Measuring drawdown and probability of ruin
A worked methodology for peak-to-trough drawdown, finite-horizon ruin estimates, and Wilson confidence intervals using 25,000 fixed-seed sessions.
Profit and loss at the final spin hides the route taken to get there. This study defines the risk measures used throughout 0xRoulette, applies them to 25,000 fixed-seed sessions per bankroll, and publishes confidence intervals instead of treating a simulation percentage as exact.
Definitions
For equity values E₀…Eₜ, the running peak at time t isMₜ = max(E₀…Eₜ). Drawdown is Dₜ = Mₜ − Eₜ; maximum drawdown is the largest Dₜ in the session. Ruin means the bankroll reached zero before the scheduled 500th spin. We estimate finite-horizon ruin as ruined sessions divided by all sessions, then attach a Wilson score interval for the unknown probability.
- Master seed
0x6d2ba4ff- Wheel / bet
- European / $10 red
- Starting bankrolls
- $100, $250, $500, $1,000
- Shared schedule
- The same 25,000 seeds at every bankroll level
Ruin depends on bankroll relative to the wager
| Bankroll | Units | Ruin estimate | 95% interval | Median max DD | P90 max DD |
|---|---|---|---|---|---|
| $100 | 10 | 81.740% | 81.256%–82.214% | $150 | $250 |
| $250 | 25 | 46.768% | 46.150%–47.387% | $270 | $350 |
| $500 | 50 | 8.440% | 8.102%–8.791% | $310 | $510 |
| $1,000 | 100 | 0.028% | 0.014%–0.058% | $310 | $530 |
Reading drawdown correctly
Maximum drawdown can exceed the initial bankroll. A session might first rise above its starting value, establish a higher peak, and then fall to zero. That peak-to-trough move is larger than the starting cash. Drawdown also says nothing about recovery time unless that is measured separately. Two paths can share a maximum drawdown and reach it at very different speeds.
The 100-unit bankroll produced only 7 ruins in 25,000 trials, so the estimate is 0.028% but the interval remains wider than the point estimate. Reporting all three numbers prevents false precision.
Limitations
Ruin here is finite-horizon: it asks what happened within 500 spins. Over an unlimited horizon, a negative-drift game answers a harsher question. Wilson intervals quantify Monte Carlo sampling error, not model error. They do not account for wheel bias, changing wagers, correlated outcomes, or a mismatch between simulated rules and a real table.