Optimal Bet Sizing in Crash Games: What the Kelly Criterion Actually Says

Most staking guides argue about how to bet: double after a loss, step along a sequence, raise and lower by a unit. This one answers a different and more honest question. Given that you cannot beat a crash game’s house edge, what is the mathematically optimal amount to stake? The tool that answers it is the Kelly Criterion, and its verdict is not a matter of opinion.

This is not another system debunk. Kelly is not a system at all; it is the formula that tells a bettor with a real edge how much to risk to grow their money fastest. Pointed at a game you cannot win, it produces the one answer that protects your bankroll: stake zero. What follows is the proof, and then the least-bad way to play if you are going to play regardless.

🧠 What the Kelly Criterion actually is

The Kelly Criterion tells you what fraction of your bankroll to stake to grow it as fast as possible, and it is a filter as much as a sizer. Its purpose is not to maximise the next bet but to maximise the long-run growth rate of your whole bankroll.

Introduced by J. L. Kelly Jr. in 1956 and later popularised for gambling by Edward Thorp, the rule works by maximising the expected logarithm of wealth, which is the same as maximising the expected geometric growth rate. Betting too much guarantees eventual ruin; betting nothing guarantees no growth. Kelly finds the single fraction that sits between the two.

The property that matters here is that Kelly is a filter, not just a sizer. When the formula returns zero or a negative number, that is the maths telling you not to bet at all. It is not an invitation to reach for a different staking pattern instead.

🔢 Why Kelly says bet zero on a crash game

Kelly returns zero for crash games because they are negative expected value, and the formula only stakes a positive amount when the edge is in your favour.

The Kelly fraction is positive only when bp – q is greater than zero, which is exactly the condition that the bet has a positive expected value. When bp – q equals zero, the game is fair and the rule says stake nothing. When bp – q is below zero, as it is for every house-edge game, the formula returns a negative fraction, which would mean betting the house’s side of the wager. A player cannot do that, so the best available stake is zero.

A 97% crash game carries a fixed 3% house edge, an expected loss of about three cents in every dollar staked. That makes bp – q negative, so the optimal fraction the formula returns is zero.

Put plainly, every positive stake has a negative expected growth rate, so any amount of play drags your bankroll’s growth below zero. That is the formal proof that no positive sizing strategy can make a negative-expected-value game grow your money. The general result behind it lives in our guide to the maths of crash gambling; the conclusion is that your expected loss is the house edge multiplied by your stake, whatever multiplier you choose.

The optimal stake on a crash game is the one number no betting system will sell you: zero.

🏆 How Kelly differs from Martingale, Fibonacci and D’Alembert

Those systems all claim to beat the house edge by rearranging the size of your bets. Kelly makes no such claim, which is exactly why it is the honest framework.

Martingale doubles after a loss, Fibonacci steps the stake along a sequence, and D’Alembert raises and lowers by a unit. We debunk each one in detail, but the reason they cannot work is the same in every case: by the linearity of expectation, the expected value of a run of bets is just the sum of the expected values, so no order, escalation or de-escalation changes the sign of the total. Worse, doubling-up systems actively raise the risk of catastrophic ruin, because a losing run long enough to bust your bankroll becomes a certainty given enough play.

Kelly is the opposite stance. It takes the odds as given and asks only how to size bets to grow wealth fastest, and when the edge is against you its answer is the honest endpoint of zero. Martingale says bet more to recover your losses; Kelly says if the bet is bad, the right exposure is none. The rational baseline once you accept the edge is flat betting, which we cover separately.

🎯 Recreational Kelly: sizing to lose more slowly

If you accept that a crash game is a loss and choose to play anyway, treating the expected loss as the price of entertainment, a small fixed fraction of your current bankroll, usually 1 to 2%, is the only defensible discipline. It is not a way to win. It is a way to lose more slowly and predictably.

In a game you can beat, professionals often bet a fraction of full Kelly to cut variance: half-Kelly delivers about three-quarters of the full growth rate at half the volatility, and the literature shows it sharply improves the odds of doubling your money before halving it. None of that rescues a crash game, because the full-Kelly base here is zero, so a fraction of Kelly is still zero. Recreational fixed-fraction is not a scaled-down growth strategy at all; it is a ruin-deceleration and session-budgeting tool. Set your loss budget first, which we cover in our bankroll management guide, and decide in advance when to stop.

📊 How long your bankroll lasts

The smaller the fraction you stake, the longer you play. Session length is inversely proportional to your bet fraction: double the percentage and you roughly halve your expected playing time for the same starting money.

The model is simple. At a 97% return to player the edge is 3%, and staking a fraction of your current balance each round, the expected number of rounds to fall to a tenth of your starting bankroll is about the natural log of 0.10 divided by the product of the edge and the fraction, which works out to roughly 76.75 divided by the fraction. At a typical pace of 100 to 200 rounds an hour, 1% staking buys around 38 to 77 hours before the average bankroll is down to a tenth; 10% staking burns through that in about 4 to 8 hours.

💡 The bottom line on bet sizing

If your goal is to make or keep money, the correct bet size is zero, and Kelly proves no method changes that. If you play purely for entertainment, the defensible approach is narrow: a small fixed fraction of your current balance, never a fixed cash stake and never a loss-chasing system.

Two further levers help only with longevity, not with the result. Where the return to player is operator-configurable, a higher setting stretches every figure above, so a 99% game lasts roughly six times longer per dollar staked than a 94% one, and lower cash-out targets reduce the variance that makes the typical path decay faster than the average. None of this turns the game positive.