Streak Calculator and calculating streaks (runs)
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https://wizardofvegas.com/forum/gambling/blackjack/4153-twist-on-martingale-system-trying-to-figure-out-the-math-here/3/
Quote: P90OK, I'll answer your question strictly in terms of math.
The odds of winning with the "never bust" strategy are approximately equal to the odds of being dealt either a 19-21 or 2-11 and upgrading to 19-21, plus the odds of dealer busting. You will win approximately 40% of hands and lose about 50%. Pushes not counting, you will lose about 55% of hands and win 45%.
The odds of losing 9 hands in a row are 0.55^9=1/217. The probability of a 9-hand losing streak is 21% in 60 hands, 40% in 120 hands, 54% in 180 hands, 65% in 240 hands, 90% in 500 hands, 99% in 1,000 hands. The formula is 1-(1-1/217)^(N-8), where N is the number of hands played.
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Your streak formula is an interesting one I have never seen before.
I come up with way different answers.
My streak calculator that I use and appears to be 100% accurate is from a friend (he said it is OK for me to post a link to a html page) who found the javascript code for it at 2+2 forum, that was "repaired" by BruceZ there, another top math good guy.
A good thread to read:
http://forumserver.twoplustwo.com/25/probability/successes-row-904091/
Html Streak Calculator
Here
(or you can save the webpage to your hard drive and use it offline also.) I have not seen any streak calculators that were accurate and even the original calc talked about at 2+2Forum still has not been corrected.
It is an "at least 1" streak calc. The default is for 20 coin tosses and "at least 1" streak of 5 or more.
My answers follow yours (I just copied and pasted)
The probability of a 9-hand losing streak is: The streak calculator calculates a 9-hand losing streak or greater.
21% in 60 hands, (10.6258487623799%)
40% in 120 hands, (21.2747764441500%)
54% in 180 hands, (30.6548846831477%)
65% in 240 hands, (38.9173532813651%)
90% in 500 hands, (64.7499509182322%)
99% in 1,000 hands.( 87.7535703014474%)
When I was studying streaks last year it was either a simulation or this streak calculator.
I was successful in Excel but a lot of math went into figuring all the binomial coefficients, Fibonacci K-step numbers, the sheets were large and it was starting to hurt my brain.
Enjoy!
Quote: nope27From a post at:
https://wizardofvegas.com/forum/gambling/blackjack/4153-twist-on-martingale-system-trying-to-figure-out-the-math-here/3/
Your streak formula is an interesting one I have never seen before.
I come up with way different answers.
Possibly. I was using a very simplified calculation. I think the error in my method comes from treating trials too independently. As a result, it appears to fail to account for shorter losing streaks increasing the overall number of hands played, and possibly also might count longer losing streaks as multiple short ones. I did some testing with matrices to verify, and that seems to be the case. From the forum discussion you linked, I see the problem is a lot harder than it appears and the solution is a lot more complex than the headbutt approach I used. Thanks for correcting.
Though the end result is still that martingale produces a considerably greater risk of ruin than flat-betting or parlay.
The calculation can only be done as a series of recursive calculations, or with a Markov matrix.
Quote: P90
Though the end result is still that martingale produces a considerably greater risk of ruin than flat-betting.
Yes, I agree with you 100%.
Michael Bluejay has a nice page about Martingale betting. Good points and not so good points.
https://easy.vegas/gambling/martingale-betting-system
When other players ask me how I try to win, I tell them not to increase your bets after a loss and to only increase your bets slightly after a win if you want to gamble and go for 2 in a row. Streaks are real, both win and lose. It is fun to catch a win streak but we know the loss streaks are longer and there are more of them.
Quote: pacomartinThe probability of a streak of 9 out of 9 is a simple calculation. The probability of 9 out of N hands is never a simple algebraic formula. You can show that it can never be done in one simple formula.
The calculation can only be done as a series of recursive calculations, or with a Markov matrix.
Yes, exactly.
If I remember correctly, it was an article or maybe a post here by you about the probabilities of coin toss streaks and a pdf file that got me hooked on studying the math about streaks.
It is fun to play Craps for 4 hours, about as long as I can stand up for that long, and know that I have a 99.0750% chance of seeing the pass line win 4 times in a row or more 1 time
And a 94.35% of seeing 2 streaks of 4 or more pass line wins. And it just happened last week in Vegas. Of course we all want the points to always win and most times it is a 45%-55% split between natural pass winners and point winners.
Anyway, streaks or runs are fun to play with, the math behind them are way more of a challenge.
Quote: nope27Yes, I agree with you 100%.
