Play the hand.
Understand the odds.
From pocket jacks on the button to a tough river call. Set the table, explore your equity, and see the thinking behind your next move.
Set up your hand
Pick cards from the menus, or type them (for example As Kd or 7c 8c 9d).
Advanced: rake and precision
Your decision, unpacked
Let’s look at your hand.
The pocket jacks example is ready. Analyze it to see equity, pot odds, sizing math and the reasoning behind them.
What the numbers mean
How your hand finishes
Technique for this spot
Equity assumes every opponent holds a hand from the range you chose and that the hand reaches showdown. Real opponents narrow their ranges with every action, and future betting, fold equity, rake, side pots, tournament payouts and player tendencies can change the decision. The suggestions are rules of thumb built on these numbers—not solver output and not a guarantee of the best action.
Kelly criterion: how much of a bankroll to risk
The Kelly criterion sizes a repeatable bet with fixed odds to grow a bankroll as fast as possible over the long run. Here it helps you see how much of your poker bankroll a bet exposes. It does not choose a bet size or a call in a poker hand.
The formula, worked through
What Kelly assumes, and why poker breaks it
- Kelly’s setting: the same bet repeated many times, independent outcomes, a known probability p, a fixed payout b, any stake you like, and a loss of exactly the stake when you lose. It maximizes the long-run growth rate (expected logarithm of the bankroll), not profit on a single bet.
- Fractional Kelly: for small edges, half Kelly often retains roughly three-quarters of the expected log growth with a smaller stake. Overbetting beyond full Kelly lowers expected log growth and increases risk; the results depend on the odds and probability.
- Estimates: Kelly treats p as known. Overestimating p can lead to overbetting and substantial losses. That is a common reason to use half or quarter Kelly.
- Equity is not a win probability: showdown equity mixes outright wins with split-pot shares and assumes the hand reaches showdown. A tie is not a win, and a split pot is not a returned stake.
- Poker odds are not fixed: changing a bet changes who calls or folds, what range continues and how much you win. Rake, side pots and later streets change the payout too, and hands are not identical repeats.
- A call is a fixed price: you can call or fold, not call part of a bet. Kelly can show how much of your bankroll that call exposes; it cannot choose the call amount.
Primary source: J. L. Kelly Jr., “A New Interpretation of Information Rate,” Bell System Technical Journal 35(4), 1956, pp. 917–926. Wiley Online Library