
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?

Re: Betting system
Sorry! Very sorry!
I miscalculate so forget this thread.

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 121212.... and the bet sequence is 212121.....It is my result but you can do better. Thank you for any clue.

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.