Bankroll Management & Survival Time

The Law of Large Numbers

The Law of Large Numbers (LLN) states that as the number of trials increases, the average result converges to the theoretical expected value. In gambling terms: the more you play, the closer your loss percentage gets to the house edge.

This is the mechanism that guarantees casino profitability. Short-term variance can produce winners, but over millions of bets the house edge is mathematically certain to collect its share.

How to Use the Law of Large Numbers Simulator

1. 1.Set the win probability and payouts. Match these to a real game — European roulette red/black, blackjack, or any even-money bet you are curious about.
2. 2.Run the simulation. The chart shows each trial alongside the running average return per bet. Watch as the line — chaotic at first — gradually straightens and flattens toward the expected value.
3. 3.Run multiple simulations. Each run follows a different random path but all eventually converge to the same destination. The path varies; the endpoint does not.

Bankroll Survival: How Long Will Your Money Last?

The Bankroll Survival simulator answers a specific question: given a starting bankroll, a fixed bet size, and a known house edge, how many bets can you typically play before going broke?

This is not a strategy guide — it is a reality check. The results consistently show that bankrolls deplete faster than most players expect, especially at common house edges.

How to Use the Bankroll Survival Simulator

1. 1.Enter your starting bankroll. The total amount available for the session.
2. 2.Enter your bet size. A fixed amount per round. Notice how halving your bet roughly doubles survival time — but also doubles the time it takes to win or lose the same amount.
3. 3.Enter the house edge. Use the actual figure for your game. Even seemingly small differences (0.5% vs 2.7%) produce dramatically different survival times.
4. 4.Run multiple simulations. The simulator runs thousands of random sessions and shows the distribution of survival times. Look at the median and the worst-case percentiles — not just the average.
5. 5.Convert bets to hours. If a typical casino game runs ~50 rounds per hour, 700 bets is about 14 hours of play. Use this to understand real-world session limits.

Practical Takeaways

• •Bet sizing matters for session length, not for outcomes. Smaller bets extend play time but cannot change expected losses.
• •Game choice matters for survival time. Blackjack with basic strategy lasts far longer than slots at the same bet size, because the house edge is 10–30× smaller.
• •The LLN is inevitable. Given enough time, all gamblers converge to the expected loss. The only winning strategy is to stop while variance is in your favor — which requires knowing when to walk away.