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)

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.

too addQuote:DanthemanThanks.

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

as an example because in an 8 deck shoe your values look to be way off to meQuote:DanthemanFor 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)

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 13

player 9514 4693 2243 1114 537 257 111 59 36 17 5 1 1

banker 9202 4701 2344 1151 628 287 158 80 43 12 10 6 3

--------------------------------------------------------------------

length 14 15 16 17

player 2 1 1 1

banker 1 0 0 1

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%

Quote:ThatDonGuyNot 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.

that appears to me to be your opinionQuote:98ClubsThe OP wanted to know the chance of 6 Banker wins and 6 Player wins in a row... nothing else.

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

ask not for my workbooks

Sally

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?

Quote:sisyphusWhat 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?

Why do streaks end? Well, that's like asking "why did the coin I flipped land on tails?" It's just probability/statistics/math.