Dantheman Joined: Apr 21, 2015
• Posts: 53
April 30th, 2015 at 7:47:52 PM permalink
Thanks.
Could anyone answer my question in other post about whether some streaks of different lengths are more reliable (hit to consistantly closer to expected probability) than others.
For example i found streaks of 2 would usually hit with in 3 of expected (expect 24 hit 21-27 times) over a shoe, where streaks of 3 or more werent as reliable (would swing more wildly)
Dalex64 Joined: Feb 10, 2013
• Posts: 1067
May 1st, 2015 at 4:40:15 AM permalink
That is because shorter streaks happen more often, so they will more quickly appear as frequently as expected.

For longer streaks which happen less often, they will tend to be farther from expectation for longer, compared to shorter streaks, since they happen less often.

Worded another way, the more frequently something happens, the more quickly it will show the expected results.
mustangsally Joined: Mar 29, 2011
• Posts: 2463
May 1st, 2015 at 8:12:35 AM permalink
Quote: Dantheman

Thanks.
Could anyone answer my question in other post about whether some streaks of different lengths are more reliable (hit to consistantly closer to expected probability) than others.

the variance for smaller streaks is smaller than the larger ones (the wait time - how long do we have to wait)

you seem to be attracted to the length of streaks
where 3
say BBBP
is NOT a streak of length 2 or longer
but exactly length 3
is this right?

that is ok too
Quote: Dantheman

For example i found streaks of 2 would usually hit with in 3 of expected (expect 24 hit 21-27 times) over a shoe, where streaks of 3 or more werent as reliable (would swing more wildly)

as an example because in an 8 deck shoe your values look to be way off to me
unless streaks of 2 for you are >=2 not just =2

here is a streaks summary of 1000 8 deck shoes (13 card ribbon)
`----------------------- frequencies [37172 streaks] ------------------------length      1    2    3    4    5    6    7    8    9   10   11   12   13player   9514 4693 2243 1114  537  257  111   59   36   17    5    1    1banker   9202 4701 2344 1151  628  287  158   80   43   12   10    6    3        --------------------------------------------------------------------length     14   15   16   17player      2    1    1    1banker      1    0    0    1`
the avg # of len2 = abouts 9.4 (4693+4701)/1000

have fun with streaks!
i do
Sally

here is a larger sim sample
1 million 8 deck shoes
P and B streaks
`       group         middle      freq  freq/100----------------------------------------------- 0.50 <= x <  1.50     1.00  18949473    50.66% 1.50 <= x <  2.50     2.00   9348285    24.99% 2.50 <= x <  3.50     3.00   4612786    12.33% 3.50 <= x <  4.50     4.00   2275990     6.09% 4.50 <= x <  5.50     5.00   1123300     3.00% 5.50 <= x <  6.50     6.00    553106     1.48% 6.50 <= x <  7.50     7.00    273695     0.73% 7.50 <= x <  8.50     8.00    134253     0.36% 8.50 <= x <  9.50     9.00     66125     0.18% 9.50 <= x < 10.50    10.00     32767     0.09%10.50 <= x < 11.50    11.00     16235     0.04%11.50 <= x < 12.50    12.00      7947     0.02%12.50 <= x < 13.50    13.00      4050     0.01%13.50 <= x < 14.50    14.00      1863     0.00%14.50 <= x < 15.50    15.00       892     0.00%15.50 <= x < 16.50    16.00       467     0.00%16.50 <= x < 17.50    17.00       264     0.00%17.50 <= x < 18.50    18.00       143     0.00%18.50 <= x < 19.50    19.00        60     0.00%19.50 <= x < 20.50    20.00        36     0.00%20.50 <= x < 21.50    21.00         8     0.00%21.50 <= x < 22.50    22.00         4     0.00%22.50 <= x < 23.50    23.00         3     0.00%23.50 <= x < 24.50    24.00         2     0.00%24.50 <= x < 25.50    25.00         1     0.00%-----------------------------------------------                  cumulative----------------------------------------------- 0.50 <= x <  1.50     1.00  18949473    50.66% 1.50 <= x <  2.50     2.00  28297758    75.66% 2.50 <= x <  3.50     3.00  32910544    87.99% 3.50 <= x <  4.50     4.00  35186534    94.08% 4.50 <= x <  5.50     5.00  36309834    97.08% 5.50 <= x <  6.50     6.00  36862940    98.56% 6.50 <= x <  7.50     7.00  37136635    99.29% 7.50 <= x <  8.50     8.00  37270888    99.65% 8.50 <= x <  9.50     9.00  37337013    99.83% 9.50 <= x < 10.50    10.00  37369780    99.91%10.50 <= x < 11.50    11.00  37386015    99.96%11.50 <= x < 12.50    12.00  37393962    99.98%12.50 <= x < 13.50    13.00  37398012    99.99%13.50 <= x < 14.50    14.00  37399875    99.99%14.50 <= x < 15.50    15.00  37400767   100.00%15.50 <= x < 16.50    16.00  37401234   100.00%16.50 <= x < 17.50    17.00  37401498   100.00%17.50 <= x < 18.50    18.00  37401641   100.00%18.50 <= x < 19.50    19.00  37401701   100.00%19.50 <= x < 20.50    20.00  37401737   100.00%20.50 <= x < 21.50    21.00  37401745   100.00%21.50 <= x < 22.50    22.00  37401749   100.00%22.50 <= x < 23.50    23.00  37401752   100.00%23.50 <= x < 24.50    24.00  37401754   100.00%24.50 <= x < 25.50    25.00  37401755   100.00%`

