jimsanders
Joined: Jul 11, 2011
• Posts: 1
July 11th, 2011 at 11:47:54 PM permalink
Does anyone know how to convert the info from this table:

to include an "or better" column?

E.g., I am not really interested in the fact that the probability of winning 3 straight banker hands followed by a player win is 6.42 percent.

Much more useful would be what is the probability of winning 3 hands or better?

So obviously it is somewhere greater than 6.42 percent, but by how much?

Edit: I think maybe this was a dumb question because I could just add up all the probabilities after the number I wanted. Tedious but it should work.
guido111
Joined: Sep 16, 2010
• Posts: 707
July 12th, 2011 at 12:18:21 AM permalink
Quote: jimsanders

Much more useful would be what is the probability of winning 3 hands or better?

using a streak calculator HERE with 70 hands per shoe (you can play with the numbers if you like) using .506825 for a banker win:
99.7426% of at least 1 run of 3 or more banker hands.
here is a table for Baccarat Banker streaks per shoe: (3+ = 3 or more)
Player streaks follow Banker streak data
Banker Streak (Run) Length - at least 1Probability
3+99.742607%
4+92.727651%
5+70.413532%
6+44.202399%
7+24.754735%
8+13.067325%
9+6.698935%
10+3.385407%
11+1.698894%
12+0.849567%

For 8 deck shoe
distribution (by simulation) of a run of length 3 or more (banker win streaks)
`# of 3+	freq	prob0	25715	0.25715% (1 in 388.88 shoes)1	218438	2.18438%2	810973	8.10973%3	1753291	17.53291%4	2442686	24.42686%5	2297366	22.97366%6	1498439	14.98439%7	682613	6.82613%8	215741	2.15741%9	47191	0.47191%10	6913	0.06913%11	601	0.00601%12	33	0.00033%		trials	10,000,000			minimum value:	0	first quartile:	3	median: 	4	third quartile:	5	maximum value:	12	 		mean value:	4.44	sample variance	2.48	sample std	1.58	`

distribution (by simulation) of a run of length 4 or more (banker win streaks)
`# of 4+	freq	prob0	726005	7.26005%  (1 in 13.77 shoes)1	2291892	22.91892%2	3100147	31.00147%3	2360153	23.60153%4	1109819	11.09819%5	336620	3.36620%6	66210	0.66210%7	8489	0.08489%8	646	0.00646%9	19	0.00019%		trials	10,000,000			minimum value:	0	first quartile:	1	median: 	2	third quartile:	3	maximum value:	9	 		mean value:	2.22	sample variance	1.59	sample std	1.26	`

distribution (by simulation) of a run of length 5 or more (banker win streaks)
`# of 5+	freq	prob0	2955327	29.55327%  (1 in 3.38 shoes)1	3987698	39.87698%2	2240241	22.40241%3	680272	6.80272%4	122561	1.22561%5	13014	0.13014%6	854	0.00854%7	32	0.00032%8	1	0.00001%trials	10,000,000			minimum value:	0	first quartile:	0	median: 	1	third quartile:	2	maximum value:	8	 		mean value:	1.11	sample variance	0.91	sample std	0.96	`

distribution (by simulation) of a run of length 6 or more (banker win streaks)
`# of 6+	freq	freq/1000	5643729    56.44%  1	3411158    34.11%2	 832931     8.33%3	 104708     1.05%4	   7196     0.07%5	    273     0.00%6	      5     0.00%trials	10,000,000			minimum value:                 0.00first quartile:                0.00median:                        0.00third quartile:                1.00maximum value:                 6.00mean value:                    0.54sample variance (n):           0.49sample std dev (n):            0.70`

from the data below per 8 deck shoe (not counting ties) the *average* number of banker and player runs (streaks)
note: each data point has it's own distribution
Banker Streakavg # of runsavg # of runs
length of runexactor more
19.37540282618.75342461
24.6892118259.378021788
32.3449450244.688809963
41.172428272.343864939
50.5860821811.171436669
60.29291870.585354488
70.1463691840.292435788
80.0731246340.146066604
90.0365247020.07294197
100.0182396230.036417268

Player STreakavg # of runsavg # of runs
length of runexactor more
19.62105704718.73977461
24.6823880979.118717568
32.2784247974.436329471
41.1084664652.157904673
50.5391738171.049438209
60.2622111290.510264391
70.1274932390.248053263
80.0619775510.120560024
90.030122450.058582473
100.0146370010.028460023

