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?