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Time to Ruin Distribution

If you play a game with a negative expected value long enough, going broke is not an “if,” but a “when” (our guide to the mathematics of Risk of Ruin explains why this boundary is absorbing). This Time to Ruin Calculator uses Monte Carlo simulation to estimate your survival lifespan, showing the median and range of hours your bankroll will last (use our general Bankroll Calculator to check your starting unit bounds).

Time to Ruin — Distribution

Probability of ruin is one number; WHEN it tends to happen is another. This tool shows the timing.

P(ruin within horizon)
Median time to ruin
Mean time to ruin
25th percentile
75th percentile

The “when” instead of the “if”

Standard risk models calculate your Risk of Ruin—the overall probability that you will eventually go broke. However, for casual players and recreational gamblers, this is only half the puzzle. If you know you have a 100% chance of eventually losing your bankroll, your primary concern is: **how long can I play before that happens?**

By modeling your bankroll as a random walk with an absorbing barrier at zero, this tool simulates thousands of gaming sessions to plot the exact probability distribution of your survival time. It reveals how many hands, spins, or hours you can expect to enjoy your capital before hitting zero.

The Volatility Lifeline: In survival math, volatility cuts both ways. High volatility can cause you to go broke incredibly quickly, but it also provides the only opportunity to hit a massive upswing that extends your playing time. Low volatility ensures a slow, predictable, and steady slide into ruin.

The math of survival time distributions

Because your bankroll’s path is path-dependent, solving for the exact distribution of survival time analytically is extremely complex. This tool uses a Monte Carlo simulation engine to track your bankroll until it hits zero:

1. Tracking the path

For each simulated session, the engine begins at $B$ (your starting bankroll) and adds random outcomes until your balance hits zero:

Bankroll_t = Bankroll_{t-1} + Outcome_t
Stop when Bankroll_t ≤ 0

The step count at termination is recorded as the session’s “Time to Ruin” ($T_{ruin}$).

2. Analyzing the distribution

The resulting dataset of survival times is highly right-skewed. A small number of sessions will hit massive hot streaks and last for tens of thousands of rounds, pulling the average (mean) upward, while most sessions end quickly. To get an accurate picture, we analyze:

  • Median Survival Time (P50): The point at which exactly 50% of your sessions have ended in ruin. This is your most realistic expectation.
  • Interquartile Range (IQR): The range between the 25th percentile (unlucky fast ruin) and the 75th percentile (lucky extended play).

Data Sandwich: $500 on Slots vs. Blackjack

Let’s audit a $500 starting bankroll, betting $5 per round at 200 rounds per hour:

Game A: High-Volatility Slot (4.00% Edge, 4.0 SD)

  • Expected Median Survival: ~2.5 hours
  • 25th Percentile: 45 minutes (ruined extremely fast due to bad variance)
  • 75th Percentile: ~6 hours (lucky jackpot extensions)

Game B: Blackjack Basic Strategy (0.50% Edge, 1.15 SD)

  • Expected Median Survival: ~24 hours
  • 25th Percentile: ~12 hours
  • 75th Percentile: ~48 hours

This demonstrates the massive difference. On the slot, you have a high probability of going broke in under an hour, whereas blackjack’s low house edge and low volatility almost guarantee you multiple sessions of entertainment.

Frequently asked questions

Why is the median survival time more accurate than the mean?

Because the distribution of survival times has a long right-tail. A few lucky simulations will hit huge winning streaks and last for millions of rounds, which distorts the “mean” (average) upward, making it look like you will play longer than you actually will. The median represents the true middle ground.

How can I extend my median time to ruin?

You can extend your survival by choosing games with a lower house edge, decreasing your bet size relative to your bankroll, slowing down your rate of play, or selecting low-volatility games that prevent massive, sudden drops.

What does an “absorbing zero” mean?

In probability models, an absorbing barrier is a state that, once entered, cannot be left. In gambling, your bankroll at zero is the ultimate absorbing barrier: you cannot place any more wagers, meaning the session is permanently terminated.