The probability of winning on the come out roll is pr(7)+pr(11) = 6/36 + 2/36 = 8/36.

To save space I do not derive the expression each time since it is worked out above. Throughout this page you will see a lot of expressions of the form p/(p+q). If a wager wins with probability p, loses with probability q, and stays active with probability 1-p-q then the probability of winning eventually is: These bets can take several rolls or more to resolve. Many of the bets in craps win if one particular event happens before another. In craps the only bets with a tie are the don't pass and the don't come. The 'average bet resolved' is the product of the initial wager and the probability that the bet was resolved. To adjust for this, when a tie is possible, divide the expected return by the average bet resolved. In general ties are ignored in house edge calculations.

The player's edge would be -0.5/11 = -1/22 ≈ -4.545%.Īn exception to the house edge rule is when a tie is possible. Assuming a 50% chance of winning the expected return would be 0.5×(10) + 0.5×(-11) = -0.5. For example when betting against the line on a sporting event you have to bet $11 to win $10. The player's edge is the expected return divided by the initial bet. ∑ (probability of event i) × (return of event i) over all possible outcomes. The general formula for the expected return of a bet is: If you didn't know or can't figure out that the probability rolling a 6 is 5/36 then a visit to that page is a prerequisite for this page.

This is explained in depth in my dice probability basics page. Not only will this give you a deeper understanding of the odds but hopefully motivate you to refresh or improve your math skills.īefore going on you must have an understanding of the probability of throwing each total in one roll. Please stay a while and work through some of the bets yourself. To avoid multiplying by -1 for every bet I shall speak of everything in term's of the player's edge, which you can expect to be negative since the house ultimately has the edge on all bets except the free odds. Outside of this appendix I usually speak about the house edge, which is just the product of the player's edge and -1. This is where I derive the player's edge for all the major bets in craps. On This Page How the House Edge for Each Bet is Derived

Craps betting don't come