Poker Risk of Ruin, Explained

Risk of ruin is the probability that your bankroll hits zero before your skill edge earns the money back. It rises when your win rate is thin, your variance is high, or your bankroll is small — and it falls fast as any of those improve. Understanding it turns “how many buy-ins do I need?” from a guess into a number you can actually control.

What risk of ruin actually measures

Every winning player still loses sometimes. Risk of ruin answers a specific question: given your edge and the swings of your game, what are the odds a bad run drops you to nothing before the good run arrives?

Three inputs drive it:

• Win rate — your average profit per unit of play (bb/100 online, or per hour live). More edge means you climb out of holes faster.
• Variance — how wildly results swing around that average. Tournaments and PLO swing far more than tight full-ring hold’em.
• Bankroll — how many buy-ins deep you are. More buy-ins means more room to absorb a downswing.

The formula

A widely used approximation for risk of ruin is:

RoR = e^(−2 × W × B ÷ V)

where W is your win rate, B is your bankroll, and V is your variance — all expressed in the same units (typically big blinds). The takeaway matters more than the algebra: risk of ruin shrinks exponentially as your edge and bankroll grow relative to variance. Double your effective edge and you don’t halve the risk — you square-root it or better.

Worked example

Suppose you’re an online cash winner with:

• Win rate: 5 bb/100
• Variance: roughly 30 bb per 100 hands squared standard-deviation profile (typical 6-max)
• Bankroll: 20 buy-ins = 2,000 big blinds

Plug those into the exponent and the risk of ruin lands in the low single digits — around 3–4%. Push the bankroll to 30 buy-ins (3,000 bb) and it drops below 1%. Halve the win rate to 2.5 bb/100 at 20 buy-ins, though, and risk of ruin jumps back up toward 15–20%. Same bankroll, thinner edge, dramatically more danger.

That’s the core lesson: a bigger edge protects you more than a bigger bankroll. You can read more on measuring that edge in the guide to win rate and ROI.

How buy-ins map to risk

You don’t need to run the exponential yourself every session. For a typical solid cash-game winner, buy-in counts translate to roughly these risk levels:

Buy-ins in bankroll	Approx. risk of ruin	Verdict
10	~15–25%	Reckless — one downswing can end you
20	~3–5%	Workable for recreational play
30	~1%	Comfortable for a serious grinder
40	well under 1%	Conservative; extra safety
50+	negligible	Diminishing returns kick in

These assume a genuine winning edge. A losing player’s risk of ruin is 100% at every bankroll size — no buy-in count saves negative EV. Confirm you’re beating the game before you trust any of these numbers.

Why tournaments need far more

The table above is for cash. Tournaments carry enormous variance because you cash rarely and rely on occasional deep runs, so their risk-of-ruin math demands 100+ buy-ins to reach the same comfort a cash player gets from 25. The exponential formula still applies — variance is just so much larger that you need a proportionally larger bankroll to push the exponent negative enough.

Using it in practice

You won’t compute e-to-the-power mid-session, but the model should shape three habits:

1. Grow your edge, not just your roll. Study and leak-fixing lower risk of ruin more efficiently than grinding out extra buy-ins. The odds and math hub is where a lot of hidden edge lives.
2. Move down when your bankroll shrinks. This is what makes real-world ruin far rarer than the static formula predicts.
3. Respect variance by format. Match your buy-in count to how swingy the game is — and expect the long downswings that variance guarantees.

Common misreadings

• Treating it as a guarantee. A 2% risk of ruin means 2% of players like you still bust. Low is not zero.
• Ignoring the win-rate input. People obsess over buy-in counts while playing a breakeven game, where no bankroll is safe.
• Forgetting you can adapt. The formula assumes static play; real players move down and cut variance, which is your biggest safety lever.

Risk of ruin turns bankroll sizing into cause and effect: edge and buy-ins push it down, variance pushes it up. Keep your risk in the low single digits, keep improving the edge underneath it, and return to the bankroll management hub to fit this into the wider system.