Bet a fixed stake over and over until you hit a target or go broke: with no edgeEdge = (win probability − loss probability) × 100. A zero edge is a fair coin-flip; negative edge means the house wins more often than you do. Even a tiny negative edge compounds relentlessly over many rounds. the smaller bankroll usually loses, and with a negative edge ruin becomes near-certain the longer you play. The gambler's ruinA classic probability problem: two players with finite bankrolls bet against each other until one is ruined. The formula for ruin probability dates to Huygens and Pascal and underpins every result in gambling mathematics. formula tells you exactly how likely that is.
Before reaching €500. Even a near-fair 49% bet ruins you 80.8% of the time at this stake; expect about 521 rounds either way.
The curve plunges through the fair-game point at 50% — at exactly even odds the ruin probability is 60% (the opponent's share of the pot), meaning the bigger bankroll wins more often simply because it has more room to absorb bad runs. Drift left into negative territory and ruin trends toward certainty as the target or round count grows. Counterintuitively, betting smaller with a negative edge makes ruin more likely — more rounds means more chances for the house cut to compound.
| Target | P(ruin) | P(reach) |
|---|---|---|
| €3001.5× | 47.2% | 52.8% |
| €4002×current | 69% | 31% |
| €6003× | 87.8% | 12.2% |
| €1k5× | 97.7% | 2.3% |
| €2k10× | 100% | 0% |
Every step up in target makes ruin more likely — you need more rounds to get there, and each one gives the edge another chance to grind you down. Greed is a tail-risk amplifier: doubling your ambition more than doubles your chance of going broke.