Walkinshaw30t
Joined: Apr 11, 2013
• Posts: 91
January 13th, 2014 at 4:02:41 AM permalink
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
dwheatley
Joined: Nov 16, 2009
• Posts: 1246
January 13th, 2014 at 4:57:25 AM permalink
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
7craps
Joined: Jan 23, 2010
• Posts: 1977
January 13th, 2014 at 8:02:59 PM permalink
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
PB hands10+P Prob
100.000851159
120.00276002
140.005613949
160.009209165
180.013343845
200.017847551
220.022585732
240.027455765
260.032380966
280.037304874
300.042186466
320.046996376
340.051713992
360.056325251
380.060820977
400.065195632
420.069446377
440.073572365
460.077574212
480.081453589
500.085212928
520.088855185
540.092383673
560.09580193
580.09911362
600.102322461
620.105432172
640.108446428
660.111368838
680.114202917
700.116952077
720.119619616
740.122208711
760.124722417
780.127163666
800.129535268
820.13183991
840.134080165
860.13625849
880.138377234
900.140438638
920.142444843
940.144397891
960.146299735
980.148152235
1000.14995717
winsome johnny (not Win some johnny)
Walkinshaw30t
Joined: Apr 11, 2013
• Posts: 91
January 14th, 2014 at 7:07:26 AM permalink
Time will tell
Walkinshaw30t
Joined: Apr 11, 2013
• Posts: 91
January 17th, 2014 at 9:39:00 AM permalink
Quote: 7craps

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

PB hands10+P Prob
100.000851159
120.00276002
140.005613949
160.009209165
180.013343845
200.017847551
220.022585732
240.027455765
260.032380966
280.037304874
300.042186466
320.046996376
340.051713992
360.056325251
380.060820977
400.065195632
420.069446377
440.073572365
460.077574212
480.081453589
500.085212928
520.088855185
540.092383673
560.09580193
580.09911362
600.102322461
620.105432172
640.108446428
660.111368838
680.114202917
700.116952077
720.119619616
740.122208711
760.124722417
780.127163666
800.129535268
820.13183991
840.134080165
860.13625849
880.138377234
900.140438638
920.142444843
940.144397891
960.146299735
980.148152235
1000.14995717

7craps would you have a similar table for other differentials in particular 7 and 15?
Time will tell