Michael Bluejay has a nice page about Martingale betting. Good points and not so good points.
https://easy.vegas/gambling/martingale-betting-system
Though I think he's being too kind to the system. It doesn't show through in figures (it would in a graph), but the issue of the system is very low positive variance with very high negative variance. It's the exact opposite of what one needs to genuinely win, as in get richer, not just enjoy the feeling of winning.
Quote: nope27From a post at:
https://wizardofvegas.com/forum/gambling/blackjack/4153-twist-on-martingale-system-trying-to-figure-out-the-math-here/3/
Your streak formula is an interesting one I have never seen before.
I come up with way different answers.
My streak calculator that I use and appears to be 100% accurate is from a friend (he said it is OK for me to post a link to a html page) who found the javascript code for it at 2+2 forum, that was "repaired" by BruceZ there, another top math good guy.
A good thread to read:
http://forumserver.twoplustwo.com/25/probability/successes-row-904091/
Html Streak Calculator
Here
(or you can save the webpage to your hard drive and use it offline also.) I have not seen any streak calculators that were accurate and even the original calc talked about at 2+2Forum still has not been corrected.
It is an "at least 1" streak calc. The default is for 20 coin tosses and "at least 1" streak of 5 or more.
My answers follow yours (I just copied and pasted)
The probability of a 9-hand losing streak is: The streak calculator calculates a 9-hand losing streak or greater.
21% in 60 hands, (10.6258487623799%)
40% in 120 hands, (21.2747764441500%)
54% in 180 hands, (30.6548846831477%)
65% in 240 hands, (38.9173532813651%)
90% in 500 hands, (64.7499509182322%)
99% in 1,000 hands.( 87.7535703014474%)
When I was studying streaks last year it was either a simulation or this streak calculator.
I was successful in Excel but a lot of math went into figuring all the binomial coefficients, Fibonacci K-step numbers, the sheets were large and it was starting to hurt my brain.
Enjoy!
Good afternoon,
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
Quote: edwardRegarding 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
The website you linked to is fairly verbose. If I could offer up the spreadsheet I put together for this same problem, you can download it and put your own probabilities in for casino win. It is set at 50/50 but you can change it to 20/38 for the casino odds if you want to look at roulette.
The spreadsheet is not LIVE, so you have to download it to change the numbers.
Streak Calculator
It provides the answer of what is the probability of a streak of k=2,3,4,..9 out of a length n=k,k+1,...50. I just stopped at 50 so it would fit on one page. You are free to copy the equations to go to some arbitrary upper limit for n.
Quote: pacomartinThe website you linked to is fairly verbose. If I could offer up the spreadsheet I put together for this same problem, you can download it and put your own probabilities in for casino win. It is set at 50/50 but you can change it to 20/38 for the casino odds if you want to look at roulette.
The spreadsheet is not LIVE, so you have to download it to change the numbers.
Streak Calculator
It provides the answer of what is the probability of a streak of k=2,3,4,..9 out of a length n=k,k+1,...50. I just stopped at 50 so it would fit on one page. You are free to copy the equations to go to some arbitrary upper limit for n.
First of all, thank You for the quick response.
However, i think i wasn't to clear about what i mean. The "streak calculator" which is at the website posted by the user nope27 returns the same probabilities as Yours and deals with the question "what is the probability of a streak of length k out of n trials".
But almost at the footer of the page, there are 2 excel sheets, one of which calculates the probability of certain patterns. For example in 3 trials of a fair coin there are 8 possible outcomes, however the excel sheet lists for the pattern HHH a probability of 1/14, for the pattern HTT 1/8, for HTH 1/10 etc. This is the issue i dont really understand, because all those probabilities for the 8 outcomes dont sum up to 1.
May be that i am a little retarded and the answer is in Your post, in this case excuse me.
Kind regards
Edward
Quote: edwardBut almost at the footer of the page, there are 2 excel sheets, one of which calculates the probability of certain patterns. For example in 3 trials of a fair coin there are 8 possible outcomes, however the excel sheet lists for the pattern HHH a probability of 1/14, for the pattern HTT 1/8, for HTH 1/10 etc. This is the issue i dont really understand, because all those probabilities for the 8 outcomes dont sum up to 1.
May be that i am a little retarded and the answer is in Your post, in this case excuse me.
Kind regards
Edward
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. That's why I said the website was "verbose" which is a nice way of calling it obscure.
The original part of the website refers to a thread that I began, and one in which I posted that spreadsheet.
Quote: pacomartinSorry,
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.
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.
silly
https://sites.google.com/view/krapstuff/home
home sweet home *****
a streak of at least 20 in a row in 1 million trials
about 0.379253961388955
Wolfram Alpha (free) will time out (trying for the exact answer)
Sally
