Calculator

Losing streak calculator

The losing streak calculator gives the probability of N losses in a row two ways: for your next N rolls, and anywhere within a session of T rolls. The second number is the one that decides whether a martingale survives, and over a long session it is much larger than the first. It also shows the average wait between streaks and the same figures for win streaks.

Inputs

Win chance

Streak length (N)

Up to 200

Number of rolls (T)

Up to 1,000,000

10 losses in a row at 49.5% win chance

Next 10 rolls all lose0.1079%1 in 927

At least one run of 10+ losses in 10,000 rolls99.53%

Average rolls between such streaks1,871Expected wait from a fresh start

10 wins in a row at 49.5% win chance

Next 10 rolls all win0.0883%1 in 1,132

At least one run of 10+ wins in 10,000 rolls98.86%

Average rolls between such streaks2,240

Streak odds for N = 5 to 30 over 10,000 rolls

Computing...
N	Next N all lose	Losing run of N+ in T rolls	Next N all win	Winning run of N+ in T rolls

Next N rolls versus somewhere in T rolls

“What are the odds of 10 losses in a row?” has two different answers. If you mean the next 10 rolls, the answer is q^N: the loss chance multiplied by itself N times. If you mean at any point during a session, you have to count every place in the session where the streak could start.

At 49.5% win chance, the next 10 rolls all lose with probability 0.1079%, or 1 in 927. Over 10,000 rolls the chance of at least one run of 10 or more losses is 99.53%. Over 1,000 rolls it is 41.30%. Such a run arrives on average once every 1,871 rolls.

Multiplying q^N by the number of rolls gives 1,078.7% here, which cannot be a probability. That shortcut counts overlapping runs more than once. The calculator avoids that by tracking the length of the current losing run roll by roll.

How the exact probability is computed

The calculation follows the length of the current losing run, which can be 0 to N − 1. Each roll either resets it to 0 (a win, probability p) or adds 1 (a loss, probability q). Reaching N means the streak happened. Summing over all paths gives the exact probability, with no simulation and no approximation.

b(t) = probability of a run of N+ losses within the first t rolls

b(t) = 0 for t < N, b(N) = q^N

b(t) = b(t − 1) + p × q^N × (1 − b(t − N − 1)) for t > N

expected rolls to the first streak = (1 − q^N) / (p × q^N)

The recurrence adds the chance that the first streak ends exactly on roll t: roll t − N was a win, the N rolls after it lost, and no streak happened before. It gives the same result as the state-by-state calculation and runs in one pass over T, so a million rolls take a few milliseconds in the browser.

Reference: chance of a losing streak somewhere in a session

Exact values for three common win chances, computed when this page was rendered.

49.5% win chance	Next N lose	In 1,000 rolls	In 10,000 rolls	In 100K rolls
8 losses	0.4230%	87.99%	>99.9999%	>99.9999%
10 losses	0.1079%	41.30%	99.53%	>99.9999%
12 losses	0.0275%	12.63%	74.40%	99.9999%
15 losses	0.00354%	1.717%	16.07%	82.69%
18 losses	0.000456%	0.2220%	2.230%	20.22%
20 losses	0.000116%	0.0566%	0.5733%	5.596%
25 losses	0.00000382%	0.00185%	0.0189%	0.1890%

10% win chance	Next N lose	In 1,000 rolls	In 10,000 rolls	In 100K rolls
20 losses	12.16%	>99.9999%	>99.9999%	>99.9999%
40 losses	1.478%	78.26%	>99.9999%	>99.9999%
60 losses	0.1797%	15.85%	83.60%	>99.9999%
80 losses	0.0218%	2.015%	19.53%	88.78%
100 losses	0.00266%	0.2415%	2.599%	23.31%
120 losses	0.000323%	0.0287%	0.3189%	3.174%

1% win chance	Next N lose	In 1,000 rolls	In 10,000 rolls	In 100K rolls
200 losses	13.40%	81.96%	>99.9999%	>99.9999%
300 losses	4.904%	36.36%	99.67%	>99.9999%
500 losses	0.6570%	3.942%	47.90%	99.89%

Using streak odds with a betting progression

A martingale fails when one losing run is longer than the balance can pay for. Find that length with the martingale calculator, then enter it here with the number of rolls you plan to play. The main crypto dice calculator turns the same idea into a risk of ruin figure. Why a streak never makes the next roll more likely to win is covered in why betting systems fail.

FAQ

Losing streak questions

What are the odds of 10 losses in a row at 49.5%?

For the next 10 rolls, 0.1079% (1 in 927). Over 10,000 rolls, the chance that a run of at least 10 losses happens somewhere is 99.53%. Over 1,000 rolls it is 41.30%.

Why is the chance over T rolls so much higher than q^N?

q^N is the chance that one specific block of N rolls all lose. A session of T rolls contains thousands of overlapping blocks, and the streak only has to happen in one of them. The calculator counts every way that can happen without double counting overlapping runs.

Does a long losing streak make a win more likely?

No. Each roll is independent and the next roll has the same win chance whatever came before. A streak that has already happened says nothing about the next roll. Believing otherwise is the gambler's fallacy.

How is the expected wait between streaks calculated?

The expected number of rolls until the first run of N losses is (1 − q^N) / ((1 − q) × q^N), where q is the chance of losing one roll. It is the same formula the main DiceSim calculator uses for the wait until a fatal martingale streak.

Can I use it for win streaks?

Yes. A win streak is a run of the other outcome, so the calculator swaps the win and loss probabilities. At 49.5% the chance of at least 10 wins in a row somewhere in 10,000 rolls is 98.86%.