How long does a bankroll survive?
Set a bankroll, a bet, a win chance and a strategy. Every number below updates as you change them. Nothing here is a prediction — it is what the mathematics of the scenario implies.
Current game: an abstract betting round — each round wins with probability 49.00%, paying 1 to 1. This is not any real casino game; to try one, pick a preset above, such as baccarat.
Drag this first. It changes the conclusion more than anything else on the page.
Advanced — win chance, payout, push, table limits, seed
Rounds are capped at 100,000.
72.5% of sessions finish ahead — typically by $245.
27.2% run out of bankroll or can no longer place the next required bet, typically down $871.
Across all 50,000 simulated sessions the expectation is −$48.
Estimated from 50,000 simulated sessions and still converging. Figures carry a margin of error that narrows as the run completes.
Expected versus typical
- Expected ending bankroll
- $952
- Typical ending bankroll
- $1,239
The average across every simulated session (−$48).
What the middle session experienced ($239).
These differ because the distribution is lopsided. The average is pulled by outcomes that occur rarely; the median describes the session in the middle.
Outcomes
- Finish ahead
- 72.5%
- Finish behind
- 27.5%
- Bankroll exhausted
- 0.1%
- Strategy could not continue
- 27.1%
Could not place even the minimum bet.
The next required bet exceeded the bankroll or the table maximum, with money still left.
Full detail — percentiles, risk metrics, and the exact figures
Distribution of ending bankroll
- P1
- $8
- P5
- $44
- P25
- $502
- P50
- $1,239
- P75
- $1,249
- P95
- $1,261
- P99
- $1,270
Risk
- Average largest bet
- $307
- Median maximum drawdown
- $255
- Average longest losing streak
- 8
- Average total wagered
- $2,244
Exact figures
Computed in closed form. No simulation, no margin of error.
- Expected loss per $100 wagered
- $2
- Fair payout for this win chance
- 1.0408 to 1
- Break-even win chance at this payout
- 50.00%
- Chance the next 10 resolved rounds all lose
- 0.12%
- Chance of at least one 10-loss streak within 500 rounds
- 25.08%
- Typical longest losing streak
- 8
A different question from the one above, and a much larger number.
95th percentile: 12.
Worked example
Starting with $1,000, betting $1 at a 49.00% win chance and doubling after every loss, over 500 rounds, simulated many times:
| Expected ending bankroll | $952 |
|---|---|
| Typical (median) ending bankroll | $1,239 |
| Chance of finishing ahead | 72.5% |
| Chance the strategy cannot continue | 27.1% |
| Expected loss per $100 wagered | $2 |
| Typical longest losing streak | 8 |
72.5% of sessions finish ahead — typically by $245.
27.2% run out of bankroll or can no longer place the next required bet, typically down $871.
Across all 50,000 simulated sessions the expectation is −$48.
Questions
How long will my bankroll last?
It depends far more on the strategy than on the bankroll. With $1,000 betting $1 and doubling after every loss, the average session completes 208 winning cycles before the progression needs a bet it cannot cover. Over 500 rounds, 27.1% of sessions reach that point.
What is risk of ruin?
The probability of being unable to place another bet within a stated number of rounds. This page separates two ways that happens: the bankroll reaching zero, and the strategy requiring a bet larger than the bankroll while money remains. The second is far more common with a doubling progression, and conflating them understates the risk.
Does doubling after a loss change the odds?
No. The expected loss is $2 per $100 wagered regardless of how the bets are sized. What doubling changes is the shape of the distribution: many small completed cycles, and rare losses large enough to end the session. Over 500 rounds 72.5% of sessions finish ahead, and the average result is still −$48.
Why is the average different from the typical result?
The average ending bankroll here is $952 while the median is $1,239. When a distribution has a long tail on one side, the average is pulled toward outcomes that occur rarely. The median describes what the middle session actually experienced.
How likely is a losing streak?
Two different questions get confused here. The chance that the next 10 resolved rounds all lose is 0.12%. The chance of seeing at least one 10-loss streak somewhere within 500 rounds is 25.08% — much larger, because there are many places for it to happen. Both are computed exactly.
Are these results exact?
Some are. Expected value, fair payout, break-even win chance and every streak probability are computed in closed form and carry no error. Flat betting is solved exactly by dynamic programming when the payout allows it. Path-dependent results — anything involving a progression, maximum drawdown, or the largest bet reached — are estimated by simulation and are shown with a margin of error. The page marks which is which.