A biased coin. Five ways to bet it. One uncomfortable lesson: being right is the smaller half of the game.
The setup
The race — same coin, different sizing
Every strategy faces the identical sequence of flips. The only difference is how much it bets.
The damage report
Strategy
Final
Multiple
Max drawdown
1,000 parallel universes
Same setup, fresh coin each time. Median outcome, and how often each strategy ends ruined (<10% of start) or doubled.
The one line that matters
f* = edge ÷ odds
At 60/40 and even money, the optimal bet is 20% of the roll per flip. Bet twice that and the growth dies — a real edge, and you’re paying for the privilege of being right.
Overbetting is just Kelly with a lie in it. Tick the checkbox above and watch the “optimal” strategy go sideways: sizing for 70% on a coin that pays 60%.