Losing streak calculator

How likely is a long losing streak? That is really two questions, and mixing them up is the easiest way to misjudge a streak. Both are computed exactly below — no simulation — and update as you change the win chance and round count.

Scenario

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.

31.13% of sessions finish ahead — typically by $12.

Across every possible sequence of 500 rounds, the expectation is −$10.

Computed exactly — no simulation involved, so there is no margin of error.

startmean · median
Ending bankroll. Grey shows flat betting on the same scenario. Computed exactly.

Expected versus typical

Expected ending bankroll
$990

The average across every simulated session (−$10).

Typical ending bankroll
$990

What the middle session experienced (−$10).

These agree closely here, which means the distribution is roughly symmetric.

Preparing sample paths…

Outcomes

Finish ahead
31.13%
Finish behind
65.64%
Bankroll exhausted
0.00%

Could not place even the minimum bet.

Strategy could not continue
0.00%

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
$938
P5
$954
P25
$974
P50
$990
P75
$1,006
P95
$1,026
P99
$1,042

Risk

Average largest bet
$1
Median maximum drawdown
$29
Average longest losing streak
9
Average total wagered
$500

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%

A different question from the one above, and a much larger number.

Typical longest losing streak
8

95th percentile: 12.

The two questions

At a 49% win chance, the probability that your next 10 resolved bets all lose is 0.12%. The probability that a 10-loss streak appears somewhere within 500 rounds is 25.08% — far larger, because the streak has hundreds of places to start. Betting systems that "wait for" streaks are priced on the first number but exposed to the second.

Over a 500-round session the typical longest losing streak is 8, and one in twenty sessions sees 12 or more. Streaks this long are not bad luck — they are the ordinary texture of independent events.

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