Risk of Ruin Calculator

The number that ends careers

You can be a winning player and still go broke. Not as a freak accident, but as a predictable statistical outcome of playing too high for your bankroll. Risk of ruin is the probability of losing your entire bankroll before running up a profit, and it is not a function of whether you're a good player. It is a function of your win rate, your variance, and how many big blinds you've chosen to sit down with.

The model

For a cash game player with a constant win rate and standard deviation, the analytical formula for risk of ruin (probability of going broke before infinite profit) is:

RoR = exp(-2 * wr * B / sd^2)

where wr is win rate in bb/100, B is the bankroll in big blinds, and sd is the standard deviation in bb/100. This is the continuous random walk approximation; the actual discrete version is very close at typical bankroll sizes.

Some things to notice immediately. RoR falls exponentially with bankroll size. A player with wr=5, sd=100 who has 100bb has a RoR of exp(-2 * 5 * 100 / 10000) = exp(-0.10) = 90.5%. Almost certain ruin. With 1,000bb: exp(-2 * 5 * 1000 / 10000) = exp(-1.0) = 36.8%. Still too high. With 5,000bb: exp(-2 * 5 * 5000 / 10000) = exp(-5.0) = 0.67%. Now we're talking about a tool, not a gamble.

Worked example

Player profile: 4bb/100 win rate, 90bb/100 standard deviation (tight-aggressive NL6max). Target: RoR below 5%.

Solve for B: 0.05 = exp(-2 * 4 * B / 8100), so ln(0.05) = -2.996 = -8B / 8100, giving B = 2.996 * 8100 / 8 = 3,033 bb.

At NL100 ($1/$2 blinds), 3,033 big blinds is about $6,066. Most players would consider that four or five buy-ins. It is actually thirty buy-ins, because most NL100 players buy in for 100bb. The intuition about "five buy-ins is fine" is almost universally wrong when the actual math is run.

What each output means

Risk of ruin percentage is the headline: given your inputs, what is the probability you go broke before reaching any positive profit target? Recommended bankroll at a chosen RoR tolerance inverts the formula and gives you the number you need to hit your target. RoR vs. bankroll curve shows the non-linear nature of the relationship: the first 1,000bb of additional bankroll buys much more safety than the next 1,000bb. Tournament mode outputs ruin probability over a fixed number of tournaments at your buy-in level, which is a finite-horizon calculation more appropriate for event-based play.

Where the model breaks

The formula assumes a constant win rate and constant variance. Neither is true. Win rates decline as you move up in stakes (tougher fields), and the standard deviation at NL200 may be different from NL100 even if you play the same style. Running the calculation at your current win rate and projecting it to higher stakes overstates how safe the move-up actually is.

The model also assumes you play forever without a stop-loss. In practice, most players stop playing when they've lost too much in a session or a week. Stop-losses dramatically reduce actual ruin probability compared to the theoretical model, because they prevent the catastrophic runs that generate most ruin events. The calculator's stop-loss field models this by capping the maximum loss per session before the bankroll resets its ruin calculation.

Finally, ruin is not the only outcome that matters. "Ruin" in the model means losing 100% of your bankroll. But getting stuck at NL25 for six months because you ran bad at NL100 is a softer form of ruin that the formula ignores. For the full picture of stake-management math, the bankroll calculator adds move-up thresholds. The variance calculator shows you what your specific downswing trajectory looks like in practice.

Advanced: the Kelly connection

The RoR formula and the Kelly criterion are two sides of the same coin. Kelly maximises log-growth, which implicitly sets ruin probability to zero over an infinite horizon. If your stake size violates Kelly, your bankroll is mathematically expected to eventually go broke. The Kelly criterion calculator gives you the bankroll-fraction version of the same constraint, framed as a bet size rather than a bankroll floor.