How expected loss works
Every crash round has the same two outcomes: the multiplier reaches your cash-out target, or it busts first. With house edge e and target x, the chance of winning a round is p = (1 − e) / x. Over N rounds at stake s, the number of wins follows a binomial distribution, and the session's net result is s · (x · wins − N).
Averaged over many repeats, the wins you'd expect are N · p, and the expected net simplifies to a clean formula that does not depend on the target at all:
expected loss = stake × rounds × edge For a $1 stake, 100 rounds and a 3% edge, that is $1 × 100 × 0.03 = $3.00 — matching the calculator above. Change the target to 5× or 100× with the same stake, rounds and edge and the expected loss stays $3.00, because the target cancels out of the average.
RTP and what it means here
Return to player (RTP) is just the flip side of house edge: RTP = 1 − edge. At the 3% edge used on this page, the engine puts expected return at 97.00% of the stake — meaning that averaged over enough rounds, about 97 cents of every dollar wagered comes back as payouts, in our reference model. This calculator only models the edge you enter in our reference model; for a real game, check the RTP and rules its provider publishes — this calculator lets you plug in any house edge and see the session math for yourself, rather than trusting a marketing number.
Variance: why single sessions don't match the average
Expected loss describes the average across many sessions, not any one session. The standard deviation (sd above) measures how far a typical session can stray from that average. With our default settings, the expected loss is $3.00 and the standard deviation is $9.9955 — two very different quantities measuring two different things, side by side. That gap between a small expected loss and a much larger standard deviation is why a 100-round session can easily finish well up or well down even though its long-run expectation is a small loss.
Same expected loss, very different odds of winning
The table below holds stake ($1), rounds (100) and edge (3%) fixed and only changes the cash-out target. Expected loss never moves — it is always stake × rounds × edge — but the chance of finishing the session in profit changes a lot, because a low target wins small and often while a high target wins big and rarely.
| Target | P(profit) | Expected loss | Std. deviation |
|---|---|---|---|
| 1.5× | 35.40% | $3.00 | $7.1701 |
| 2× | 34.43% | $3.00 | $9.9955 |
| 5× | 38.14% | $3.00 | $19.7714 |
| 10× | 37.74% | $3.00 | $29.5958 |
| 100× | 25.31% | $3.00 | $98.0097 |
This is the main lesson of the page: changing your target or your "strategy" moves variance around, not the house edge. A 1.5× target feels safer because it wins more often, and a 100× target feels thrilling because of the rare big win — but both lose the same 3 cents on every dollar wagered, on average, at this 3% edge.
Why "loss chasing" and martingale don't fix the math
Loss chasing — raising your stake after a loss to try to "win it back" — and the martingale system — doubling the stake after every loss — are popular because they can make a session look like it is heading for a guaranteed small profit. Neither changes the probability of winning any individual round, and neither changes the expected loss of the rounds you've already played. What they do change is the size of the loss on a bad streak: a doubling sequence turns a routine run of busts into a much larger single loss, and every round still carries the same house edge. No staking pattern — flat, martingale, or otherwise — turns a negative expected value into a positive one.
If you want to see how a bankroll fails under repeated betting, the risk of ruin calculator works through the exact probability of dropping below the next stake (being unable to place another bet). To watch many simulated rounds play out instead of just the averages, try the crash simulator.
