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Win Streak Probability

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  • 04-04-2017 3:21pm
    #1
    Division
    Registered Users Posts: 501 ✭✭✭


    Anybody know of an online calculator that will calculate the probability of a win streak of X games from a series of Y bets or can go through the method to calculate it? Thanks.

    E.G) If I place 500 bets at odds of 1.25 with a strike rate of 80% what is the probability that I will win 20 bets in a row?


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    #2
    Bit cynical
    Registered Users Posts: 2,338 ✭✭✭Bit cynical


    I don't know of an online calculator but I think you should be able to do it in a spreadsheet. I would appreciate if someone could point out possible flaws in my reasoning.

    The formula would be

    =1-(1-Probability^StreakLength)^(Bets - StreakLength+1)

    Probability: the probability of winning any one bet (e.g. 0.8 for 80%)
    StreakLength: how many winning bets count for a streak (e.g. 20)
    Bets: The total number of bets (e.g. 500).

    Reasoning:

    Probability of winning one streak is Probability^Streak Length.

    Probability of losing a winning streak is 1 - Probability^Streak Length.

    We get Bets - StreakLength + 1 chances of getting a a winning streak.

    Probability of failing to get a winning streak in all our chances is
    (1 - Probability^Streak Length)^(Bets - StreakLength + 1)

    and therefore the chances of getting at least one winning streak is
    1-(1 - Probability^Streak Length)^(Bets - StreakLength + 1)


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