The Kelly Criterion for Poker and Sports Betting (Plain English)
What the Kelly criterion actually says, why most pros use a fractional version, and how to apply it to poker buy-ins and sports betting stake sizing.
Kelly is the bet-sizing formula that maximizes the long-term geometric growth of your bankroll. It's also the formula that, used at full strength, will give you a 50% drawdown roughly every other year. Understanding both halves matters.
The formula in one line
For a bet with probability p of winning and odds b (decimal − 1), the Kelly fraction is:
f* = (p × (b + 1) − 1) / b
For a coin flip at 2.10 odds (b = 1.10, p = 0.5): f* = (0.5 × 2.10 − 1) / 1.10 ≈ 4.5% of bankroll.
Why nobody plays full Kelly
Full Kelly is mathematically optimal under one giant assumption: your edge estimate is perfect. In poker and betting, it never is. A 10% overestimate of your edge with full Kelly produces wild swings and frequent 30–50% drawdowns. Most pros run half Kelly or even quarter Kelly.
Kelly for poker cash games
You can approximate cash game Kelly by treating "buy-ins risked per session" as the Kelly fraction. If your edge is 5bb/100 and your standard deviation is 100bb/100:
- Full Kelly ≈ 5% of bankroll per session
- Half Kelly ≈ 2.5%, which is roughly the classic "20–40 buy-ins" rule
In other words, the buy-in rules you've already seen are basically half-Kelly in disguise.
Kelly for sports betting
Most edges in sports betting are 2–6%. Half-Kelly on a 4% edge at 1.95 odds is about 2% of bankroll. Track your closing line value — if you're consistently beating the close, your edge estimate is real.
When Kelly breaks
- Correlated bets — three parlays on the same team are one bet, not three. Size accordingly.
- Soft edges — if you only "think" you have an edge, your edge is probably zero. Don't apply Kelly to vibes.
- Withdrawal pressure — Kelly assumes you reinvest. If you need to withdraw monthly, drop another notch.
The practical rule
For 95% of players, fractional Kelly + a tracker that updates your bankroll automatically beats every spreadsheet model. The math punishes overconfidence more than it rewards optimization.