Below table shows average number of hands for the run length or more and the median number of hands for Baccarat Banker win streaks. 2+ = 2 or more.
Baccarat Banker win streaks
runaverage # of handsmedian # of handsmedian prob
2+7.8926451.034934%
3+15.57031052.161036%
4+30.71682151.424335%
5+60.59734250.689012%
6+119.54508350.273484%
7+235.835416450.158229%
8+465.250332350.044911%
9+917.834563750.022250%
10+1810.6816125650.006342%
11+3572.0686247750.000344%
12+7046.8902488650.001116%

Below table shows average number of hands for the run length or more and the median number of hands for Baccarat Player win streaks

Baccarat Player win streaks
runaverage # of handsmedian # of handsmedian prob
2+8.1135558.293387%
3+16.45401153.317153%
4+33.36862351.491927%
5+67.67104750.650740%
6+137.23599550.117952%
7+278.312519350.042576%
8+564.413939250.056113%
9+1144.623679450.006768%
10+2321.2808161050.005510%
11+4707.5255326550.009921%
12+9546.7968661950.001570%

Baccarat Player streaks
All 8 deck simulations
`Baccarat Player Streaks 3+ in a row       group         middle    freq  freq/100----------------------------------------------0.50 <= x <  0.50     0.00     286     0.29% 0.50 <= x <  1.50     1.00    2553     2.55% 1.50 <= x <  2.50     2.00    8674     8.67% 2.50 <= x <  3.50     3.00   17779    17.78% 3.50 <= x <  4.50     4.00   23970    23.97% 4.50 <= x <  5.50     5.00   22205    22.20% 5.50 <= x <  6.50     6.00   14736    14.74% 6.50 <= x <  7.50     7.00    6909     6.91% 7.50 <= x <  8.50     8.00    2226     2.23% 8.50 <= x <  9.50     9.00     563     0.56% 9.50 <= x < 10.50    10.00      82     0.08%10.50 <= x < 11.50    11.00      15     0.02%11.50 <= x < 12.50    12.00       1     0.00%12.50 <= x < 13.50    13.00       1     0.00%---------------------------------------------                      grouped dataitems:                  100000   minimum value:               0.00first quartile:              3.00median:                      4.00third quartile:              5.00maximum value:              13.00mean value:                  4.41midrange:                    6.50range:                      13.00interquartile range:         2.00mean abs deviation:          1.31sample variance (n):         2.60sample variance (n-1):       2.60sample std dev (n):          1.61sample std dev (n-1):        1.61---------------------------------------------                 cumulative----------------------------------------------0.50 <= x <  0.50     0.00     286     0.29% 0.50 <= x <  1.50     1.00    2839     2.84% 1.50 <= x <  2.50     2.00   11513    11.51% 2.50 <= x <  3.50     3.00   29292    29.29% 3.50 <= x <  4.50     4.00   53262    53.26% 4.50 <= x <  5.50     5.00   75467    75.47% 5.50 <= x <  6.50     6.00   90203    90.20% 6.50 <= x <  7.50     7.00   97112    97.11% 7.50 <= x <  8.50     8.00   99338    99.34% 8.50 <= x <  9.50     9.00   99901    99.90% 9.50 <= x < 10.50    10.00   99983    99.98%10.50 <= x < 11.50    11.00   99998   100.00%11.50 <= x < 12.50    12.00   99999   100.00%12.50 <= x < 13.50    13.00  100000   100.00%---------------------------------------------  Baccarat Player Streaks  4+ in a row        group        middle    freq  freq/100--------------------------------------------0.5 <= x < 0.50     0.00    8245     8.24%0.50 <= x < 1.50     1.00   24203    24.20%1.50 <= x < 2.50     2.00   31280    31.28%2.50 <= x < 3.50     3.00   22190    22.19%3.50 <= x < 4.50     4.00   10236    10.24%4.50 <= x < 5.50     5.00    3092     3.09%5.50 <= x < 6.50     6.00     661     0.66%6.50 <= x < 7.50     7.00      86     0.09%7.50 <= x < 8.50     8.00       7     0.01%-------------------------------------------                   grouped dataitems:                  100000   minimum value:               0.00first