Game 04 · Static · measures: bet sizing
Kelly Run
Twenty flips of a biased coin, even money. The bias is never told to you — you have to infer it from outcomes while you bet on it. The machine line is a bot running full Kelly on the same posterior and the same coin.
The bias is fixed for this seed. First few flips are cheap information — bet accordingly.
Ledger
No flips yet. The first bet is the cheapest information you will ever buy.
How it works
The coin's bias p is drawn once from the page seed and never revealed until the run ends. After every flip the posterior over p updates as Beta(1 + heads, 1 + tails), and the Kelly fraction for an even-money bet is f* = 2p̂ − 1 on whichever side the posterior favours. The bot bets exactly that; you bet whatever the slider says. The chart is log-scaled because that is the only scale on which compounding is legible — and it is why over-betting kills you even when you are right about the coin.