Poker Bankroll Calculator

One formula, read two ways

Treat your profit graph as a random walk with an upward drift: each block of 100 hands adds a draw whose mean is your win rate and whose spread is your standard deviation. The chance such a walk ever falls by the whole bankroll has a closed form.

Risk of ruin = exp(−2 × bankroll × win rate ÷ standard deviation²)

Rearranged, it sizes the roll instead of judging it:

Bankroll = −standard deviation² × ln(target risk) ÷ (2 × win rate)

That is the whole calculator. A player winning 5 bb/100 with a standard deviation of 100 bb/100 who accepts a 5% chance of ruin needs 2,996 big blinds, which at 100 big blinds a buy-in is 30 buy-ins — the famous thirty, derived rather than asserted. Put it back through the first equation and it returns 5.0%. A "unit" is only another word for a buy-in, so the answer reads the same either way.

Two properties worth carrying around

Two consequences matter more than the formula itself. The bankroll is inversely proportional to the win rate, so doubling the win rate halves the roll exactly: 10 bb/100 needs 1,498 big blinds rather than 2,996, or 15 buy-ins against 30. Beating the game better is much the cheapest way to be safe.

And the bankroll goes with the square of the standard deviation, so variance is charged twice. PLO 6-max at 140 bb/100 needs 2.2 times the roll of NLHE 6-max at 95 bb/100, not 1.5times. That is how PLO players go broke: they cross over with a hold'em roll and a hold'em win rate, and the square term eats them.

What each bankroll size actually buys

The same 5 bb/100 winner in NLHE 6-max at 95 bb/100, holding different numbers of buy-ins:

Read the shape, not the rows. 10 buy-ins to 30 takes the risk from 33% to 3.6%; 30 to 100 takes it from 3.6% to less than 0.01%. Each extra buy-in divides the risk by a constant factor, so the early buy-ins do nearly all the work and the later ones buy comfort. At 3.6% ruin is unlikely, and moving down a stake during a bad run would make it unlikelier still.

The win rate is the number that matters

At NLHE 6-max variance and a 5% target, the requirement by win rate:

The top row deserves a second look. A genuine but thin 1 bb/100 wants 135.2 buy-ins, more than almost anybody carries, and a thin win rate is the one you are least sure of. Size the roll on the bottom of your confidence interval rather than the middle; the win rate calculator works out that interval and says how many hands would narrow it.

Standard deviation by game, and why it is only an estimate

Your own standard deviation comes out of your tracking software, and it is the one to trust. The values below are typical observed ranges that players report from tracked samples rather than laws. Each row shows what a 5 bb/100 winner needs at a 5% target.

NLHE heads-up is high because every hand gets played and nothing is folded in the blinds: 43.1 buy-ins against 27 for six-max. 5-card PLO 6-max has the fewest public samples of anything here, so its range is the widest; assume the top of it.

Choosing a risk you can live with

The target is the only genuinely personal input, because it prices the thing the maths has no view on: what happens to you if the money goes.

Notice how little the careful end costs. Going from 20% to 0.10% cuts the risk by a factor of 200 and multiplies the requirement by only 4.3, because the bankroll depends on the logarithm of the risk rather than on the risk. Safety is on sale.

Moving up, and the more important business of moving down

The requirement in big blinds is the same at every stake, because a win rate in bb/100 is already a rate per big blind. Only the cash changes. A $2,000 roll for our example player covers NL50, where the risk is 1.2%; NL100 wants $2,703.65 and is $703.65 away; and the line at which dropping back to NL25 becomes correct is $1,039.04.

That move-down line sits below the move-up line, at 77% of the requirement, because it is set by a looser risk — 10% rather than 5.0%. One line for both would bounce you between two stakes for weeks during any ordinary downswing.

A career is also shorter than forever. Over 100,000 hands rather than a lifetime, the same 30-buy-in roll runs 4.3% against the 5.0% lifetime figure.

Tournaments and MTTs

Only the ratio of drift to variance matters, so the same arithmetic answers the tournament question with one tournament as the unit of time: ROI is the drift, the deviation in buy-ins per tournament is the spread, and the answer comes out in buy-ins. Guessing that deviation is where most tournament bankroll advice goes wrong, because it can be worked out from a payout structure instead.

The last column assumes a 20% ROI and a 5% target. A 9-man single table, 50/30/20 is the steadiest format there is, at 1.56 buy-ins of deviation and 19 buy-ins of bankroll. The 1,000-runner, 15% paid structure produces 8.03, because the winner collects 179.3 buy-ins and most of the field collects nothing, and it wants 484. The commonly quoted 3 buy-ins, with its range of 2.5 to 3.5, gives only 68, so treat the quoted range as a floor.

Read any tournament answer as a lower bound, because the model treats the swings as symmetric and tournament results are not. ROI is also harder to measure than a cash win rate, which the ROI calculator will show you, and selling action is a legitimate way to shed variance you cannot afford — the staking calculator prices the mark-up.

If you do not beat the game, no bankroll helps

For a break-even or losing player no finite bankroll reaches any target, and this calculator refuses to print one: a walk with no upward drift reaches every level below it sooner or later, zero included. Even 300 buy-ins leaves a player with no edge at 100%. A bigger roll postpones ruin; only an edge prevents it. Move down, where the games are softer and the same money is more buy-ins, and read bankroll management next to the rake comparison — at small stakes the rake is often the whole difference.

What this model assumes

• Ruin here means losing the whole bankroll while playing the same game at the same stake forever. Nobody does that, and moving down when the roll shrinks cuts the real risk well below the figure.
• The win rate is treated as known and constant. It is neither, and a win rate measured over a small sample is the largest single source of error in the answer.
• Each block of hands is assumed to be an independent draw from a normal distribution. Tilt, table selection and games that get tougher as you move up all break that assumption.
• Withdrawals, rakeback and bonuses are ignored. Taking money out raises the risk, and a regular payout is best modelled by lowering the win rate instead.
• For tournaments the normal approximation is optimistic, because the results are so one-sided. Treat a tournament answer as a floor.

Where to go from here

This page sizes a bankroll; it does not track one. Logging sessions and letting your real win rate emerge is the job of the bankroll tracker, and the two belong together: track first, then size on your own numbers. For the swings inside a roll that never breaks, the downswing calculator says how deep an ordinary bad run goes and the variance simulator draws a few hundred careers. If the question underneath is whether this adds up to a living, can you make a living playing poker works through the rest of it.