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Math Help - High Low Probability

  1. #1
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    High Low Probability

    Evening All,

    Basically I am trying to work out how to calculate the probablity of the number of hands that will be played in a straight forward game of High / Low using cards numbered from 1 to 25. The first card is blindly chosen and then based on probability the choice is made, higher or lower. You only proceed when the guess was correct. That's straight forward enough even for me. But how do I work out the probability for the number of cards to be chosen until the incorrect decision is made. Initially I actually did a trial of 50 plays and came out with an average of 4,37 but how do I actually provide a calculation of the probability.

    Any help or advice would be greatly appreciated.

    Thanks in advance.

    Graham.
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  2. #2
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    Re: High Low Probability

    Hey AppliedMath.

    Are you aware of Markov Chains?
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  3. #3
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    Re: High Low Probability

    Hi Chiro.

    I'm not aware of Markov Chains. Is he on Facebook? If I befriend him will he tell me the answer? Only Joking!
    I am now aware of Markov Chains but am also aware that, due to my lack of a mathematical background there is no way that I will be able to apply it successfully.
    If I could just clarify exactly what I'm trying to work out; I'm being asked to value the risk for a casino that has a high low promotion whereby the particpant starts with a guaranteed amount in the bank of $500 and for every time the participant guesses correctly they receive a bonus of $250. The game is a straight forward high or low with 25 cards numbered from 1 to 25 and every pick is blind. I need to confirm what the calculated risk would be to the casino with each participant. As a layman I did a rudimentary trial run which came out to an average payout of $1,430 based on the average of 50 games. However, actually being able to prove and show a calculated risk is, quite obviously, alot more difficult.
    Not really sure where that leaves us now, to be honest. Any further help or advice would be appreciated.
    Thanks again.
    Graham.
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  4. #4
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    Re: High Low Probability

    Basically markov chains are conditional systems. So what you would do is model probabilities for the next state based on the current state.

    With this you can then do things like get probabilities after n tries or get the long time distribution. Once you have this you can get the long term expectation and variance.

    Basically your probabilities will be affect by the card you have (since you need to consider probabilities for higher and lower).

    Alternatively another way to do analysis is to do Monte Carlo. Basically what this does is you simulate a random variable and then you write the process that goes on in the casino as a computer program and you'll have a final distribution which you can plot and get expectation and variance figures.

    I'd recommend the Monte Carlo if you don't know much about Markov chains because Monte Carlo only needs knowledge of basic probability and statistics.
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  5. #5
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    Re: High Low Probability

    Thanks Chiro for taking the time to reply again, however, it's apparent that I'm in way over my mathematical head here! I've now done 200 trial runs and I come out with an average of 3,14 plays per game. I'll have to leave it there.

    Thanks again.

    Graham.
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