• Craps

    Don't Pass Math

    Guest Posted on
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    Posted by: Guest on August 20, 2012, 9:23 am

    There are two acceptable results for the Don’t Pass bet:

    -0.01364 = -1.36%

    or

    -0.01403 = -1.40%

    The formulas are different. It depends upon your belief on how to handle the 12.

    Posted by: Guest on August 20, 2012, 9:26 am

    ((-8/36)+(3/36))-(1/36*3/9)*3-(1/36*4/10)*4-(1/36*5/11)*5-(1/36*5/11)*5-(1/36*4/10)*4-(1/36*3/9)*3+(1/36*6/9)*3+(1/36*6/10)*4+(1/36*6/11)*5+(1/36*6/11)*5+(1/36*6/10)*4+(1/36*6/9)*3=-0.0136363636363638[/tds]

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    Posted by: Guest on August 20, 2012, 9:36 am

    Posted by: Guest on August 20, 2012, 7:56 pm

    It is interesting to note that various authors use different methods to arrive at the Math of Craps:

    http://wizardofodds.com/games/craps/appendix/1/

    Don’t Pass/Don’t Come

    The probability of winning on the come out roll is pr(2)+pr(3) = 1/36 + 2/36 = 3/36.
    The probability of pushing on the come out roll is pr(12) = 1/36.
    The probability of establishing a point and then winning is pr(4)×pr(7 before 4) + pr(5)×pr(7 before 5) + pr(6)×pr(7 before 6) + pr(8)×pr(7 before 8) + pr(9)×pr(7 before 9) + pr(10)×pr(7 before 10) =
    (3/36)×(6/9) + (4/36)×(6/10) + (5/36)×(6/11) + (5/36)×(6/11) + (4/36)×(6/10) + (3/36)×(6/9) =
    (2/36) × (18/9 + 24/10 + 30/11) =
    (2/36) × (1980/990 + 2376/990 + 2700/990) =
    (2/36) × (7056/990) = 14112/35640
    The total probability of winning is 3/36 + 14112/35640 = 17082/35640 = 2847/5940
    The probability of losing is 1-(2847/5940 + 1/36) = 1-(3012/5940) = 2928/5940
    The expected return is 2847/5940×(+1) + 2928/5940×(-1) = -81/5940 = -3/220 ≈ 1.364%

    Most other sources on craps will claim that the house edge on the don’t pass bet is 1.403%. The source of the discrepancy lies is whether or not to count ties. I prefer to count ties as money bet and others do not. I’m not saying that one side is right or wrong, just that I prefer counting them. If you don’t count ties as money bet then you should divide by figure above by the probability that the bet will be resolved in a win or loss (35/36). So 1.364%/(35/36) ≈ -1.403%. This is the house edge assuming that the player never rolls a 12 on the come out roll.

    Posted by: Guest on August 23, 2012, 5:54 pm

    Right click on the chart and chose View Image to see the full chart:

    Guest
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    ((-8/35)+(3/35))-(1/35*3/9)*3-(1/35*4/10)*4-(1/35*5/11)*5-(1/35*5/11)*5-(1/35*4/10)*4-(1/35*3/9)*3+(1/35*6/9)*3+(1/35*6/10)*4+(1/35*6/11)*5+(1/35*6/11)*5+(1/35*6/10)*4+(1/35*6/9)*3=-0.014025974025974[/tds]