Roulette strategy research: start here
You cannot change what roulette costs you, but you can choose what a typical session looks like, and a cash-out is what locks it in.
Chapter 0 of the spinner roulette research (chapters 0 to 9): Start here.
Three things hold for every strategy in this report. The edge never changes: every dollar you bet costs 2.7 cents on average, no matter how you bet it. You can change the shape of your results: a ladder that raises the bet after a loss turns most sessions into small wins and a few into big losses. And a cash-out locks the typical session in: you stop the moment you are up a set amount.
The table puts $25 flat on red beside the c9 ladder with a cash-out, both from $5,000 for up to 500 spins. The typical session moves from −$350 to +$286. The worst sessions get worse.
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The numbers
| Measure | Flat $25 on red | Streets with a cash-out |
|---|---|---|
| Typical session | -$350 | +$286 |
| Chance of ending ahead | 25.5% | 90.3% |
| Average | -$338.21 | -$46.25 |
| Worst 5 % of sessions | -$1,479.60 | -$3,210.44 |
| Ended broke | 0.0% | 0.0% |
| Wagered per session | $12,500 | $1,961.68 |
Takeaways
- The typical session moves from −$350 to +$286, and 90.3 % of sessions end ahead instead of 25.5 %.
- The average stays negative (−$46.25), because the edge does not move.
- The worst 5 % of sessions lose more: about −$3,210 against −$1,480 for flat red.
The math
The expected value of a session is fixed by the wheel: −1/37 = −2.70 % of the total wagered on the single-zero wheel. A strategy changes the expected turnover and the shape of the distribution of net results, never the edge.
The median (the typical session) is the 50 % quantile of net. It can sit above zero while the mean is negative when the distribution is skewed: many small wins, a few large losses. CVaR 5 % (the worst 5 %) is the mean of the worst 5 % of sessions.
Flat red wagers $12,500: predicted mean −$337.84, measured −$338.21. The c9 cash-out wagers $1,961.68 on average: predicted −$53.02, measured −$46.25 (realized edge −2.36 %, sampling noise; the other three seeds give −$53.65 to −$60.90). Its median is $286 and its CVaR 5 % −$3,210.
EV(session) = −(1/37) × E[wagered] ≈ −0.0270 × E[wagered]
flat red: −0.0270 × $12,500 = −$337.84
c9 cash-out: −0.0270 × $1,961.68 = −$53.02