Poker bankroll calculator.

the calculator

The fields hold a 2,000 bankroll at 0.50 and 1, for a player winning 5 big blinds per 100 hands. Put your own numbers in, honestly, and see what the arithmetic makes of them.

where the numbers come from

Two formulas, no folklore.

Risk of ruin is the chance you lose the whole bankroll before your edge shows up. For a player who keeps playing the same game it comes out as e to the power of minus two times win rate times bankroll, divided by the square of your standard deviation, with the win rate and the spread measured per 100 hands and the bankroll in big blinds. Everything on this page is that one line, rearranged.

Rearranged the other way it answers the useful question. Fix the risk you are willing to accept, and the bankroll follows: the spread squared, times the natural log of one over that risk, divided by twice your win rate. A player beating the game for 5 big blinds per 100 with a spread of 100 needs 30 buy-ins to hold the risk at 5 percent and 46 to hold it at 1 percent. At 20 buy-ins that same player goes broke 14 percent of the time.

The Kelly criterion asks a different question: how big a game can you take on before the swings eat the growth. Its answer for poker is a bankroll of the spread squared divided by the win rate. Half Kelly, which is 40 buy-ins for the same player, is what people actually play, and it is no accident that it lands near the same place as a 1 percent risk of ruin.

Three assumptions hold this up, and you should know all three. Your win rate is real, not a hope. Your results are roughly normally distributed, which they are over enough hands. And you never move down, which is the assumption that makes these numbers pessimistic: anyone who drops a stake when the roll halves is safer than the formula says. Tournaments use the same line with the units changed, buy-ins instead of big blinds, because there the swing comes from cashing rarely rather than from any single hand.

What the formula cannot see is the part that empties most bankrolls. It assumes every hand is played as well as your average hand, which stops being true about an hour into a losing session. A bankroll buys you the right to keep playing badly for longer, which only helps if the rest of your game is in order: knowing what the betting rounds actually allow, knowing which hand beats which without stopping to think, and knowing the price you are being laid on every call. Those three cost nothing and they move your win rate, which is the input the risk is most sensitive to. Doubling your win rate halves the exponent; there is no bankroll size that does the same job.

One warning about tournament numbers in particular. A return on investment measured over a few hundred entries is barely measured at all, and a single deep run can flatter it for a year. If the number you type in came from fewer than a thousand tournaments, treat the answer as the optimistic end of a wide range, and check what the equity of the spots you keep taking says about whether that return is even repeatable.

next

A bankroll protects you from variance, not from yourself.

The formula assumes you keep playing your normal game. The cheapest way to make that assumption true is to know the game cold, so that a bad run costs you chips and not your judgement. Start where every leak eventually traces back to.