Risk of ruin

The probability that a bankroll is fully depleted before it either reaches a chosen target or the play horizon ends. Every bet-sizing rule — flat betting, Kelly criterion, stop-loss — is ultimately a lever for pushing this number down.

Three inputs drive it:

1. Edge — expected value per unit wagered. Negative edge (the default in casino games) makes ruin inevitable given infinite play; the only questions become how fast and what’s the chance you hit a target first.
2. Volatility — per-outcome standard deviation. High-vol slots widen the swing distribution, so even a decent bankroll faces meaningful ruin probability in a short session.
3. Bet fraction — stake as a share of remaining bankroll. Doubling your bet size roughly squares your ruin probability at the same horizon; halving it cuts ruin far more aggressively than it cuts expected loss.

For a −EV game (all casino slots), the closed-form ruin probability over N bets is dominated by the bet-to-bankroll ratio. Rule of thumb from bankroll management: keeping single-bet stakes ≤ 1–2% of session bankroll pushes 500-spin ruin below 5% for medium-volatility slots at 96% RTP; jump to 5% stakes and ruin over the same session climbs past 30%.

CasiMath’s Portfolio Builder reports ruin probability alongside EV. Bonus terms with max-bet caps and non-sticky structures usually lower it; sticky bonuses with high wagering usually raise it, even at identical headline EV. A bonus that clears 55% of the time but busts the other 45% has very different psychology from one that clears 85% and busts 15% — same expected value, wildly different ruin exposure.

Related: variance, Monte Carlo, expected value, Kelly criterion.