Poker bankroll management: buy-ins, risk of ruin, and when to move down
Bankroll management is sizing your poker money so normal variance cannot break you. Here is the risk-of-ruin formula, honest buy-in guidelines for cash and tournaments, and the move-down rules that make ruin nearly impossible.
Bankroll management is sizing the money you play poker with so that the game's normal variance cannot break you. The operative word is normal: the downswings that hit winning players are not rare accidents but scheduled weather, and a bankroll is the roof built for it. Sized right, it buys the thing that actually earns money, which is the freedom to play correctly without fear. Sized wrong, it converts ordinary variance into ruin, and no amount of skill at the table can out-play arithmetic that was lost before sitting down.
Two ground rules before the numbers. A bankroll is poker money only, fully separate from rent, savings and obligations; the moment table money and life money share a wallet, every decision at the table is contaminated by consequences poker should never touch. And if setting that boundary is itself a struggle, treat it as a stop sign rather than a technicality: never play with money you cannot afford to lose.
The formula: risk of ruin
For a winning player, the chance that variance busts a bankroll before the edge compounds away from danger has a clean approximation:
risk of ruin = e^( -2 x win rate x bankroll / variance )
with the win rate in bb per 100 hands, the bankroll in big blinds, and variance the square of your standard deviation per 100 hands (around 90bb/100 for typical no-limit hold'em, so variance near 8,100). Run it for a solid 5bb/100 winner at 100 big blind buy-ins:
| Bankroll | Risk of ruin (5bb/100) | Risk of ruin (2.5bb/100) |
|---|---|---|
| 20 buy-ins | ~8% | ~29% |
| 30 buy-ins | ~2.5% | ~16% |
| 40 buy-ins | ~0.7% | ~8.5% |
| 50 buy-ins | ~0.2% | ~4.6% |
| 60 buy-ins | ~0.06% | ~2.5% |
Two lessons sit in that table. Risk falls exponentially with bankroll: at a 5bb/100 win rate, each extra ten buy-ins cuts the remaining bust chance to under a third of what it was. And the win rate matters enormously: the thinner your edge, the bigger the roll the same safety costs. A marginal winner needs roughly double the cushion of a solid one, which is the quantitative reason rake, which eats win rate directly, is also a bankroll problem.
The formula's honest limits: it assumes your win rate is what you think it is (it is probably lower; see variance on why even 100,000 hands measures it loosely), assumes the games stay the same, and assumes you never move down. The last assumption is the one you should violate on purpose.
Guidelines by format
- Cash games: 25 to 40 buy-ins of 100 big blinds as a working range at small stakes, the low end only alongside strict move-down rules. Push toward the high end when the win rate is unproven, the games are tough or aggressive, or the rake is heavy.
- Tournaments: about 100 buy-ins as a floor, more for large fields. Tournament returns concentrate in rare deep runs, so the standard deviation per event is a multiple of a cash session's, and 50-event droughts happen to excellent players.
- Fast formats and shot-takes: anything that raises variance, wider ranges, deeper aggression, satellites into bigger events, gets budgeted separately rather than bled from the main roll.
These are deliberately ranges rather than single numbers, because the right figure depends on inputs only you know: how replaceable the money is, how proven the win rate is, and how honestly you will follow the next section.
Move-down rules: the real safety mechanism
The risk-of-ruin table assumed you stubbornly play the same stake to the last big blind. Nobody sensible does, and the escape hatch is the most powerful tool in the system: when the roll shrinks to a threshold, drop stakes. Halving the stake instantly doubles the buy-in count, which collapses the risk of ruin, and it does so exactly when the extra safety is needed.
A workable ladder, decided in advance and written down:
- Take a shot at the next stake when your roll covers about 40 buy-ins there, and give the shot a fixed budget of three to five buy-ins before you sit.
- Retreat the moment the shot budget is spent, without renegotiating with yourself at the table. Separately, if the roll ever falls below roughly 25 buy-ins at your regular stake, drop a level there too.
- Repeat. A failed shot costs its budget and nothing more; the ladder guarantees it is an expense, never a catastrophe.
The rule only works if it is mechanical. The moment moving down becomes a debate held mid-downswing, it is being decided by the exact psychology, ego, chase, denial, that tilt runs on, and it will lose. Decide once, cold; obey later, hot.
Bottom line
Bankroll management is applied arithmetic: a win rate, a variance, and a cushion sized so the exponent in the risk-of-ruin formula comes out comfortably small. For cash that means somewhere between 25 and 40 hundred-blind buy-ins depending on your edge and honesty; for tournaments, triple digits. Keep poker money sealed off from life money, write the move-down thresholds before the downswing arrives, and let the ladder, not your nerve, carry the safety load. Skill decides how fast the roll grows; bankroll management decides whether it survives long enough for skill to matter.
Frequently asked questions
- How many buy-ins do you need for cash games?
- A common working range is 25 to 40 buy-ins of 100 big blinds for a winning player at small stakes, with the low end acceptable only if you will move down when losses come. Thin win rates, tough games and heavy rake all push the number up, and 20 buy-ins carries a real bust chance near 8 percent for a typical winner.
- How many buy-ins do you need for tournaments?
- Around 100 buy-ins as a floor, and more for large-field events. Tournament variance dwarfs cash variance because most of the return sits in rare deep runs, so even strong players go 50 or more events between significant scores.
- What is risk of ruin?
- The probability that normal variance exhausts your bankroll before your edge can compound, assuming you keep playing the same stakes. It falls exponentially as the bankroll grows: the formula is e to the power of minus two times win rate times bankroll divided by variance, with win rate and variance measured per 100 hands and the bankroll in plain big blinds.
- When should you move up or down in stakes?
- Set the thresholds before you need them. A workable pattern: take a shot at the next stake when the roll covers about 40 buy-ins there, with a fixed budget of a few buy-ins for the attempt, and drop back the moment the budget is spent or the roll falls under roughly 25 buy-ins at the current stake. Moving down early is the mechanism that makes going broke nearly impossible.