Risk of Ruin: The Chance of Losing It All
Updated
Having an edge does not protect you from losing everything. It only makes it less likely. With a 1% edge and 100 units of bankroll, the chance of going broke before the math rescues you is about 21%.
- Risk of ruin depends on edge, bankroll and swing — nothing else.
- At a 1% edge, 100 units means about 21% chance of ruin.
- 400 units at the same edge brings it to 0.2%.
- The standard deviation of one hand is 1.13 bets. We computed it.
The table
Chance of losing the entire bankroll before the edge asserts itself, for a flat bet. The standard deviation used is 1.1322 bets per hand, computed by carrying the second moment through the same solver that produces our house-edge figures.
| Bankroll | 0.5% edge | 1% edge | 1.5% edge | 2% edge |
|---|---|---|---|---|
| 100 units | 45.84% | 21.01% | 9.63% | 4.41% |
| 200 units | 21.01% | 4.41% | 0.93% | 0.19% |
| 400 units | 4.41% | 0.19% | under 0.01% | under 0.01% |
| 600 units | 0.93% | under 0.01% | under 0.01% | under 0.01% |
| 1000 units | 0.04% | under 0.01% | under 0.01% | under 0.01% |
What the numbers are telling you
Read down the 1% column. Doubling the bankroll from 100 to 200 units cuts ruin from 21% to 4.4%. Doubling again brings it to 0.19%. The relationship is exponential, which is why advantage players talk about bankroll in hundreds of units rather than dollars.
Read across a row instead and you see the other lever: at 200 units, going from a 0.5% edge to 2% takes ruin from 21% to 0.19%. Edge and bankroll are interchangeable up to a point.
The number this table cannot show you
Risk of ruin says nothing about how long the bad stretch lasts. A player with a 400-unit bank and a 1% edge will almost certainly not go broke — and can still be down 150 units for months. That is what variance looks like from inside.
If you have no edge at all, this table does not apply: without one, ruin is certain given enough hands. The only question is when. That is worth being clear about.
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By Martin Kosek · every number on this site is computed by us, not copied.
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