Probability of player winning by 10 or more hands than banker in x spins?
January 13th, 2014 at 4:02:41 AM
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Can anybody tell me the math to work out the probability of player winning 10 + hands more than banker in x hands?
Time will tell
January 13th, 2014 at 4:57:25 AM
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One reasonable approach is to use the cumulative Bernoulli distribution. Set the probability of success equal to the probability of winning your game (Baccarat or Roulette, I can't tell). X is the number of trials, and (x+10)/2 is the number of successes.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
January 13th, 2014 at 8:02:59 PM
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using ((x+10)/2)-1 and Excel
= 1 - BINOMDIST(((A2+10)/2)-1,A2,0.493175,TRUE)
0.493175 = Player win for 8 deck Bacc
the cumulative Bernoulli distribution is for x or less
example where x = 36 hands
(36+10)/2 = 23 wins (and 13 losses for the 10 margin)
but using the BINOMDIST() we need to calculate 22 or less wins (22 to 0)
and subtract that value from 1
of course one can use the binomial probability dist formula and calculate the probability of exactly
23 to 36 successes and add them all up
a lot of math work if doing by hand by either method
here is a table that just appeared
close to some simulations I have seen
= 1 - BINOMDIST(((A2+10)/2)-1,A2,0.493175,TRUE)
0.493175 = Player win for 8 deck Bacc
the cumulative Bernoulli distribution is for x or less
example where x = 36 hands
(36+10)/2 = 23 wins (and 13 losses for the 10 margin)
but using the BINOMDIST() we need to calculate 22 or less wins (22 to 0)
and subtract that value from 1
of course one can use the binomial probability dist formula and calculate the probability of exactly
23 to 36 successes and add them all up
a lot of math work if doing by hand by either method
here is a table that just appeared
close to some simulations I have seen
| PB hands | 10+P Prob |
|---|---|
| 10 | 0.000851159 |
| 12 | 0.00276002 |
| 14 | 0.005613949 |
| 16 | 0.009209165 |
| 18 | 0.013343845 |
| 20 | 0.017847551 |
| 22 | 0.022585732 |
| 24 | 0.027455765 |
| 26 | 0.032380966 |
| 28 | 0.037304874 |
| 30 | 0.042186466 |
| 32 | 0.046996376 |
| 34 | 0.051713992 |
| 36 | 0.056325251 |
| 38 | 0.060820977 |
| 40 | 0.065195632 |
| 42 | 0.069446377 |
| 44 | 0.073572365 |
| 46 | 0.077574212 |
| 48 | 0.081453589 |
| 50 | 0.085212928 |
| 52 | 0.088855185 |
| 54 | 0.092383673 |
| 56 | 0.09580193 |
| 58 | 0.09911362 |
| 60 | 0.102322461 |
| 62 | 0.105432172 |
| 64 | 0.108446428 |
| 66 | 0.111368838 |
| 68 | 0.114202917 |
| 70 | 0.116952077 |
| 72 | 0.119619616 |
| 74 | 0.122208711 |
| 76 | 0.124722417 |
| 78 | 0.127163666 |
| 80 | 0.129535268 |
| 82 | 0.13183991 |
| 84 | 0.134080165 |
| 86 | 0.13625849 |
| 88 | 0.138377234 |
| 90 | 0.140438638 |
| 92 | 0.142444843 |
| 94 | 0.144397891 |
| 96 | 0.146299735 |
| 98 | 0.148152235 |
| 100 | 0.14995717 |
winsome johnny (not Win some johnny)
January 14th, 2014 at 7:07:26 AM
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Thanks guys appreciate your help
Time will tell
January 17th, 2014 at 9:39:00 AM
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Quote: 7crapsusing ((x+10)/2)-1 and Excel
= 1 - BINOMDIST(((A2+10)/2)-1,A2,0.493175,TRUE)
0.493175 = Player win for 8 deck Bacc
the cumulative Bernoulli distribution is for x or less
example where x = 36 hands
(36+10)/2 = 23 wins (and 13 losses for the 10 margin)
but using the BINOMDIST() we need to calculate 22 or less wins (22 to 0)
and subtract that value from 1
of course one can use the binomial probability dist formula and calculate the probability of exactly
23 to 36 successes and add them all up
a lot of math work if doing by hand by either method
here is a table that just appeared
close to some simulations I have seen
PB hands 10+P Prob 10 0.000851159 12 0.00276002 14 0.005613949 16 0.009209165 18 0.013343845 20 0.017847551 22 0.022585732 24 0.027455765 26 0.032380966 28 0.037304874 30 0.042186466 32 0.046996376 34 0.051713992 36 0.056325251 38 0.060820977 40 0.065195632 42 0.069446377 44 0.073572365 46 0.077574212 48 0.081453589 50 0.085212928 52 0.088855185 54 0.092383673 56 0.09580193 58 0.09911362 60 0.102322461 62 0.105432172 64 0.108446428 66 0.111368838 68 0.114202917 70 0.116952077 72 0.119619616 74 0.122208711 76 0.124722417 78 0.127163666 80 0.129535268 82 0.13183991 84 0.134080165 86 0.13625849 88 0.138377234 90 0.140438638 92 0.142444843 94 0.144397891 96 0.146299735 98 0.148152235 100 0.14995717
7craps would you have a similar table for other differentials in particular 7 and 15?
Time will tell
