The first step in the analysis of craps should be finding the probability of any However they all carry a different house edge, %, %, and we must calculate the ratio of "true odds" portion of the bet to the commission.

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Craps House Advantage Calculator with X Odds input. Roll Ways Pass$Odds$βRisk$WtAvg WinEV Analysis LossEV Analysis (uses Risk$).

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Field Bets; Snake Eyes; Ace Deuce; Yo; Boxcars; Craps; Any 7; The Horn. Optimal Strategy and House Edge; Fairness Calculator; Etiquette of the Game.

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Craps House Advantage Calculator with X Odds input. Roll Ways Pass$Odds$βRisk$WtAvg WinEV Analysis LossEV Analysis (uses Risk$).

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Calculate the house advantage by dividing our $1 net loss by our $66 total investment (1 / 66 = , which rounds to %). A % house advantageβ.

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The house edge on the pass line is one of the more involved calculations in craps, because pass is a multipart bet. You have to account for both.

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Field Bets; Snake Eyes; Ace Deuce; Yo; Boxcars; Craps; Any 7; The Horn. Optimal Strategy and House Edge; Fairness Calculator; Etiquette of the Game.

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Calculating the House Edge. Before starting to calculate the house advantage for a game of craps, players.

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Craps House Advantage Calculator with X Odds input. Roll Ways Pass$Odds$βRisk$WtAvg WinEV Analysis LossEV Analysis (uses Risk$).

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For example the Place 4 bets wins if a 4 is rolled before a 7. For example "" times odds allows the bettor it bet 3 times the pass line bet on points of 4 or 10, 4 times on 5 or 9, and 5 times on 6 or 8. As I write this it is one week before the Super Bowl. What will Donovan McNabb Phil do first vs. Odd bet Prob. The expected value is 0. However they all carry a different house edge, 1. The odds are the same for the place 8 bet. Note that there are three ways to make the exact same bet: the place 6, buy 6, and big 6. The Lay 5 bet wins if a 7 is rolled before a 5. The same method of analyzing many craps bets can also arguably be used to analyze Super Bowl proposition bets. Throw a touchdown pass or an interception. The Hard 4 bet wins if a hard 4 is rolled before a 7 or an easy 4. The bet wins if the shooter throws a 7 or 11 on the first roll, known as the come out roll. The bet pays 9 to 1. The pass bet is the most fundamental bet in craps. The following graph shows the frequency of each total. Otherwise whatever number is thrown becomes known as the point and a dealer will put a big white puck on that number so players remember what the point is. In other words, if my assumptions are correct a big if , the player would have an In other words the house edge on the interception first is Die 1. So overall it pays 39 to In gambling terminology "lay" means to risk more than you stand to win. Because the 1 and 3 is more likely it is called the "easy" way and the 2 and 2 is the "hard" way. There are 2 ways to roll an easy 4 and 6 ways to roll a 7. Many bets in craps take more than one role to evaluate. The next table shows all the possible outcomes, the probability of each, what it pays, and the return. Some gambling books state the house edge as 1. It is important to note that the frequency decreases on a linear basis as the total moves away from 7. The any craps bet wins if a 2, 3, or 12 is rolled on the next throw. The Hard 6 bet wins if a hard 6 is rolled before a 7 or an easy 6. This is because they incorrectly define the house edge as the expected loss per bet resolved, thus ignoring the push on Odds bets by definition always pay true odds. There are 3 ways to roll a 4: 2 ways to roll a 1 and 3, and 1 way to roll a 2 and 2. The Lay 6 bet wins if a 7 is rolled before a 6. The dice will be rolled indefinitely until a 4 or 7 is rolled. So the expected value is 0. Odds Allowed House Edge 1 0. Thus the actual odds are 19 to The odds are the same on the lay 10 bet.

The first step in the analysis of craps should be finding the probability of any given total. Die 1 Die 2. Calculating house advantage craps following table shows the total of each possible outcome of calculating house advantage craps dice. Dice Total Frequency Probability 2 1 0.

The odds are the same on the lay 8 bet. The bet loses if the shooter throws a 2, 3, or 12 on the come out roll. The craps 2 bet pays 30 to 1 often stated as 31 for 1 on the felt if the player rolls a total of 2 on the next roll. Die 2.

However it pays only 1 to 1. So in Europe the odds would look like this:. Almost every player makes it. For example betting against the spread or on a total in sports the bettor must generally lay or risk 11 to win In craps the player can lay odds that a 7 will appear before a 4 or any other "place number". Then the shooter will keep rolling until he either rolls a 7 or the point again. The any 7 bet pays 4 to 1 if the player rolls a total of 7 on the next roll. As we see from the decimal conversion the player will get back 1. The yo 11 bet pays 15 to 1 if the player rolls a total of 11 on the next roll. The bet wins if a 4 is thrown before a 7. The following table shows the probability of winning and true odds of each odds bet. For example Caesars Tahoe has the following bet. The odds are the same on the lay 9 bet. The odds are the same on the hard 8 bet. If we assume perhaps incorrectly that any given pass by McNabb is likely to result in a touchdown pass or interception with constant probabilities then we can look at some past data to estimate the probability of each. You would think players would only bet the place 6 of the three, but alas players still bet the other two. There is 1 way to roll a 2, 2 ways to roll a 3, and 1 way to roll a The bet pays 7 to 1. There is only 1 way to roll a hard 6. If you wish to calculate the expected return by the averaging method as show for the Buy 4 bet then we must calculate the ratio of "true odds" portion of the bet to the commission. There are 4 ways to roll an easy 6 2 ways of 1 and 5, and 2 ways of 2 and 4 and 6 ways to roll a 7, for a total of 10 ways to lose. Note that if the player takes the maximum allowed odds he always stands to win six times his pass line bet on the odds. The player will always bet 1 unit on the pass line. In my opinion I think the European notation makes more sense and I hope, but doubt, the U. The odds are exactly the same for the Place 10 bet. There is only 1 way to roll a hard 4. Another way to analyze this bet is to break it down into two bets. Please take the following on faith. The probability of x shall be denoted as pr x and the probability of y as pr y. The odds are the same for the place 9 bet. However if he wins it will be deducted from the win. In Europe they use decimal notation, showing how much the player gets back, including his original wager, for a 1 unit bet. The Big 6 is yet another bet that pays if a 6 is rolled before a 7. The odds are the same on the hard 10 bet. If he rolls the point first the pass bet wins, if he rolls a 7 first the pass loses. The buy 4 bet is the same as the place 4 bet, except in payoff. One unit is his original bet back and the 0.