Only P streaks
`       group         streak      freq  freq/100      ----------------------------------------------- 0.50 <= x <  1.50     1.00   9591472    51.31% 1.50 <= x <  2.50     2.00   4674314    25.00% 2.50 <= x <  3.50     3.00   2273436    12.16% 3.50 <= x <  4.50     4.00   1107294     5.92% 4.50 <= x <  5.50     5.00    538186     2.88% 5.50 <= x <  6.50     6.00    261965     1.40% 6.50 <= x <  7.50     7.00    127691     0.68% 7.50 <= x <  8.50     8.00     61671     0.33% 8.50 <= x <  9.50     9.00     29881     0.16% 9.50 <= x < 10.50    10.00     14511     0.08%10.50 <= x < 11.50    11.00      7095     0.04%11.50 <= x < 12.50    12.00      3395     0.02%12.50 <= x < 13.50    13.00      1748     0.01%13.50 <= x < 14.50    14.00       766     0.00%14.50 <= x < 15.50    15.00       372     0.00%15.50 <= x < 16.50    16.00       185     0.00%16.50 <= x < 17.50    17.00        92     0.00%17.50 <= x < 18.50    18.00        57     0.00%18.50 <= x < 19.50    19.00        22     0.00%19.50 <= x < 20.50    20.00        12     0.00%20.50 <= x < 21.50    21.00         3     0.00%21.50 <= x < 22.50    22.00         1     0.00%22.50 <= x < 23.50    23.00         0   23.50 <= x < 24.50    24.00         2     0.00%24.50 <= x < 25.50    25.00         1     0.00%-----------------------------------------------                  cumulative----------------------------------------------- 0.50 <= x <  1.50     1.00   9591472    51.31% 1.50 <= x <  2.50     2.00  14265786    76.31% 2.50 <= x <  3.50     3.00  16539222    88.47% 3.50 <= x <  4.50     4.00  17646516    94.40% 4.50 <= x <  5.50     5.00  18184702    97.27% 5.50 <= x <  6.50     6.00  18446667    98.68% 6.50 <= x <  7.50     7.00  18574358    99.36% 7.50 <= x <  8.50     8.00  18636029    99.69% 8.50 <= x <  9.50     9.00  18665910    99.85% 9.50 <= x < 10.50    10.00  18680421    99.93%10.50 <= x < 11.50    11.00  18687516    99.96%11.50 <= x < 12.50    12.00  18690911    99.98%12.50 <= x < 13.50    13.00  18692659    99.99%13.50 <= x < 14.50    14.00  18693425   100.00%14.50 <= x < 15.50    15.00  18693797   100.00%15.50 <= x < 16.50    16.00  18693982   100.00%16.50 <= x < 17.50    17.00  18694074   100.00%17.50 <= x < 18.50    18.00  18694131   100.00%18.50 <= x < 19.50    19.00  18694153   100.00%19.50 <= x < 20.50    20.00  18694165   100.00%20.50 <= x < 21.50    21.00  18694168   100.00%21.50 <= x < 22.50    22.00  18694169   100.00%22.50 <= x < 23.50    23.00  18694169   100.00%23.50 <= x < 24.50    24.00  18694171   100.00%24.50 <= x < 25.50    25.00  18694172   100.00%`