quartile:              1.00median:                      2.00third quartile:              3.00maximum value:               8.00mean value:                  2.14midrange:                    4.00range:                       8.00interquartile range:         2.00mean abs deviation:          1.00sample variance (n):         1.59sample variance (n-1):       1.59sample std dev (n):          1.26sample std dev (n-1):        1.26-------------------------------------------                cumulative--------------------------------------------0.5 <= x < 0.50     0.00    8245     8.24%0.50 <= x < 1.50     1.00   32448    32.45%1.50 <= x < 2.50     2.00   63728    63.73%2.50 <= x < 3.50     3.00   85918    85.92%3.50 <= x < 4.50     4.00   96154    96.15%4.50 <= x < 5.50     5.00   99246    99.25%5.50 <= x < 6.50     6.00   99907    99.91%6.50 <= x < 7.50     7.00   99993    99.99%7.50 <= x < 8.50     8.00  100000   100.00%------------------------------------------- Baccarat Player Streaks 5+ in a row       group        middle    freq  freq/100--------------------------------------------0.5 <= x < 0.50     0.00   32194    32.19%0.50 <= x < 1.50     1.00   39825    39.82%1.50 <= x < 2.50     2.00   20806    20.81%2.50 <= x < 3.50     3.00    5958     5.96%3.50 <= x < 4.50     4.00    1099     1.10%4.50 <= x < 5.50     5.00     112     0.11%5.50 <= x < 6.50     6.00       6     0.01%-------------------------------------------                  grouped dataitems:                  100000   minimum value:               0.00first quartile:              0.00median:                      1.00third quartile:              2.00maximum value:               6.00mean value:                  1.04midrange:                    3.00range:                       6.00interquartile range:         2.00mean abs deviation:          0.71sample variance (n):         0.88sample variance (n-1):       0.88sample std dev (n):          0.94sample std dev (n-1):        0.94-------------------------------------------                cumulative--------------------------------------------0.5 <= x < 0.50     0.00   32194    32.19%0.50 <= x < 1.50     1.00   72019    72.02%1.50 <= x < 2.50     2.00   92825    92.82%2.50 <= x < 3.50     3.00   98783    98.78%3.50 <= x < 4.50     4.00   99882    99.88%4.50 <= x < 5.50     5.00   99994    99.99%5.50 <= x < 6.50     6.00  100000   100.00%------------------------------------------- Baccarat Player Streaks 6+ in a row       group        middle    freq  freq/100--------------------------------------------0.5 <= x < 0.50     0.00   58541    58.54%0.50 <= x < 1.50     1.00   32958    32.96%1.50 <= x < 2.50     2.00    7517     7.52%2.50 <= x < 3.50     3.00     893     0.89%3.50 <= x < 4.50     4.00      87     0.09%4.50 <= x < 5.50     5.00       4     0.00%-------------------------------------------                   grouped dataitems:                  100000   minimum value:               0.00first quartile:              0.00median:                      0.00third quartile:              1.00maximum value:               5.00mean value:                  0.51midrange:                    2.50range:                       5.00interquartile range:         1.00mean abs deviation:          0.60sample variance (n):         0.47sample variance (n-1):       0.47sample std dev (n):          0.68sample std dev (n-1):        0.68-------------------------------------------                cumulative--------------------------------------------0.5 <= x < 0.50     0.00   58541    58.54%0.50 <= x < 1.50     1.00   91499    91.50%1.50 <= x < 2.50     2.00   99016    99.02%2.50 <= x < 3.50     3.00   99909    99.91%3.50 <= x < 4.50     4.00   99996   100.00%4.50 <= x < 5.50     5.00  100000   100.00%-------------------------------------------          `

