Cash out: the stop that moves the typical session
Decide before you sit down how much profit you will walk away with: a modest target is reached most of the time, and a stop-loss at half the ladder limits the damage when it is not.
Chapter 7 of the spinner roulette research (chapters 0 to 9): Cash out: the stop that moves the typical session.
A cash-out ends the session the moment you are up the target, so the typical session is the target, a few dollars over. The lower the target, the more often you reach it before losing the ladder: c9 reaches $70 in 98.2 % of sessions, $280 in 93.2 % and $1,400 in 70.4 %.
A stop-loss at half the ladder ($2,459.50) costs three points of that chance (90.3 %) but cuts the worst 5 % from −$4,820 to −$3,210. Its sibling c8 with a $200 target and no stop-loss gets there more often (94.5 %) but keeps a worst 5 % of −$4,515. On Martingale red a half-ladder stop-loss never fires; stopping after seven losses does.
Open this chapter in spinner, with the interactive chartsTest your own system
The numbers
| Target | Measured | Predicted (1 − q)^W | Typical session | Average |
|---|---|---|---|---|
| 5 wins | 98.2% | 98.2% | +$77 | -$11.38 |
| 10 wins | 96.5% | 96.5% | +$146 | -$27.46 |
| 20 wins | 93.2% | 93.1% | +$286 | -$56.21 |
| 50 wins | 83.9% | 83.7% | +$705 | -$142.92 |
| 100 wins | 70.4% | 70.0% | +$1,404 | -$268.52 |
| Version | Chance of ending ahead | Worst 5 % of sessions | Average |
|---|---|---|---|
| c9, no cash-out | 67.1% | -$4,820.13 | -$295.45 |
| c9, cash out at 20 wins | 93.2% | -$4,820.13 | -$56.21 |
| c9, 20 wins + stop-loss | 90.3% | -$3,210.44 | -$46.25 |
| Martingale, 8 levels, cash out at 20 wins | 88.8% | -$5,000 | -$113.80 |
| Martingale, 7 levels + stop | 83.0% | -$3,119.20 | -$87.03 |
Takeaways
- The typical session equals your target as long as more than half of sessions reach it.
- Higher targets are reached less often, and the average loss grows with the time you play.
- Pair the cash-out with a stop-loss sized to the ladder, not to the bankroll.
The math
With a stop-win of W cycle profits a session ends ahead if it collects W cycles before a cap: P(win) ≈ (1 − q)^W ≈ e^(−q·W). c9, q = 0.00356: W = 5, 10, 20, 50, 100 predicts 0.982, 0.965, 0.931, 0.837, 0.700; measured 0.982, 0.965, 0.932, 0.839, 0.704. The median equals the target while P(win) > ½, that is while q·W < ln 2. The mean stays at −2.70 % of a smaller turnover: c9 at W20 wagers $2,157, mean −$56.21.
The half-ladder stop-loss is checked after the round, so it overshoots by one level: CVaR 5 % −$3,210, worst session −$3,275. Martingale red at W20: e^(−q·W) predicts 0.908, measured 0.888, because after seven losses (−$3,175) the eighth $3,200 bet does not fit the remaining $1,825 and is cut. A 7-loss stop (maxSteps 7, onCap stop): q = (19/37)^7 = 0.0094, (1 − q)^20 = 0.828, measured 0.830, CVaR 5 % −$3,119, bust 0.
P(win) ≈ (1 − q)^W
c9 at W = 20: (1 − 0.00356)^20 = 0.931
median = target while q·W < ln 2