Baccarat Streaks question
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July 11th, 2011 at 11:47:54 PM
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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.
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.
July 12th, 2011 at 12:18:21 AM
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Quote: jimsandersMuch 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 1 | Probability |
|---|---|
| 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 prob
0 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 prob
0 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 prob
0 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/100
0 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: 0.00
first quartile: 0.00
median: 0.00
third quartile: 1.00
maximum value: 6.00
mean value: 0.54
sample variance (n): 0.49
sample 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 Streak | avg # of runs | avg # of runs |
|---|---|---|
| length of run | exact | or more |
| 1 | 9.375402826 | 18.75342461 |
| 2 | 4.689211825 | 9.378021788 |
| 3 | 2.344945024 | 4.688809963 |
| 4 | 1.17242827 | 2.343864939 |
| 5 | 0.586082181 | 1.171436669 |
| 6 | 0.2929187 | 0.585354488 |
| 7 | 0.146369184 | 0.292435788 |
| 8 | 0.073124634 | 0.146066604 |
| 9 | 0.036524702 | 0.07294197 |
| 10 | 0.018239623 | 0.036417268 |
| Player STreak | avg # of runs | avg # of runs |
|---|---|---|
| length of run | exact | or more |
| 1 | 9.621057047 | 18.73977461 |
| 2 | 4.682388097 | 9.118717568 |
| 3 | 2.278424797 | 4.436329471 |
| 4 | 1.108466465 | 2.157904673 |
| 5 | 0.539173817 | 1.049438209 |
| 6 | 0.262211129 | 0.510264391 |
| 7 | 0.127493239 | 0.248053263 |
| 8 | 0.061977551 | 0.120560024 |
| 9 | 0.03012245 | 0.058582473 |
| 10 | 0.014637001 | 0.028460023 |
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 | |||
|---|---|---|---|
| run | average # of hands | median # of hands | median prob |
| 2+ | 7.8926 | 4 | 51.034934% |
| 3+ | 15.5703 | 10 | 52.161036% |
| 4+ | 30.7168 | 21 | 51.424335% |
| 5+ | 60.5973 | 42 | 50.689012% |
| 6+ | 119.5450 | 83 | 50.273484% |
| 7+ | 235.8354 | 164 | 50.158229% |
| 8+ | 465.2503 | 323 | 50.044911% |
| 9+ | 917.8345 | 637 | 50.022250% |
| 10+ | 1810.6816 | 1256 | 50.006342% |
| 11+ | 3572.0686 | 2477 | 50.000344% |
| 12+ | 7046.8902 | 4886 | 50.001116% |
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 | |||
|---|---|---|---|
| run | average # of hands | median # of hands | median prob |
| 2+ | 8.1135 | 5 | 58.293387% |
| 3+ | 16.4540 | 11 | 53.317153% |
| 4+ | 33.3686 | 23 | 51.491927% |
| 5+ | 67.6710 | 47 | 50.650740% |
| 6+ | 137.2359 | 95 | 50.117952% |
| 7+ | 278.3125 | 193 | 50.042576% |
| 8+ | 564.4139 | 392 | 50.056113% |
| 9+ | 1144.6236 | 794 | 50.006768% |
| 10+ | 2321.2808 | 1610 | 50.005510% |
| 11+ | 4707.5255 | 3265 | 50.009921% |
| 12+ | 9546.7968 | 6619 | 50.001570% |
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 data
items: 100000
minimum value: 0.00
first quartile: 3.00
median: 4.00
third quartile: 5.00
maximum value: 13.00
mean value: 4.41
midrange: 6.50
range: 13.00
interquartile range: 2.00
mean abs deviation: 1.31
sample variance (n): 2.60
sample variance (n-1): 2.60
sample std dev (n): 1.61
sample 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 data
items: 100000
minimum value: 0.00
first quartile: 1.00
median: 2.00
third quartile: 3.00
maximum value: 8.00
mean value: 2.14
midrange: 4.00
range: 8.00
interquartile range: 2.00
mean abs deviation: 1.00
sample variance (n): 1.59
sample variance (n-1): 1.59
sample std dev (n): 1.26
sample 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 data
items: 100000
minimum value: 0.00
first quartile: 0.00
median: 1.00
third quartile: 2.00
maximum value: 6.00
mean value: 1.04
midrange: 3.00
range: 6.00
interquartile range: 2.00
mean abs deviation: 0.71
sample variance (n): 0.88
sample variance (n-1): 0.88
sample std dev (n): 0.94
sample 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 data
items: 100000
minimum value: 0.00
first quartile: 0.00
median: 0.00
third quartile: 1.00
maximum value: 5.00
mean value: 0.51
midrange: 2.50
range: 5.00
interquartile range: 1.00
mean abs deviation: 0.60
sample variance (n): 0.47
sample variance (n-1): 0.47
sample std dev (n): 0.68
sample 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 data
items: 100000
minimum value: 2.00
first quartile: 4.00
median: 5.00
third quartile: 7.00
maximum value: 22.00
mean value: 5.65
midrange: 12.00
range: 20.00
interquartile range: 3.00
mean abs deviation: 1.40
sample variance (n): 3.28
sample variance (n-1): 3.28
sample std dev (n): 1.81
sample 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 data
items: 100000
minimum value: 2.00
first quartile: 4.00
median: 5.00
third quartile: 6.00
maximum value: 20.00
mean value: 5.46
midrange: 11.00
range: 18.00
interquartile range: 2.00
mean abs deviation: 1.35
sample variance (n): 3.01
sample variance (n-1): 3.01
sample std dev (n): 1.74
sample 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.
July 12th, 2011 at 4:51:28 AM
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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!
July 12th, 2011 at 9:29:07 AM
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Quote: FleaStiffSo 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!
July 12th, 2011 at 10:37:19 AM
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The only way to win with JJ is to fold :)
June 24th, 2013 at 3:35:50 AM
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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?
For example did you often get through more than 2 shoes without seeing a player streak of 4 or more?
Time will tell
July 1st, 2013 at 3:10:52 PM
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Quote: Walkinshaw30tHi- 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
.
July 12th, 2013 at 9:43:28 PM
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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
July 31st, 2013 at 6:42:06 PM
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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%
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%
Some people need to reimagine their thinking.
July 31st, 2013 at 6:45:43 PM
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what?
Each day is better than the next
April 19th, 2015 at 5:44:29 AM
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How about in a 6 deck shoes ?
I really would like to know the numbers exactly
Cheers
I really would like to know the numbers exactly
Cheers
April 19th, 2015 at 5:50:39 AM
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Thanks for giving us a plethora of reddish names!
When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
September 11th, 2016 at 11:12:55 PM
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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 t in the same shoe ofcourse
Best ive done as a dealer is 16 Player streak and 22 Banker t in the same shoe ofcourse
