EdgeLV
Risk-of-ruin calculator
Sit down with a bankroll — what is the chance you bust before you walk away? Ten thousand Monte Carlo runs at the real payouts and commission.
Calculating…
View as a table
| Ending range | Runs | Share |
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Method
Where these numbers come from
Real payouts, hand by hand
Banker: wins 45.86% paying 0.95 (after the 5% commission), loses 44.62%, ties 9.52% and pushes. Player: wins 44.62% paying 1.00, loses 45.86%, ties push.
Why simulate instead of using a formula
The classic gambler’s-ruin formula assumes every result is ±1 unit. Banker pays only 0.95 and ties push, so the payouts are asymmetric and the formula gives the wrong answer. Simulation handles it exactly.
What counts as ruin
Not being able to place another bet. That is closer to reality than "bankroll hits zero": with 200 left and a 500 unit, you are already done.
Results move slightly
Ten thousand runs carry roughly ±0.5 percentage points of sampling error, so each run differs a little. That is inherent to the method, not a bug.
How to read it
A bankroll is a ratio, not an amount
What counts is units, not currency
Sitting down with 10,000 and betting 500 a hand carries exactly the same risk of ruin as sitting down with 1,000 and betting 50. Both are 20 units. The amount on its own means nothing; bankroll divided by unit size means everything. That is why the rows below are labelled in units — the table holds for any currency and any stake.
Ruin rises with hands played, and it rises fast
Twenty units over 100 hands busts 4.4% of the time, which sounds safe. The same bankroll over 1,000 hands busts 62.7% of the time. The cards did not get worse. Every extra hand is one more chance for variance to push you to zero, while the expected loss grinds steadily downward underneath. Time is on the house’s side twice over.
Not busting is not the same as not losing
A hundred units over 500 hands busts 0.0% of the time — it simply never happened. In that same calculation, only 40.1% of sessions end above where they started. A deep bankroll does not buy you a profit; it buys you the right to lose slowly. As the ruin probability goes to zero, the probability of finishing down approaches six in ten. The two numbers have to be read together.
| Bankroll | 100 hands | 300 hands | 500 hands | 1,000 hands |
|---|---|---|---|---|
| 10 units | 34.5% | 62.0% | 72.1% | 82.7% |
| 20 units | 4.4% | 28.4% | 43.5% | 62.7% |
| 40 units | 0.0% | 2.2% | 9.1% | 27.8% |
| 100 units | 0.0% | 0.0% | 0.0% | 0.2% |
Ruin is defined as "cannot cover another bet", not "balance reached zero" — with 200 left and a 500 unit, you are already done. A shoe produces roughly 74 decided hands, so 500 hands is about seven shoes, or one evening.
Frequently asked
- How many units should a bankroll be?
- It depends entirely on how long you play. Over 100 hands, 40 units almost never busts (0.0%). Over 1,000 hands, those same 40 units bust 27.8% of the time, and holding ruin below 1% takes around 100 units. There is no universal number — risk of ruin is a function of two variables, bankroll and hands.
- Does this use the classic gambler’s-ruin formula?
- No. The classic formula assumes every result is ±1 unit, but a winning banker bet pays 0.95 and a tie returns the stake, so the payouts are asymmetric and the formula gives the wrong answer. This table comes from an exact dynamic program on a grid of 1/20 of a unit, propagating the full distribution hand by hand, with no sampling error.
- Does betting smaller reduce the risk of ruin?
- Yes, substantially — halving your unit doubles your bankroll in units and ruin falls sharply. The trade is that you also put half as much money through the table in the same time, so the expected loss halves too. What you buy is a longer game, not a better one.
- Four in ten sessions finish ahead — doesn’t that mean short runs can win?
- Short runs can absolutely win; that is why casinos exist. But the figure falls monotonically with hands played: 44.7% at 100 hands, 35.8% at 1,000. And it only asks whether you finished ahead, not by how much. The average result is negative in every cell of the table.