only B streaks
`         group         streak     freq   freq/100		----------------------------------------------- 0.50 <= x <  1.50     1.00   9358001    50.02% 1.50 <= x <  2.50     2.00   4673971    24.98% 2.50 <= x <  3.50     3.00   2339350    12.50% 3.50 <= x <  4.50     4.00   1168696     6.25% 4.50 <= x <  5.50     5.00    585114     3.13% 5.50 <= x <  6.50     6.00    291141     1.56% 6.50 <= x <  7.50     7.00    146004     0.78% 7.50 <= x <  8.50     8.00     72582     0.39% 8.50 <= x <  9.50     9.00     36244     0.19% 9.50 <= x < 10.50    10.00     18256     0.10%10.50 <= x < 11.50    11.00      9140     0.05%11.50 <= x < 12.50    12.00      4552     0.02%12.50 <= x < 13.50    13.00      2302     0.01%13.50 <= x < 14.50    14.00      1097     0.01%14.50 <= x < 15.50    15.00       520     0.00%15.50 <= x < 16.50    16.00       282     0.00%16.50 <= x < 17.50    17.00       172     0.00%17.50 <= x < 18.50    18.00        86     0.00%18.50 <= x < 19.50    19.00        38     0.00%19.50 <= x < 20.50    20.00        24     0.00%20.50 <= x < 21.50    21.00         5     0.00%21.50 <= x < 22.50    22.00         3     0.00%22.50 <= x < 23.50    23.00         3     0.00%-----------------------------------------------                  cumulative----------------------------------------------- 0.50 <= x <  1.50     1.00   9358001    50.02% 1.50 <= x <  2.50     2.00  14031972    75.01% 2.50 <= x <  3.50     3.00  16371322    87.51% 3.50 <= x <  4.50     4.00  17540018    93.76% 4.50 <= x <  5.50     5.00  18125132    96.89% 5.50 <= x <  6.50     6.00  18416273    98.44% 6.50 <= x <  7.50     7.00  18562277    99.22% 7.50 <= x <  8.50     8.00  18634859    99.61% 8.50 <= x <  9.50     9.00  18671103    99.80% 9.50 <= x < 10.50    10.00  18689359    99.90%10.50 <= x < 11.50    11.00  18698499    99.95%11.50 <= x < 12.50    12.00  18703051    99.98%12.50 <= x < 13.50    13.00  18705353    99.99%13.50 <= x < 14.50    14.00  18706450    99.99%14.50 <= x < 15.50    15.00  18706970   100.00%15.50 <= x < 16.50    16.00  18707252   100.00%16.50 <= x < 17.50    17.00  18707424   100.00%17.50 <= x < 18.50    18.00  18707510   100.00%18.50 <= x < 19.50    19.00  18707548   100.00%19.50 <= x < 20.50    20.00  18707572   100.00%20.50 <= x < 21.50    21.00  18707577   100.00%21.50 <= x < 22.50    22.00  18707580   100.00%22.50 <= x < 23.50    23.00  18707583   100.00%`
I Heart Vi Hart
98Clubs Joined: Jun 3, 2010
• Posts: 1728
May 1st, 2015 at 1:23:52 PM permalink
Quote: ThatDonGuy

Not quite. You are assuming that each group of 6 hands (hands 1-6, hands 2-7, hands 3-8, ..., hands 76-81) is independent of the others. If hands 1-5 are player wins and hand 6 is a bank win, then none of the groups 1-6, 2-7, 3-8, 4-9, 5-10, and 6-11 have player wins.

All I did was take the chance of a win and raise it to the 6th power. Then inverted the fraction for 1 in x analysis.
For 6 Before a loss the chance of a tie was added to the chance of a win, then raised to the 6th power. Again the fraction was inverted for '1 in x' analysis.

Streak analysis involves "less than, greater than, or equal to" phrasing. The OP wanted to know the chance of 6 Banker wins and 6 Player wins in a row... nothing else. The simple math used does not presume when the streak starts. It only states the probabiliity of the occurance based upon winning percentage. In fact, neither 6 consecutive or 6 before a loss presumes such will occur in one shoe ( hands 79, 80, 81, Shuffle/cut/burn. 1, 2, and 3).

I made no assumption, just did the easy math of chance ^6.
Some people need to reimagine their thinking.
mustangsally Joined: Mar 29, 2011
• Posts: 2463
May 4th, 2015 at 8:03:23 PM permalink
Quote: 98Clubs

The OP wanted to know the chance of 6 Banker wins and 6 Player wins in a row... nothing else.

that appears to me to be your opinion
OP used the word either and or
that means, to me, one or the other and not both
but we may never really know
OP seems happy :)

my Excel shows this (as well as a few sims)
example 1
Banker run of 6 in 81 hands (Ties do NOT break the run): 0.457656307
Player run of 6 in 81 hands (Ties do NOT break the run): 0.411091138
Either (NOT both): 0.694798211
Banker AND Player 6 run: 0.173949235

example 2
Banker run of 6 in 74 hands (Ties do NOT break the run): 0.426386042
Player run of 6 in 74 hands (Ties do NOT break the run): 0.381806137
Either (NOT both): 0.659687823
Banker AND Player 6 run: 0.148504355 Sally
I Heart Vi Hart
Dantheman Joined: Apr 21, 2015
• Posts: 53
May 6th, 2015 at 3:11:14 PM permalink
Thankyou.
So the variance on shorter streaks is less, does this include streaks of 1 or more?
As the simple banker/ player appears to be have a higher variance at a glance?
sisyphus Joined: Dec 7, 2015
• Posts: 20
December 13th, 2016 at 4:57:35 PM permalink
What role does probability play in games of chance? Assuming, Banker/Player is 50/50, what difference does it make if we have a 10 in a row banker run? Apparently probability never changes even after a banker run of 23. It's always 50/50? But why do streaks end?
RS Joined: Feb 11, 2014