The Kelly Criterion Applied to Crash Auto-Cashout
Kelly tells you the EV-optimal fraction of your bankroll to bet. For Crash, it tells you to bet zero. The honest answer.
Kelly in one formula
f* = (bp - q) / b where b is the payout per dollar won, p is the win probability, q is 1 minus p. f* is the fraction of your bankroll to stake per bet.
Positive f*: bet that fraction. Negative f*: don't bet. Zero f*: don't bet. The formula doesn't moralize — it tells you the size that maximizes long-run logarithmic bankroll growth, and on losing bets, that size is zero.
The Kelly criterion doesn't lie. When it says zero, the game has no positive-EV strategy. Believing otherwise is the gambler talking.
Applied to Crash
At a 2x cashout target with 96% effective RTP: b = 1, p = 0.48, q = 0.52. Plug in: f* = (1 × 0.48 - 0.52) / 1 = -0.04. Negative four percent. Don't bet.
At a 10x target: b = 9, p = 0.096, q = 0.904. f* = (9 × 0.096 - 0.904) / 9 = -0.004. Still negative. Same answer.
Every cashout target on a 96% game produces negative Kelly. Because every cashout target has the same long-run EV, the result is structural: when the underlying game loses money long-run, no bet size on top of it makes money.
When Kelly turns positive
Stack 15% rakeback (Glacier tier) on a 96% RTP Crash game and your effective RTP rises to about 99.4%. Now Kelly at a 2x target is barely positive — about 0.4% of bankroll. Quarter-Kelly, which is what most professional gamblers use, would be 0.1% of bankroll.
On a $1,000 bankroll, that's a $1 bet. Long-run expected profit per round: about six-tenths of a cent. Real, but glacial. Stacking bonuses on top of low-edge games is the only honest path to positive Kelly numbers, and even then the returns are grinder-grade.
Why quarter-Kelly
Full Kelly maximizes growth rate but with massive volatility. Full-Kelly bankrolls regularly swing 50%+. Most pros take a quarter of the recommended stake — way less volatility, only modest growth penalty.
Our /tools/bankroll calculator caps suggestions at quarter-Kelly so the recommended stake actually survives the variance on small bankrolls. If you're playing a positive-EV bet, that's the stake. If Kelly returns zero or negative, the calculator surfaces that honestly.
Frequently asked questions
- Should I use Kelly on every bet?
- Only positive-EV ones. For every casino game without bonus stacking, Kelly returns zero. That's the correct answer.
- Why does Kelly recommend zero?
- Because the game has negative EV. The formula is honest about it. Anything you bet loses money long-run.
- What's quarter-Kelly?
- A quarter of the full Kelly stake. Reduces variance dramatically. Standard pro practice.
- How do I find positive-EV opportunities?
- Stack rakeback on low-edge games like Mines or Blackjack. At Yeti rakeback on Mines, the effective edge can tip positive. /tools/bankroll handles the math.