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Math Help - Betting system

  1. #1
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    Betting system

    Here is the challenge.
    We flip a coin 100 times.
    If the outcome is equal to the bet (k dollars) the gambler receive 2*k dollars (return = 1 k). If not the gambler loose k.
    I simulated the game with 2 gamblers : John and Paul.
    John bets always head.
    Paul always tail.
    But each one of the players bet different sum of money.
    John bets a(i) dollars and Paul b(i) dollars.
    i is the index of each toss.
    i vary from 1 to 100.
    John and Paul start with a bankroll of 200 dollars each.
    Can you find the 2 bet sequences a(i) and b(i) such as the 2 players have 95% chance to make BOTH a profit of at least 1 dollar? They stop betting once their profit is equal to at least 1 dollar
    I have found a solution. What about you?
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  2. #2
    Junior Member
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    Re: Betting system

    Sorry! Very sorry!
    I miscalculate so forget this thread.
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  3. #3
    Junior Member
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    Re: Betting system

    The simulation was right. Here is my problem : there is ALWAYS during the 100 tosses an interval where the value is positive (more than one dollar) if the 2 players bet the right sequences a(i) and b(i). Now is there a way to compute when to leave the game? When some positive value is reached? Which value? The 2 players have 38% chance to loose during 10 consecutive tosses. If we can find when to stop the bet then any player can bet for 2 fictive players and win every day 1000 dollars or more (depending on the bet limit fixed by the casinos). I made an exhaustive study of 10 consecutive tosses and I expect that with 100 tosses the loss probability will decrease. I want you to help me to make an exhaustive study of at least 30 consecutive tosses. The bet sequence a(i) is 1-2-1-2-1-2.... and the bet sequence is 2-1-2-1-2-1.....It is my result but you can do better. Thank you for any clue.
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  4. #4
    Junior Member
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    Re: Betting system

    Anyone is free to answer or not to any thread. But it is frustrating not to have any feedback or to talk like an autist. Have a good time. Thank you for reading me.
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