Is there a best cash-out multiplier in crash games?

"1.5× or 2×?" That is almost always how the question reaches us, sometimes with 10× thrown in as the wild option. The answer is a flat one. Neither, and not 10× either. The chance of reaching a target falls at the same rate the payout rises, so with payouts left un-rounded each one hands back the same fraction of every dollar staked. Your choice of target settles how often you win and how hard the swings land, and has no say at all in the average.

Which leaves a great deal still worth saying, because nobody plays an average. They play a Tuesday evening with forty dollars.

Why the target cannot move the return

The chance of reaching a multiplier x is proportional to (1 − edge) / x. Double the target, roughly halve the win chance. "How often you win" multiplied by "how much you win" ends up where it started. A deliberately wide spread of targets at a 3% edge makes the cancellation visible.

Read down the right-hand column and nothing happens: every row gives back 97.00% of the stake in our model, with the 3% edge keeping the rest. A 1.2× target arrives constantly and pays almost nothing for arriving; a 100× target is the mirror image. Any target you like can be pushed through the crash simulator, which runs the same formula in live and bulk modes.

There is one honest wrinkle before you compare tools to tables. The clean equality belongs to the un-rounded maths above, and to the session figures below it. Tools that round each payout down to the cent, round by round, do not inherit that equality cleanly. Say your stake is small enough that the profit a win should add comes to less than a cent. The floor rounds that fraction away, the win pays back the stake alone, and the edge on that round is larger than the stated one.

A hundred rounds at a dollar

That is closer to a real session, so it is a better place to look for differences. Low targets accumulate wins constantly. High targets accumulate almost nothing, then land once and pay whatever that multiplier pays on a single stake, which may or may not cover what the dry spell cost. Whether the frequent winner is also the more likely to finish ahead is not something the per-round win rate will tell you, which is the point of the next table.

At 1.5×, 35.40% of hundred-round sessions end in profit in our model. Move to 10× and the chance of finishing ahead is actually a little higher, at 37.74%, because the rare win counts for so much when it lands. Losing all hundred rounds at 10× sits at 0.0037%, which is a real way for an evening to end rather than a rounding error. The column that genuinely separates the targets is the right-hand one, where results at the high target scatter far further from the average, in both directions. The expected loss, meanwhile, is stake × rounds × edge whichever row you are on, and the expected loss calculator will break that down for your own numbers.

Streaks, bankrolls and the comfort of winning often

Variance also decides how long a fixed bankroll survives, and here the targets really do part company. Fifty dollars, one-dollar stakes, two hundred rounds, identical edge on every bet.

A low target keeps a small bankroll breathing longer in our model. Wins arrive often enough that the balance swings less from round to round, and the gap in ruin risk between the rows is substantial (for this bankroll, stake and number of rounds). The average return sitting underneath has not moved a millimetre.

This is where "1.5× is the safe one" starts to mislead people. Winning most rounds feels like control, and the lower variance behind that feeling is doing something genuine. The losing streaks still arrive on schedule. In any given run of five rounds at 1.5×, the chance that all five lose is 0.55%; ten consecutive losses sit at 0.0030%. Over a full hundred-round session, running into a stretch that bad somewhere is likelier than either figure suggests on its own, simply because a hundred rounds contains a great many five-round windows. At 10×, five straight losses come in at 60.04% for the obvious reason that wins are scarce there. When the bad run lands at 1.5× it takes back several wins' worth of profit at once, which is how a comfortable balance halves inside twenty minutes.

Tversky and Kahneman gave the underlying mistake a name in their 1971 paper "Belief in the law of small numbers", the expectation that a short run will carry the properties of a long one. A target that wins most of the time is unusually good at feeding that expectation. Finish one evening ahead at 1.5× and the evidence feels overwhelming, because it arrives as dozens of separate confirmations, and a run of confirmations is what most of us accept as proof that something works. The identical evening at 10× would have read as an hour of nothing followed by a single payout, and nobody mistakes that for a system. Neither session tells you anything about the long-run average return of its target, since the edge fixes that in advance. What the two sessions do differ in is the shape of the short run, the size of the swings and the length of the dry spells, and those differences are visible in the tables above rather than in one evening's result. It also runs the other way. Once you expect the short run to behave, five losses in a row at a target that usually pays start to feel like a fault in the game.

The two workarounds, and picking a target anyway

The first is splitting the stake across two panels, cashing one at 1.5× and letting the other ride to 10×, which looks like buying safety and upside in the same round. Both panels sit on one crash point, so the outcomes are dependent. The late panel can only win if the round survives past both targets in turn, which is partly the same event that settled the early one. Add the two expected payouts and the total is (1 − edge) times everything staked, precisely what a single bet returns at that edge. Splitting changes which combinations of win and loss a round can produce, and stops there.

The second is doubling after a loss, and its clean version only exists at one target. At 2× with no rounding, a doubled stake recovers the whole losing run plus a unit the moment a win arrives. At 1.5× it does not, because the payout multiple no longer matches the way the stake grows, and that mismatch reappears at most other targets. Then the practical ceiling closes in, because "eventually" has to fit inside a finite bankroll and under a maximum stake, and a losing run of the length described above can demand a bet beyond both. Every wager in the sequence carries the same house edge as a flat dollar. Doubling decides how loud the ending is, not whether it comes.

What a target choice buys you, then, is a distribution rather than an advantage. A low target gives frequent small wins and smaller swings; a high target gives long dry spells and the occasional large payout, with a much wider spread of outcomes around the same negative average. Letting a round run on past your planned exit is the same trade in miniature, with the amount you could already have taken now at stake. Neither end of the table is a strategy in the sense people usually mean by the word, and the 3% edge is charging the same rate while you think about it.

Everything here is play money and arithmetic. We take no bets and we recommend gambling to nobody. If you find yourself changing targets because a session needs to come good, that is the moment to stop, and our responsible gambling page lists services that can help.