between the numbers of the two variables is approximately as shown in table 7. The first column is the difference between the expected number of the more likely variable and the expected number of the other. The second
column is the probability of achieving more of the more likely variable, in percent. The third column is the probability of achieving more of the less
likely variable, in percent. For example, suppose you find a prop relating the number of A to

CURRENT SUMMARY:
Or you can find 7.6 versus 7.4, which is 47, 43, 10. Exact calculations yield 47, 43,
11, which does not sum to 100 percent due to rounding.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has given me a few excerpts and wants me to extract the most important information and present it in a specific knowledge card


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Table 7 says that the probability that the game will see more of A than B is around 65 percent. Table 7 is reproduced at the end of Appendix C. Summary
Identifying edges in bets that can be analyzed by the Poisson distribution is an aspect of sports betting that I have found to be most enjoyable
and rewarding. I hope you have as much fun as I have in finding and exploiting these opportunities. Sample Problems
The first seven sample problems are props copied from the Imperial Palace’s offerings for Super Bowl XXXV. Expected values for things like
number of tackles are not part of the props and are given here merely so that the problems have precise numerical solutions. Problem 1
Total tackles by J. Armstead (Giants):
Over 5
-130
Under 5
EV
Assume the expected number of tackles is 4.8. Probl

CURRENT SUMMARY:
Table 7 says that the probability that the game will see more of A than B is around 65 percent. Table 7 is reproduced at the end of Appendix C.

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Summary: <1-2 sentences capturing the main point about sports betting>
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Problem 2
Who will have more:
Ravens touchdowns + 1/2 -115
Blackhawks goals - 1/2
-115
Assume the Ravens are expected to score 1.6 touchdowns, and the Blackhawks are expected to score 2.5 goals. Problem 3
Who will have more:
T. Dilfer (Ravens) Completions -2
-115
S. O’Neal (LA) Missed Free Throws +2 -115
Assume Dilfer is expected to complete 12 passes. Assume O’Neal is expected to miss 7.3 free throws. Problem 4
Who will have more:
Dilfer (Ravens) Gross Passing Yds +32 -115
76ers + Pacers Points -32
-115
Assume Dilfer is expected to pass for 160 yards. Assume the 76ers and Pacers are expected to combine for 184.6 points. Problem 5
Will the Giants convert a 4th down attempt? Yes +160
No
-200
Assume the Giants convert an average of 0.4 fourth downs per game. Problem 6
Will the game ever be t

CURRENT SUMMARY:
Problem 2
Who will have more:
Ravens touchdowns + 1/2 -115
Blackhawks goals - 1/2
-115
Assume the Ravens are expected to score 1.6 touchdowns, and the Blackhawks are expected to score 2.5 goals. Problem 3
Who will have more:
T.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Yes
EV
No -130
Problem 7
Total number of players to have a passing attempt:
Over 2.5
-130
Under 2.5
EV
Obviously one quarterback minimum per team will have passing attempts. Assume that the probability of a second player attempting a pass
for the Giants is 10 percent, and the probability of a second player attempting a pass for the Ravens is 30 percent. Problem 8
Duke averages 10.6 three-pointers per game. Harrah’s offers +120 on Duke to shoot over 10.5 three-pointers. Is this a good bet? Problem 9
Maryland averages 20 assists per game. Harrah’s offers EV for over 19.5, and -120 for under 19.5. If you assume that the expected number of
assists for Maryland is 20, is either of these a good bet? Problem 10
Stardust has a prop on Maryland free throw attempts versus Duke three-point attempts.

CURRENT SUMMARY:
Yes
EV
No -130
Problem 7
Total number of players to have a passing attempt:
Over 2.5
-130
Under 2.5
EV
Obviously one quarterback minimum per team will have passing attempts. Assume that the probability of a second player attempting a pass
for the Giants is 10 percent, and the probability of a second player attempting a pass for the Ravens is 30 percent.

Provide an improved knowledge card in this exact format:
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Thus you can bet on Maryland free
throw attempts plus 6.5 versus Duke three-point attempts, or on Duke three-point attempts minus 6.5 versus Maryland free-throw attempts. Duke
has been allowing 18.0 free-throw attempts per game, and has been attempting 26.6 three pointers per game. Using those numbers as the
expectations for the upcoming game, is Duke -6.5 a good bet at -110? Problem 11
Several sportsbooks have a prop on free throws made: Duke -1.5 or Maryland +1.5. The line on Duke -1.5 is -120. Duke has been allowing

CURRENT SUMMARY:
Thus you can bet on Maryland free
throw attempts plus 6.5 versus Duke three-point attempts, or on Duke three-point attempts minus 6.5 versus Maryland free-throw attempts. Duke
has been allowing 18.0 free-throw attempts per game, and has been attempting 26.6 three pointers per game.

