Streak Calculator and calculating streaks (runs)

Quote: pacomartin

Sorry,
I don't know what he means by that calculation. I put in p=.50 and N=4 and the calculations are 1/6 1/6 1/4 and 1/4. It's not clear what he is calculating.

Yes, thats exactly what i mean. Well, maybe nope27 turns by and gives an answer.

Thanks anyway.

Quote: edward

I know this post is a little old, but i've just discovered it and I have some questions if its possible :-)

Regarding the linked website to this post, there is an live excel worksheet which calculates the various probabilities of different sequences of patterns by setting a win and lose probability. However, if i set win probability to 50%, the probabilities for the sequences SS, FF, SF and FS dont add up to 1. Its the same for the other patterns aswell, no sequence of pattern adds up to 1.

How is this possible, could you explain me this? For instance the 2 length patterns have according to the spreadsheet probabilities of .25 (for SF and FS) and .16666 respectively for SS and FF.

Kind regards and i hope for an answer.
Edward

Here is an older post.

The way the spreadsheet is labelled is confusing. It is not calculating the probability out of N trials.The spreadsheet is giving you the expected number of trials for these sequences to occur. That's why the probabilities don't add up to 1. You expect one SS to show up in 6 trials, and you expect on SF to show up in 4 trials.

Thanx for the specification. After Mustangsally has posted the formulas, i've begun to suspect thats what it is.

Although, could You tell me how to calculate the probability for a streak of SF to happen in N trials?? (let's say probab. success 95%, loss=5%)

Later added: nevermind, i was a little distracted - sorry i figured it out so ignore the question. Thanx.

To tie this thread to pacomartin's thread about calculating streaks and online calculators see
Ask the Wizard correction

Quote: edward

Although, could You tell me how to calculate the probability for a streak of SF to happen in N trials?? (let's say probab. success 95%, loss=5%)

For those that want to learn more to calculate sequences like runs and patterns, here is a link to a pdf and Excel worksheet.
sub-sequence-probs.pdf - page 699
pattern-prob.xls

Since a run (SSSSS) is a special type of sequence and has been studied many times, a pattern (SSFSS) has been studied less often and more particular to just a few fields of study. (DNA research leads the pack)

The probability of SF in N trials can be solved using a recursive approach as shown in the pdf I liked to.
Examples in the Excel worksheet for sequences of length 2 and 3.
It looks for the first occurrence in a sequence so therefore is looking at the relative probability.
From there the cumulative can be easily found.

Here is a small example of the SF pattern (10) with p = 0.5 and p = .95

pattern 10,01
trial	p=0.5	p=0.95
2	0.25	0.0475
3	0.5	0.095
4	0.6875	0.14024375
5	0.8125	0.18323125
6	0.890625	0.224069672
7	0.9375	0.262866188
8	0.96484375	0.299722878
9	0.98046875	0.334736734
10	0.989257813	0.367999897
11	0.994140625	0.399599903
12	0.996826172	0.429619907
13	0.998291016	0.458138912
14	0.999084473	0.485231966
15	0.999511719	0.510970368
16	0.999740601	0.53542185
17	0.999862671	0.558650757
18	0.999927521	0.580718219
19	0.999961853	0.601682308