Risk of ruin calculator
The probability of hitting a target before hitting zero, given a bankroll, a bet size and a house edge. The result is usually less comfortable than people expect.
| Bankroll in units | 100 |
|---|---|
| House edge | 4.00% |
| Chance of reaching target first | 0.0% |
| Chance of ruin first | 100.0% |
| Expected bets before ruin, if you never stop | 2,500 |
| Expected loss per 1,000 bets | $400.00 |
With a house edge of 4.00%, ruin is certain given unlimited time. The only variable that changes the outcome is when you stop, not how you stake.
The gambler’s ruin problem
This is one of the oldest results in probability. A player with a finite bankroll, betting against an opponent with effectively unlimited funds, at odds slightly against them, goes broke with probability approaching one given enough time. It is not a claim about luck. It is arithmetic about absorbing barriers.
The calculator models even-money bets at the stated edge and computes the chance of reaching your target before reaching zero. The asymmetry that drives the result is small per bet and decisive in aggregate: a 96 percent RTP game means each unit wagered returns 0.96 units in expectation, and the shortfall accumulates.
Raising the bet size raises the chance of reaching the target and raises the chance of ruin arriving sooner. Lowering it does the reverse. What it cannot do is change the sign of the expectation, which is why no staking pattern appears in the formula.
Why variance is not your friend for long
Over a short session variance dominates and the edge is almost invisible. This is the entire experience of casino gambling, and it is why the games feel winnable, because in any given hour they genuinely are.
Over a long run the opposite is true. Variance grows with the square root of the number of bets while expected loss grows linearly with it, so the edge overtakes the noise and does so permanently. The crossover is measured in thousands of bets, which a slot player reaches in a few hours.
The practical reading is that a short session with a hard stop is a different proposition from regular play, and the difference is not willpower, it is the shape of two curves. If you intend to play, the stopping rule is the only meaningful control you hold.
Reading the output honestly
The expected-bets-before-ruin figure assumes no stopping. It is included because it makes the structure visible, not because anyone plays that way. Almost everyone stops somewhere, and where they stop is what actually determines their result.
The expected loss per thousand bets is the more useful number day to day. It converts an abstract house edge into a cost per session at your actual bet size, and it is the figure worth knowing before choosing a game instead of after.
Slots carry far higher variance per spin than this even-money model, which widens both tails. You are more likely to end a session well ahead and more likely to lose the bankroll quickly. The expectation is unchanged, which is the point.