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Summary: <1-2 sentences capturing the main point about sports betting>
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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Saturday’s game, Duke’s expectation is to make 15.4 free throws and Maryland’s is to make 12.4 free throws. Is Duke -1.5 free throws a good bet at -120? Solutions to Sample Problems
The solutions to the sample prop problems are:
Problem 1
Total tackles by J. Armstead (Giants)
Over
-130
Under 5
EV
Assume the expected average number of tackles is 4.8. This is a typical use of appendix B. That table says the probability of four or fewer tackles is 48 percent, and the probability of five or fewer
tackles is 65 percent. Subtraction gives the probability of more than five tackles being 35 percent. For a bet on over five tackles to be profitable, the odds would have to be 48/35 x 100 = +137 or more, and the sportsbook is offering
considerably less than that. For a bet on under five tackles to be

CURRENT SUMMARY:
Saturday’s game, Duke’s expectation is to make 15.4 free throws and Maryland’s is to make 12.4 free throws. Is Duke -1.5 free throws a good bet at -120?

Provide an improved knowledge card in this exact format:
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Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Thus you have a
healthy edge betting on J. Armstead to produce under five tackles if the estimate of 4.8 tackles per game is accurate. Note that the solution depends on getting a refund of the bet if Armstead makes exactly five tackles. You have 48 percent probability of
winning, 35 percent probability of losing, and 17 percent probability of getting the bet refunded. Problem 2
Who will have more:
Ravens touchdowns + 1/2 -115
Blackhawks goals - 1/2
-115
Assume the Ravens are expected to score 1.6 touchdowns, and the Blackhawks are expected to score 2.5 goals. This is a typical use of appendix C. Look for 1.6 of one thing and 2.5 of the other. You should find 57, 24, and 19. Which number is probability of most Ravens touchdowns? If you are expecting 1.6 touchdowns and 2.5 goals, then on ave

CURRENT SUMMARY:
Thus you have a
healthy edge betting on J. Armstead to produce under five tackles if the estimate of 4.8 tackles per game is accurate.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
If you are expecting 1.6 touchdowns and 2.5 goals, then on average you will get
more goals than touchdowns. That logic says 57 percent probability of more Blackhawks goals, 24 percent probability of more Ravens
touchdowns, and 19 percent probability of Ravens touchdowns equaling Blackhawk goals. The terms of the prop give ties to the Ravens. Ravens touchdowns plus ties will win with probability 43 percent, and Blackhawk goals will
win with probability 57 percent. To break even on a bet on Blackhawk goals, you need a better price than - 57/43 x 100 = -132. You are offered the bet at -115 and that is a
better price than -132, so you have an edge betting Blackhawk goals -1/2. The amount of edge is .57/1.15 - .43, or 6.5 percent. Problem 3
Who will have more:
T. Dilfer (Ravens) Completions -2

CURRENT SUMMARY:
If you are expecting 1.6 touchdowns and 2.5 goals, then on average you will get
more goals than touchdowns. That logic says 57 percent probability of more Blackhawks goals, 24 percent probability of more Ravens
touchdowns, and 19 percent probability of Ravens touchdowns equaling Blackhawk goals.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific kno


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Use appendix C, looking for 7.3 and 10. You will not find 7.3, and will have to interpolate between 7.0 and 7.5. You should find Dilfer completions to win with probability 70 percent, O’Neal missed free throws to win with probability 23 percent, and a tie
(Dilfer completions exceeding O’Neal free throws by exactly 2) to occur with probability 8 percent. Or you can look for 9.3 and 12 in appendix C, and you will come up with about the same numbers. Or you could look up 8.3 and 11. Whichever numbers you use to solve the problem, you will discover that there is a huge edge betting on Dilfer completions -2. This prop actually was offered by the Imperial Palace, and Dilfer -2 looked like a fabulous bet to all who commented on it on the Football
page of BJ21.com. Unfortunately, O’Neal did not pl

CURRENT SUMMARY:
Use appendix C, looking for 7.3 and 10. You will not find 7.3, and will have to interpolate between 7.0 and 7.5.

