craps
dice rolls
2 -> 1 3 -> 2 4 -> 3 5 -> 4 6 -> 5 7 -> 6 8 -> 5 9 -> 4 10 -> 3 11 -> 2 12 -> 1
win on pass
7, 11 6/36 + 2/36 = 8/36 = 0.222
lose on pass
2, 3, 12 1/36 + 2/36 + 1/36 = 4/36 = 0.111
calculating probability of x rolling before y
pr(x before y) = [pr(x) / pr(x) + pr(y)]
pass or come odds
pays 1:1 comeout win = pr(7) + pr(11) = 8/36 after comeout = pr(4)×pr(4 before 7) + pr(5)×pr(5 before 7) + pr(6)×pr(6 before 7) + pr(8)×pr(8 before 7) + pr(9)×pr(9 before 7) + pr(10)×pr(10 before 7) = (3/36 * 3/9) + (4/36 * 4/10) + 5/36 * 5/11 + 5/36 * 5/11 + 4/36 * 4/10 + 3/36 * 3/9 the overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495 the probability of losing is obviously 1-(244/495) = 251/495 the player's edge is thus (244/495)×(+1) + (251/495)×(-1) = -7/495 ≈ -1.414%. (house edge)
244/495 * x - 251/495 = 0 244/495 * x = 251/495 244 * x = 251 x = 251/244 (payout if 0% edge)
buying the odds
0% house edge pays:
- 2/1 on 4, 10
- 3/2 on 5, 9
- 6/5 on 6, 8
edge = pr(4 before 7) * payout - pr(7 before 4)
4 and 10: 3/9 × 2/1 + -6/9 = 0.000% 5 and 9: 4/10 × 3/2 + -6/10 = 0.000% 6 and 8: 5/11 × 6/5 + -6/11 = 0.000%
place bet
place 6 and 8: pays 7/6
target: 80-100 rolls per hour. start at 6pm -> play until 2-3am: 6hours
6 * 100 = 600 rolls -> i want to play 6h with $300 $300/600 = 50c per roll loss
plapayouts
pass/come, 1.41% house edge
- 1
taking the odds, 0% house edge
- 2/1 on 4, 10
- 3/2 on 5, 9
- 6/5 on 6, 8
place bets:
- 7/6 on 6, 8 with 1.52% house edge
strategies
- always place 6/8
- have 4 numbers working
- use $30 per shooter on a table min. of $15