Length of the Longest Run per 8 deck shoe
`    Length of the Longest Run Banker : mean 5.65   	   group         middle    freq  freq/100--------------------------------------------- 1.50 <= x <  2.50     2.00     183     0.18% 2.50 <= x <  3.50     3.00    6150     6.15% 3.50 <= x <  4.50     4.00   21684    21.68% 4.50 <= x <  5.50     5.00   26405    26.40% 5.50 <= x <  6.50     6.00   19549    19.55% 6.50 <= x <  7.50     7.00   12276    12.28% 7.50 <= x <  8.50     8.00    6587     6.59% 8.50 <= x <  9.50     9.00    3491     3.49% 9.50 <= x < 10.50    10.00    1821     1.82%10.50 <= x < 11.50    11.00     922     0.92%11.50 <= x < 12.50    12.00     479     0.48%12.50 <= x < 13.50    13.00     215     0.22%13.50 <= x < 14.50    14.00     140     0.14%14.50 <= x < 15.50    15.00      49     0.05%15.50 <= x < 16.50    16.00      27     0.03%16.50 <= x < 17.50    17.00      14     0.01%17.50 <= x < 18.50    18.00       4     0.00%18.50 <= x < 19.50    19.00       0   19.50 <= x < 20.50    20.00       2     0.00%20.50 <= x < 21.50    21.00       1     0.00%21.50 <= x < 22.50    22.00       1     0.00%---------------------------------------------                      grouped dataitems:                  100000   minimum value:               2.00first quartile:              4.00median:                      5.00third quartile:              7.00maximum value:              22.00mean value:                  5.65midrange:                   12.00range:                      20.00interquartile range:         3.00mean abs deviation:          1.40sample variance (n):         3.28sample variance (n-1):       3.28sample std dev (n):          1.81sample std dev (n-1):        1.81---------------------------------------------                 cumulative--------------------------------------------- 1.50 <= x <  2.50     2.00     183     0.18% 2.50 <= x <  3.50     3.00    6333     6.33% 3.50 <= x <  4.50     4.00   28017    28.02% 4.50 <= x <  5.50     5.00   54422    54.42% 5.50 <= x <  6.50     6.00   73971    73.97% 6.50 <= x <  7.50     7.00   86247    86.25% 7.50 <= x <  8.50     8.00   92834    92.83% 8.50 <= x <  9.50     9.00   96325    96.32% 9.50 <= x < 10.50    10.00   98146    98.15%10.50 <= x < 11.50    11.00   99068    99.07%11.50 <= x < 12.50    12.00   99547    99.55%12.50 <= x < 13.50    13.00   99762    99.76%13.50 <= x < 14.50    14.00   99902    99.90%14.50 <= x < 15.50    15.00   99951    99.95%15.50 <= x < 16.50    16.00   99978    99.98%16.50 <= x < 17.50    17.00   99992    99.99%17.50 <= x < 18.50    18.00   99996   100.00%18.50 <= x < 19.50    19.00   99996   100.00%19.50 <= x < 20.50    20.00   99998   100.00%20.50 <= x < 21.50    21.00   99999   100.00%21.50 <= x < 22.50    22.00  100000   100.00%---------------------------------------------   Length of the Longest Run Player : mean 5.46                 group         middle    freq  freq/100--------------------------------------------- 1.50 <= x <  2.50     2.00     288     0.29% 2.50 <= x <  3.50     3.00    7905     7.90% 3.50 <= x <  4.50     4.00   23929    23.93% 4.50 <= x <  5.50     5.00   26577    26.58% 5.50 <= x <  6.50     6.00   18789    18.79% 6.50 <= x <  7.50     7.00   10985    10.98% 7.50 <= x <  8.50     8.00    5777     5.78% 8.50 <= x <  9.50     9.00    3011     3.01% 9.50 <= x < 10.50    10.00    1411     1.41%10.50 <= x < 11.50    11.00     705     0.70%11.50 <= x < 12.50    12.00     304     0.30%12.50 <= x < 13.50    13.00     172     0.17%13.50 <= x < 14.50    14.00      81     0.08%14.50 <= x < 15.50    15.00      32     0.03%15.50 <= x < 16.50    16.00      16     0.02%16.50 <= x < 17.50    17.00      11     0.01%17.50 <= x < 18.50    18.00       3     0.00%18.50 <= x < 19.50    19.00       2     0.00%19.50 <= x < 20.50    20.00       2     0.00%---------------------------------------------                     grouped dataitems:                  100000   minimum value:               2.00first quartile:              4.00median:                      5.00third quartile:              6.00maximum value:              20.00mean value:                  5.46midrange:                   11.00range:                      18.00interquartile range:         2.00mean abs deviation:          1.35sample variance (n):         3.01sample variance (n-1):       3.01sample std dev (n):          1.74sample std dev (n-1):        1.74---------------------------------------------                 cumulative--------------------------------------------- 1.50 <= x <  2.50     2.00     288     0.29% 2.50 <= x <  3.50     3.00    8193     8.19% 3.50 <= x <  4.50     4.00   32122    32.12% 4.50 <= x <  5.50     5.00   58699    58.70% 5.50 <= x <  6.50     6.00   77488    77.49% 6.50 <= x <  7.50     7.00   88473    88.47% 7.50 <= x <  8.50     8.00   94250    94.25% 8.50 <= x <  9.50     9.00   97261    97.26% 9.50 <= x < 10.50    10.00   98672    98.67%10.50 <= x < 11.50    11.00   99377    99.38%11.50 <= x < 12.50    12.00   99681    99.68%12.50 <= x < 13.50    13.00   99853    99.85%13.50 <= x < 14.50    14.00   99934    99.93%14.50 <= x < 15.50    15.00   99966    99.97%15.50 <= x < 16.50    16.00   99982    99.98%16.50 <= x < 17.50    17.00   99993    99.99%17.50 <= x < 18.50    18.00   99996   100.00%18.50 <= x < 19.50    19.00   99998   100.00%19.50 <= x < 20.50    20.00  100000   100.00%                    `

