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What is risk of ruin?

Article updated: Portrait of KirillKirill

In games with a house edge, if you play long enough without a stop, the risk of ruin approaches 100%. What you control is how fast: three things push it up.

  1. Bet size relative to bankroll. Betting 10% of your bankroll per bet busts far more often than betting 1%.
  2. Variance. High-risk settings mean long losing stretches between hits.
  3. Progressive systems. Martingale-style doubling makes bets grow until one streak takes the whole bankroll.

Example. Dice at 2× with 49.5% to win, Martingale from 1 unit with a 127-unit bankroll: about a 57% chance of being wiped out within 200 bets, and about 99% within 1,000 bets. The same bankroll with flat 1-unit bets loses about 10 units on average over 1,000 bets and almost never hits zero.

In ProvablyHero tools

The simulator shows the share of sessions that went bust for any settings.

  • What is the Martingale system?Martingale doubles your bet after every loss. Why it wins small most of the time, how a losing streak wipes it out, and the exact odds with an example.
  • What is drawdown?Drawdown is how far your bankroll falls from its highest point. How to read median and max drawdown, with a worked example from a betting session.
  • What is variance?Variance measures how widely results spread around the average. Why high-risk Plinko swings harder, how it relates to RTP, and how to see it in a simulator.
  • Median vs mean: which "average" should you trust?Why the median session result is usually below the average in casino games, how a few big wins distort the mean, and which number to trust.