Risk of Ruin

Risk of ruin is the probability that a bankroll falls far enough that you can no longer place your normal bet — that you run out of money before your edge has time to pay.

It matters more than expected value, because a positive edge is worth nothing to someone who went broke waiting for it.

Two things drive it, and only two: how large your edge is, and how many bets deep your bankroll goes. The second is usually the binding one. Fifteen bets deep is dangerous no matter how good you are, because a losing run of fifteen happens to everybody.

Risk of ruin is the probability that a bankroll falls far enough that you can no longer place your normal bet. It is the question that matters more than expected value, because a positive edge is worth nothing to someone who ran out of money before it arrived.

Two things drive it, and only two. How big your edge is, and how many bets deep your bankroll goes. The second is usually the binding one: a bettor with a real 3% edge and only fifteen bets in the bankroll is in far more danger than one with a 1% edge and two hundred.

The rough guidance that falls out of running this repeatedly: under twenty-five bets deep is dangerous at any edge. Fifty is where flat staking starts to be defensible. A hundred or more, with a genuine edge, makes ruin a remote possibility rather than a live risk. That maps onto the standard 1–2% unit advice, which is where it comes from.

Monte Carlo rather than a closed form, deliberately. The textbook risk-of-ruin formulas assume symmetric even-money bets and an infinite horizon, and betting is neither — prices are asymmetric and seasons end. Simulating the actual sequence of bets you are describing gives an answer to the question you asked rather than to a tidier one.

This models flat staking, which is the only plan where strict ruin is really reachable. Under percentage or Kelly staking the stake shrinks with the bankroll, so it can approach zero without ever failing to cover the next bet — for those, read the drawdown figures instead, or use the bankroll simulator to compare plans directly.

$10,000 bankroll, $200 flat at −110, a 53% win rate, 500 bets ahead. The edge is 0.62 points — thin but positive — and the bankroll is 50 bets deep.

Ruin is unlikely over that horizon, but the drawdowns are not: a substantial share of runs dip 25% below their peak at some point. That is a $2,500 swing on a bankroll where the median outcome is a modest profit.

Now raise the stake to $1,000. Same edge, same 500 bets, but the bankroll is only ten bets deep — and the risk of ruin climbs sharply. Nothing about the quality of the betting changed. The staking did.

Set the stake above the bankroll and the calculator does not simulate at all: the strategy is infeasible before the first bet, and that is an answer rather than a number.

What is an acceptable risk of ruin?

Most bettors target under 1–2% over their planning horizon. If the figure is above 5%, the stake is too large for the bankroll — that is nearly always the fix, rather than finding a better edge.

Why does my risk of ruin stay high even with a good edge?

Because bankroll depth matters more than edge size. Fifteen bets deep is dangerous no matter how good you are; a losing run of fifteen happens to everyone. Add bankroll or cut the stake — improving the edge barely moves this number.

Why simulate instead of using a formula?

The standard closed-form results assume symmetric even-money bets over an infinite horizon. Real betting has asymmetric prices and a finite season, and the shortcuts are misleading in exactly the cases people care about.

Does this work for percentage or Kelly staking?

No — it models flat staking. Under proportional staking the stake shrinks with the bankroll, so strict ruin is nearly unreachable and the meaningful risk is drawdown. The bankroll simulator compares all three plans.

My stake is larger than my bankroll. What happens?

Nothing is simulated. The strategy is infeasible before the first bet, and the calculator says so rather than returning a number that implies the sequence could have been placed.

• Bankroll Management: Units, Flat Betting and RuinA real edge with the wrong stake size still goes broke. What a unit is, why flat betting wins, and how deep a normal losing run goes.11 min read
• The Kelly Criterion, Explained Without the CalculusThe mathematically optimal stake — and the reason almost nobody who understands it bets the full amount.10 min read

• Bankroll SimulatorTen thousand seasons of the same edge, and where they end up.
• Bankroll / Unit CalculatorWhat a unit is worth, and what bankroll a unit implies.
• Maximum DrawdownThe worst stretch in a record, in money and in duration.
• Streak ProbabilityThe losing runs a winning bettor should still expect to hit.