Hope this helps. My computer simulations shows the theoretical numbers to be correct.

EZ Baccarat fans: The win streaks for Banker and Player are almost identical.
Banker win (not including ties) 0.494242387
Player win (not including ties) 0.493163022
I am actually finishing my Baccarat stats formulas and should have them in my blog soon.
FleaStiff
Joined: Oct 19, 2009
• Posts: 10963
July 12th, 2011 at 4:51:28 AM permalink
So where is the printout that will show me that it is the very next three hands that will be a Banker Streak. Now that is the printout I'd surely love to have!
guido111
Joined: Sep 16, 2010
• Posts: 707
July 12th, 2011 at 9:29:07 AM permalink
Quote: FleaStiff

So where is the printout that will show me that it is the very next three hands that will be a Banker Streak. Now that is the printout I'd surely love to have!

Me too!
The story goes, my wife and one of her girlfriends did the math last year on just that, but was not happy with the results (huh?) and when we were all in Las Vegas last year this time during the WSOP she gave the only printout to Maria Ho in exchange for her autographed photo.

I now have that signed photo!

FYI: Maria will win the Main Event next year. Took a bad beat yesterday.

Who ever wins with JJ these days? Not me.

update:she lost to JJ, she flopped a straight but JJ saw a set and the river paired the board for Jacks full.
Still love Maria!
slyther
Joined: Feb 1, 2010
• Posts: 691
July 12th, 2011 at 10:37:19 AM permalink
The only way to win with JJ is to fold :)
Walkinshaw30t
Joined: Apr 11, 2013
• Posts: 91
June 24th, 2013 at 3:35:50 AM permalink
Hi- Ive just been checking out some old threads and was wondering what the variance was like for these various number of streaks?
For example did you often get through more than 2 shoes without seeing a player streak of 4 or more?
Time will tell
Givag327
Joined: Jul 1, 2013
• Posts: 17
July 1st, 2013 at 3:10:52 PM permalink
Quote: Walkinshaw30t

Hi- Ive just been checking out some old threads and was wondering what the variance was like for these various number of streaks?
For example did you often get through more than 2 shoes without seeing a player streak of 4 or more?

Its kinda inevitable that the player has a 4+ streak. Its very very rare to not have a player streak of 4+. Espically on a 8 deck shoe

Best ive done as a dealer is 16 Player streak and 22 Banker streak...not in the same shoe ofcourse haha

.
baccarattutor
Joined: Jul 9, 2013
• Posts: 4
July 12th, 2013 at 9:43:28 PM permalink
Did you know that you can use a long streak of up to 5 to 6 outcomes in the first 12 to 17 hands and compare it to 25 to 30 outcomes later and it would jump within 3 to four hands? Find out how this works at the School of Baccarat using the 7TWELVE17 method! =D
98Clubs
Joined: Jun 3, 2010
• Posts: 1715
July 31st, 2013 at 6:42:06 PM permalink
I must ask a question here. Suppose there is a streak of WWWWTWWWTWWWL. Is this being accounted as 10-in a row?, or as 4-3-3? (typo)

I ask because using WoO data in Baccarat--->Appendix 1 one can conclude that 81 hands on average will be dealt from an 8-deck shoe given the traditional and standard rules of the game. Out of those 81 hands, 7.7 will be a Tie (lets call it 8 for the purpose of the Java sim linked to previously).

**EDIT** My analysis above was off.... for some reason I wrote 13 burn cards, it is 16 by tradition. This changes the analysis by removing one round from the mistaken computations.
The OP was corrected, and finalized below.

The stop-card at 16 cards with an average burn of 6.5 cards yields 22.5 cards
79 Full rounds are contested. Upon the 80th, the stop card appears. On average 2 cards past stop card.
The last round (81st) is played at an average of 5 cards... total 7 cards past stop card.
Penetration is therefore 416-22.5+7 = 400.5 cards or 96.27%
Recent epitaph: Found dead by a Pokemon Go Player
treetopbuddy
Joined: Jan 12, 2013