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- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Begin the card now:

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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Unfortunately, O’Neal did not play in the game specified in the prop, and so all bets on that prop were refunded. Problem 4
Who will have more:
Dilfer (Ravens) Gross Passing Yards +32 -115
76ers + Pacers Points -32
-115
Assume Dilfer is expected to pass for 160 yards. Assume the 76ers and Pacers are expected to combine for 184.6 points. This is a trick question. The answer is: Poisson is an inappropriate tool to use to analyze the prop. One reason is: Yards are gained in
chunks, rather than one at a time. Another reason is: In basketball, points sometimes are scored two or more at a time, instead of always one at a
time. The methods of this chapter will not help you to decide whether this prop is worth betting. Problem 5
Will the Giants convert a 4th down attempt? Yes +160
No
-200
Assume t

CURRENT SUMMARY:
Unfortunately, O’Neal did not play in the game specified in the prop, and so all bets on that prop were refunded. Problem 4
Who will have more:
Dilfer (Ravens) Gross Passing Yards +32 -115
76ers + Pacers Points -32
-115
Assume Dilfer is expected to pass for 160 yards.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Yes +160
No
-200
Assume the Giants convert an average of 0.4 fourth downs per game. This prop can be analyzed with the help of appendix A. 0.4 converted fourth downs per game is associated with a 67 percent chance of no
fourth-down conversions. That means the “No” would be a break-even bet, and there is no worthwhile bet on this prop. Problem 6
Will the game ever be tied after 0-0? Yes
EV
No -130
This prop cannot be analyzed by the methods of this chapter. Problem 7
Total number of players to have a passing attempt:
Over 2.5
-130
Under 2.5
EV
Obviously one quarterback minimum per team will have passing attempts. Assume that the probability of a second player attempting a pass
for the Giants is 10 percent, and the probability of a second player attempting a pass for the Ravens is 30 percent

CURRENT SUMMARY:
Yes +160
No
-200
Assume the Giants convert an average of 0.4 fourth downs per game. This prop can be analyzed with the help of appendix A.

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Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
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Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific


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You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
The tables in this chapter will
not give you the solution to this problem. The probability of the Giants not getting a pass attempt from a second player is 90 percent and the probability of the Ravens not getting a
pass attempt from a second player is 70 percent, and multiplying those two numbers together gives you the probability that neither team will get a
pass attempt from a second player: 63 percent. Subtracting from 100 percent gives 37 percent as the probability that either or both teams will get a
pass attempt from a second player. Getting even money for something that happens with probability 63 percent is a great investment; your edge is 26 percent. If the 90 percent
and 70 percent are correct, you should bet that the total number of players to have a passing attempt will be unde

CURRENT SUMMARY:
The tables in this chapter will
not give you the solution to this problem. The probability of the Giants not getting a pass attempt from a second player is 90 percent and the probability of the Ravens not getting a
pass attempt from a second player is 70 percent, and multiplying those two numbers together gives you the probability that neither team will get a
pass attempt from a second player: 63

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Okay, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific kno


Question:
You are refining a knowledge card for a sports betting document. Extract the most important information.

EXCERPT:
Look at appendix B. For a mean of 10.6 and a frequency of 10, you see 51. That means there is 51 percent chance that Duke will hit ten or
fewer threes. That leaves a 49 percent chance that Duke will hit eleven or more threes. A $100 bet on that prop yields a 51 percent chance of
losing $100 and a 49 percent chance of winning $120. That means the average $100 wins $7.80. You must decide for yourself whether 7.8
percent expected return on a bet that will be decided in a day or two is worthwhile. Problem 9
Maryland averages 20 assists per game. Harrah’s offers EV for over 19.5, and -120 for under 19.5. If you assume that the expected number of
assists for Maryland is 20, is either of these a good bet? Appendix B says there is a 47 percent chance that Maryland will have 19 or fewer assists, me

CURRENT SUMMARY:
Look at appendix B. For a mean of 10.6 and a frequency of 10, you see 51.

Provide an improved knowledge card in this exact format:
Summary: <1-2 sentences capturing the main point about sports betting>
Key Points:
- <concise bullet 1>
- <concise bullet 2>
- <concise bullet 3>
Themes: theme1, theme2, theme3

Begin the card now:

Alright, so I'm trying to understand this sports betting thing. The user has provided several excerpts and summaries, and I need to extract the most important information and present it in a specific