Casino Calculator

Risk of Ruin Calculator

Enter a win probability, a bankroll and a win goal. The calculator shows the chance that a flat bettor loses the whole bankroll before getting that far ahead, the chance of reaching the goal, and how many bets it takes on average.

Game / betWins 18 of 37 spins (48.65%), pays 1 to 1Bankroll (units)How many bets your bankroll covers. $500 at $10 a bet is 50 units.Win goal (units)You stop as soon as you are this many units ahead.

Risk of ruin75.43%Bankroll gone before the goal

Reach the goal24.57%Bankroll grows to 75 units

Average length1,168 betsUntil ruin or goal

Win probability48.65%Pays 1 to 1

How to Use the Calculator

1Pick a game. Roulette red/black and the two main baccarat bets fill in the win probability for you. “Custom win probability” lets you enter any even-money bet, including one with a player edge.
2Enter your bankroll in units, meaning how many flat bets it covers. A $500 bankroll at $10 a bet is 50 units; $2,000 at $25 a bet is 80 units.
3Enter your win goal in units: the profit at which you would walk away. A goal of 25 units at $10 a bet means stopping once you are $250 ahead.
4Read the results: the risk of ruin, the chance of reaching the goal (the two add up to 100%), and the average number of bets before one of them happens.

The formula: gambler's ruin

r = q ÷ p, N = bankroll + goal (in units)
P(reach goal) = (1 − r^bankroll) ÷ (1 − r^N)
Risk of ruin = 1 − P(reach goal) (when p = ½: goal ÷ N)
Average bets = bankroll ÷ (q − p) − N ÷ (q − p) × P(reach goal)

Each bet either wins 1 unit or loses 1 unit. Play continues until the bankroll hits zero or reaches the bankroll plus the goal. p is the chance of winning a single bet and q = 1 − p is the chance of losing it. This is the classic gambler's ruin problem, and for an even-money bet the answer has an exact closed form.

Baccarat Banker needs special handling. Ignoring ties, Banker wins about 50.68% of hands, so plugging that into the formula would make it look like a winning bet. But a winning Banker bet pays only 0.95 units after the 5% commission. For Banker the calculator therefore models “win 0.95 units, lose 1 unit”, splits the bankroll into 1/20-unit steps, and solves the resulting system of equations exactly. You are counted as ruined once you can no longer cover a 1-unit bet.

A tie in baccarat returns your stake and leaves the bankroll unchanged, so the baccarat presets use win probabilities with ties removed. The average number of bets for those presets also excludes ties.

Worked Examples

Doubling $500 at European roulette

You bring $500 and bet $50 on red each spin, so the bankroll is 10 units and doubling it is a goal of 10 units. The risk of ruin is 63.2%: you will reach $1,000 only 36.8% of the time. On average the session lasts about 98 spins.

Same money, smaller bets

Now bet $10 a spin toward the same $500 profit: 50 units of bankroll and a goal of 50 units. Smaller bets feel safer, but the risk of ruin rises to 93.7%. With a negative-edge bet, the longer the house edge has to work, the less likely you are to reach a fixed target.

A modest goal with a deep bankroll

With 100 units and a goal of only 10 units at European red, the risk of ruin is 41.9%. Even with an unlimited bankroll it could never drop below 41.8% for that goal, because (18/19)^10 ≈ 58.2% is the best possible chance of ever getting 10 units ahead.

Reference Tables

Risk of ruin by bankroll and win goal
Bankroll → goal	European	American	Banker
10 → +5	42.6%	51.6%	40.7%
10 → +10	63.2%	74.1%	58.4%
20 → +10	52.0%	68.0%	43.4%
20 → +20	74.7%	89.2%	63.1%
50 → +10	43.5%	65.2%	29.3%
50 → +25	75.4%	92.9%	55.2%
50 → +50	93.7%	99.5%	77.7%
100 → +10	41.9%	65.1%	24.2%
100 → +50	93.3%	99.5%	72.9%
100 → +100	99.6%	>99.9%	92.2%
200 → +20	66.1%	87.8%	39.7%
200 → +100	99.6%	>99.9%	91.6%

Bankroll and goal are in units (one unit = one flat bet). European and American are red/black at roulette (wins 18/37 and 18/38, pays 1 to 1). Banker is the baccarat Banker bet: it wins about 50.68% of non-tie hands but pays 0.95 units after the 5% commission. Each figure is the chance of losing the bankroll before getting the goal ahead, betting 1 unit at a time.

What the Calculator Does Not Cover

—It assumes flat betting: the same 1-unit stake every time. Progressions such as the Martingale or D'Alembert change the bet size, so their ruin risk is different (and usually higher for a given target).
—It assumes you stop at the goal. Without a stopping point, a bet with a house edge loses the whole bankroll with probability approaching 100% if play continues long enough, whatever the bankroll.
—Each bet is treated as independent with a fixed win probability. That fits roulette and is a close approximation for baccarat dealt from a deep shoe. It does not model card counting, table maximums or changing bet sizes.
—The results are probabilities over many sessions, not a forecast of your next one.

Frequently Asked Questions

What does risk of ruin mean in gambling?

Risk of ruin is the probability of losing your entire bankroll before you reach a set profit target. This calculator assumes you bet the same amount every time and quit as soon as you reach the target or run out of money.

What are the odds of doubling my money on red at roulette?

Betting 1 unit at a time at European roulette, turning 10 units into 20 succeeds 36.8% of the time (a 63.2% risk of ruin). Turning 50 units into 100 with smaller bets succeeds only 6.3% of the time. The more bets it takes to reach the target, the more the house edge wears you down.

Does a bigger bankroll lower my risk of ruin?

Only if the goal stays small, and only down to a floor. At European red with a 10-unit goal, the risk of ruin is 52.0% with a 20-unit bankroll and 41.9% with 100 units, but it can never fall below 41.8% however much money you bring. Without a goal, a bet with a house edge leads to ruin with near certainty in the long run.

Why is baccarat Banker not a winning bet if it wins more than half the time?

Ignoring ties, Banker wins about 50.68% of hands, but a win pays only 0.95 units after the 5% commission while a loss costs a full unit, so each bet has a negative expected value. With the commission included, a 50-unit bankroll aiming for a 50-unit profit has a 77.7% risk of ruin.

Is American roulette much worse than European roulette for risk of ruin?

Yes. The extra 00 pocket lowers the chance of winning red/black from 48.65% to 47.37%. With 20 units aiming for a 20-unit profit, the risk of ruin is 74.7% at a European wheel and 89.2% at an American wheel.

Can I use this for poker or card counting?

You can enter a custom win probability above 50% to see how a player edge changes the picture. Poker and card counting have uneven payouts and changing bet sizes, though, so serious bankroll planning for them uses the approximation based on win rate and standard deviation explained in our risk of ruin guide.

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