Beyond red: grow at the right rate (Martingale on dozens and inside bets)
Off even money, doubling is the wrong raise: multiply each bet by 36 ÷ (36 − numbers covered), which is ×1.5 on a dozen, and the ladder lasts as long as the formula says.
Chapter 4 of the spinner roulette research (chapters 0 to 9): Beyond red: grow at the right rate.
“Only even money works” is about the size of the raise, not the numbers. A dozen pays 2 to 1, so doubling after a loss wins back more than needed and uses up the ladder in 7 bets: the typical session is ahead only until spin 70. Raising by half instead (×1.5) fits 11 bets and holds until spin 150, as the formula predicts. Two dozens, six-lines, corners and runs of single numbers behave the same way.
But at $25 a spin from $5,000 no placement stays ahead to spin 500. A $5 base on a dozen (15 bets) does: typical +$1,611, average −$345.44, 16.4 % bust.
Open this chapter in spinner, with the interactive chartsTest your own system
The numbers
| Placement | Growth factor | Right factor (spins ahead) | Doubling (spins ahead) | Predicted n½ (spins) | Average, right factor |
|---|---|---|---|---|---|
| Dozen | ×1.5 | 150 | 70 | 159 | -$566.78 |
| Dozen, $5 base | ×1.5 | 500+ | 70 | 765 | -$311.20 |
| Two dozens | ×3 | 200 | 220 | 200 | -$613.50 |
| Six-line | ×1.2 | 140 | 9 | 147 | -$486.93 |
| Corner | ×1.13 | 130 | never | 141 | -$466.35 |
| 25 numbers | ×3.27 | 280 | 130 | 286 | -$877.20 |
| 35 numbers | ×36 | 240 | 12 | 251 | -$719.48 |
Takeaways
- Use the right raise for the bet: ×2 for 18 numbers, ×1.5 for 12, ×3 for 24, ×1.2 for 6.
- With the right raise every placement reaches its predicted horizon; with doubling, the dozen, six-line and corner collapse within 70 spins.
- Even with the right raise, base stakes decide: the dozen needed a $5 base to stay ahead for 500 spins.
The math
A layout covering c numbers pays m = (36 − c)/c. To recover the deficit D plus the level-0 profit τ, the next stake s must satisfy s·m ≥ D + τ. Each lost stake adds to D, so s(k+1) = s(k)·(1 + 1/m) = g·s(k) with g = 36/(36 − c). The table and the bankroll set the levels: L ≈ ln(max/min) / ln g.
Dozen (c = 12, p = 0.324): doubling fits L = 7, q = (25/37)^7 = 0.0643, n½ = 33; measured median ahead until 70 (a flat, noisy crossing). g = 1.5 fits L = 11, q = 0.0134, n½ = 159; the onCap-stop twin is ahead until 150. At equal bankroll the horizon ranks by B/(m·p), so wider coverage holds longer: predicted n½ 286 (25 straight-ups), 200 (two dozens), 159 (dozen), 147 (six-line), 141 (corner); measured 280, 200, 150, 140, 130. The $5-base dozen: L = 15, q = 0.0028, n½ = 765, median $1,611, mean −$345.44, CVaR 5 % −$5,000.
g = 36 / (36 − c)
s(k+1) = g × s(k)
q = (1 − c/37)^L
n½ = ln 2 / (q × c/37)