Risk of ruin: how likely you are to go broke
Risk of ruin is the chance that a run of losses wipes out your whole bankroll. It depends on your edge and how many bets your bankroll can cover. With a house edge and no stop point, ruin is certain in the long run.
Reviewed Oct 15, 2026
Answer first
90s- 01More units in your bankroll means lower risk.
- 02A small edge cuts risk sharply as units grow.
- 03With a negative edge, ruin is only a matter of time.
Key numbers
Risk of ruin examples
In short
Key takeaways
- Bet size matters as much as edge.
- Units are your bankroll divided by your bet.
- Even good bettors face real ruin risk with small bankrolls.
- Lowering bet size is the simplest fix.
Progress
What drives risk of ruin
- 1
Win chance
p
- 2
Loss chance
q = 1 − p
- 3
Units
Bankroll ÷ bet
- 4
Ratio
q ÷ p
- 5
Risk
Ratio to the power of units
For even-money bets and no target amount.
Risk of ruin, even-money bets
| Units | 52% win rate | 55% win rate |
|---|---|---|
| 10 | 44.9% | 13.4% |
| 20 | 20.2% | 1.8% |
| 50 | 1.8% | Under 0.01% |
| 100 | 0.03% | Near zero |
Our own calculation with (q ÷ p) to the power of units.
How the formula works
For bets that pay even money, if you win with chance p and lose with chance q, and you never stop, the chance of losing N units before you reach your target is (q ÷ p) to the power of N. At 52% wins, q ÷ p is 0.923.
With 20 units, 0.923 to the 20th power is about 0.20, so one bettor in five goes broke despite a real edge. With 50 units it drops to about 1.8%. Doubling or tripling units has a huge effect.
The formula assumes flat bets. Raising bets after wins or losses changes the numbers, often for the worse.
Same bankroll, different bet sizes (52% win rate)
| Bankroll | Bet | Units | Risk of ruin |
|---|---|---|---|
| $1,000 | $100 | 10 | 44.9% |
| $1,000 | $50 | 20 | 20.2% |
| $1,000 | $20 | 50 | 1.8% |
| $1,000 | $10 | 100 | 0.03% |
Our own sums.
Why a house edge ends at zero
If p is below q, the ratio q ÷ p is above 1. Raised to any power it stays at or above 1, which means ruin is certain over an endless session. Slots, roulette and most bets at fair sportsbook prices fall here.
In practice players stop before the end. They set a loss limit or a goal, and the real question becomes how often they hit the limit first. With a house edge that chance is always above half for an equal win goal.
For example, at 47.4% wins on red in American roulette, a player chasing 10 units of profit before losing 10 units succeeds only about 26% of the time.
Sequence
Lowering your risk
Step 01
Count your units
Bankroll ÷ bet.
Step 02
Know your edge
Use real records.
Step 03
Cut bet size
More units, less risk.
Step 04
Set a stop
A loss limit per session.
Step 05
Review often
Resize as the bankroll moves.
Risk of ruin and bettors
Sports bettors at -110 need over 52.4% just to break even, so a 54% bettor has a small edge per bet. Many use 1% to 2% units, or 50 to 100 units, to keep ruin risk low through cold streaks.
Poker players use a similar idea for buy-ins. A cash game player might keep 20 to 40 buy-ins, and tournament players often far more, because their results swing more.
Ruin is not only about money. Chasing losses with bigger bets raises risk fast. If gambling stops being fun, free help is available at 1-800-GAMBLER.
Floor rules
Ruin terms
Know before you sit
- Risk of ruin
- Chance of losing the whole bankroll.
- Unit
- One standard bet size.
- Edge
- Your expected profit per bet.
- Bankroll
- Money set aside only for betting.
Common mistakes
- Betting too large
- Few units means high risk.
- Assuming an edge
- Many bettors have none.
- Chasing losses
- Bigger bets raise risk.
- Ignoring variance
- Streaks are normal.
Keep reading
Related pages
Go play
Where to play in Las Vegas
Tap a resort — each row opens that casino’s White Gambling page (hours, game mix, floor facts). Venues with this game in official counts, sorted high to low.
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Questions before and after you play
A 90-second guide cannot cover every table moment. Tap a group, then a question — answers are short paragraphs, not one-liners.
01Basics
What is risk of ruin?
The chance that losses use up your whole bankroll before you stop or reach a goal.
What is the formula?
For even-money flat bets with no goal, (q ÷ p) to the power of N, where N is your bankroll in units.
Does a house edge mean certain ruin?
Over an endless session, yes. In real play you stop sooner, but losing is more likely than winning.
02Numbers
How many units do I need?
At a 52% win rate, 50 units gives about 1.8% risk, while 20 units gives about 20%.
Why does bet size matter so much?
Smaller bets give more units, and risk falls very fast as units grow. Rules differ between licensed sportsbooks, so read the house rules.
Does a better win rate help?
A lot. At 55% wins, 20 units carries only about 1.8% risk. Rules differ between licensed sportsbooks, so read the house rules.
03Practice
Do poker players use risk of ruin?
Yes. They keep many buy-ins, often 20 to 40 for cash games, to survive swings. Rules differ between licensed sportsbooks, so read the house rules.
Is progressive betting safer?
No. Raising bets after losses usually raises risk of ruin. Rules differ between licensed sportsbooks, so read the house rules.
Where can I get help?
If betting is a problem, call or text 1-800-GAMBLER for free, private help. Rules differ between licensed sportsbooks, so read the house rules.
Sources
- Wikipedia — Gambler’s ruin Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Ruin probability formulas
- Wikipedia — Kelly criterion Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Bet sizing and growth
- Wizard of Odds — Sports betting Not from a registry (Reference source, not an official registry)The gaming industry’s standard reference for casino-game math, by actuary Michael Shackleford. Not an official registry; our calculators compute these numbers independently. · accessed Oct 15, 2026Sports betting math
- National Council on Problem Gambling — Help and resources Not from a registry (Reference source, not an official registry) · accessed Oct 15, 2026Free, confidential help: call or text 1-800-GAMBLER