How risk of ruin works
Risk of ruin is the chance that a fixed bankroll drops below the size of a single stake before a session of a fixed number of rounds ends. Each round the player bets a fixed stake; with probability p the round wins and the balance moves up by a fixed net amount, and with probability 1 − p the round loses the stake. Once the balance falls below the stake, no further bet can be placed — that state is permanent (an "absorbing" state in probability terms), and it is still counted as ruin even if it happens on the very last round.
The calculator does not sample random outcomes. It builds the full tree of every possible sequence of wins and losses up to the chosen number of rounds, tracks how much probability mass ends in each possible final balance, and sums the mass that ends below the stake. That is why the result is exact rather than an estimate with sampling noise — the same inputs always produce the same answer.
Why ruin is (eventually) certain
With a house edge above zero, the expected value of each round is negative: on average the player gives back a fixed percentage of the stake every time. Over any single session of a few hundred rounds, that drag only makes a bankroll loss more likely, not certain — a lucky run can still finish ahead. But stretch the number of rounds toward infinity and the picture changes: — assuming independent rounds, a fixed positive stake, a fixed target and a positive edge — the probability of eventually dropping below the next stake (so you can no longer place it) approaches 100%, because a finite bankroll cannot absorb an unlimited number of expected losses. Our comparison table shows the trend already forming over just 50 to 500 rounds with the default inputs: longer play, same edge, higher ruin probability.
What this calculator assumes
- Fixed stake: the same amount is bet every round — no doubling, no scaling with the current balance.
- Fixed cash-out target: every winning round pays the same multiplier.
- Independent rounds: each round's outcome does not depend on previous rounds, which matches how provably fair games are built.
- Ruin = balance below stake: once the balance can no longer cover one more bet, the session is over for that path.
- Cent rounding: every payout is rounded down to the nearest cent, the same way a real balance is tracked.
Expected vs. median final balance
Expected final balance is a probability-weighted average across every possible path, including the rare ones where a long winning streak produces a large balance. Median final balance is the middle outcome: at least 50% of the probability mass is at or below it, and at least 50% is at or above it (weighted by probability, not by counting paths). With a 50.00 bankroll, 1.00 stake, a 2× target and 200 rounds, the expected final balance is 44.00 and the median is 44.00. When the two diverge noticeably, it is usually a sign that a small share of lucky paths is pulling the average upward while the typical outcome looks different. The ratio table above shows how both numbers shift as the bankroll grows relative to the stake — a 10× bankroll behaves very differently from a 200× bankroll even though every other input is identical.
Stop-loss and stop-win rules don't change the edge — but they can change what this calculator measures
A common myth is that a stop-loss (walk away after losing X) or a stop-win (walk away after gaining Y) changes the underlying odds. It doesn't: the house edge is a property of the game's payout rule, applied the same way to every round regardless of what the player decided beforehand, so stopping rules never raise the expected value of a single bet. That's a separate question from what this calculator reports, though. Risk of ruin here is the probability that a fixed-stake session with no stopping rule reaches the floor within a set number of rounds. A real stopping rule — for example, walking away for good the first time the balance reaches a target — removes some of the paths that would otherwise keep playing (and eventually ruin), so it can lower the probability of ever going bust in that session, even though it does nothing to the edge of any single round played along the way. This calculator does not model stop-loss or stop-win behaviour: it assumes the same fixed stake is bet every round, for the full number of rounds entered, with no exit condition. For the expected loss of a whole session with no stopping rule, see the expected loss calculator; to watch ruin probability play out round by round, try the crash simulator.
