Complete probability analysis • Always prefer European wheel
{
"european": {
"slots": 37,
"zeros": [0],
"house_edge": 0.027,
"recommendation": "PREFER"
},
"american": {
"slots": 38,
"zeros": [0, "00"],
"house_edge": 0.0526,
"recommendation": "AVOID"
}
}| Bet Type | Numbers Covered | Payout | Probability | House Edge |
|---|---|---|---|---|
| Straight (single number) | 1 | 35:1 | 2.70% | 2.70% |
| Split (2 numbers) | 2 | 17:1 | 5.41% | 2.70% |
| Street (3 numbers) | 3 | 11:1 | 8.11% | 2.70% |
| Corner (4 numbers) | 4 | 8:1 | 10.81% | 2.70% |
| Six Line (6 numbers) | 6 | 5:1 | 16.22% | 2.70% |
| Dozen (12 numbers) | 12 | 2:1 | 32.43% | 2.70% |
| Column (12 numbers) | 12 | 2:1 | 32.43% | 2.70% |
| Red/Black | 18 | 1:1 | 48.65% | 2.70% |
| Odd/Even | 18 | 1:1 | 48.65% | 2.70% |
| High/Low (1-18/19-36) | 18 | 1:1 | 48.65% | 2.70% |
{
"key_fact": "All bets have identical house edge on the same wheel",
"implication": "No betting pattern or combination reduces the house edge",
"systems_debunked": [
"Martingale",
"Fibonacci",
"D'Alembert",
"Labouchere"
],
"why_systems_fail": "Expected value is negative regardless of bet sizing. Increasing bets after losses just increases variance and risk of ruin."
}// European Wheel (37 slots)
P(win) = numbers_covered / 37
// Expected Value calculation
EV = (P(win) × payout) - (P(lose) × 1)
EV = (1/37 × 35) - (36/37 × 1)
EV = 0.9459 - 0.9730
EV = -0.027 // -2.7% house edge
// American Wheel (38 slots)
EV = (1/38 × 35) - (37/38 × 1)
EV = -0.0526 // -5.26% house edge{
"la_partage": {
"description": "Get half back on even-money bets when ball lands on zero",
"house_edge": 0.0135,
"available": "Some European casinos"
},
"en_prison": {
"description": "Even-money bet 'imprisoned' on zero, wins if next spin hits",
"house_edge": 0.0135,
"available": "Some European casinos"
}
}{
"strategy": [
"1. Always play European wheel over American",
"2. Seek La Partage or En Prison rules if available",
"3. All bets are equivalent - choose based on variance preference",
"4. Set loss limits and stick to them",
"5. Accept that no strategy beats the house edge long-term"
],
"for_agents": "Roulette has negative expected value. Not suitable for profit-seeking automated betting."
}