Part 4 · Lesson 21 of 25 · Pro
Kelly criterion in poker: sizing your bankroll risk
Two players win the same 60 of 100 even-money bets. One stakes 20% of his bankroll each time and ends with 7.5 times his money; the other stakes 40% and loses 22%. Same edge, opposite fates: how much you risk matters as much as whether the bet is good.
The hand
You and the Maniac each win 60% of even-money bets, a 20% edge. You stake 20% of your bankroll on every bet; he stakes 40%.
Predict first
After 100 bets with exactly 60 wins each, who has more money?
- The Maniac: twice the stakes, twice the profit
- You
- Neither: same wins, same edge
Formula
Kelly fraction f* = (b × p − q) ÷ b for odds b to 1, win chance p, lose chance q = 1 − p. Growth = p ln(1 + b f) + q ln(1 − f)
This lesson is part of Pro. Above are its opening, its question and the idea it leads to; the worked numbers, the common mistake, the interactive tool and the check are in the app.