Maximize Your Vegas Winnings

One bet size, locked in for 100 rounds.

Same $10,000, same fair coin. Now you win +50% of your stake on a right call and lose −40% of your stake on a wrong one. You must play all 100 rounds and pick one fixed fraction of your remaining bankroll to wager every time. A rational player maximizing compound growth bets what?

Fraction of bankroll you stake each round

60%

Expected (average) wealth Typical (median) wealth Your bet Starting $10,000

Expected wealth predicts — —

Typical wealth predicts — —

Finished ahead of $10k — of 10,000 gamblers

Effectively wiped out — left with under $100