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Martingale calculator: bankroll needed for N losses

This martingale calculator shows how many losses in a row your balance can pay for, the bankroll needed for any streak length, the bet you would place next and what you would have lost by then. Enter a win chance, house edge, base bet and the multiplier you apply after each loss. Everything runs in your browser.

Inputs

Win chance

House edge

Base bet

Any unit: coins, sats or dollars

Multiply bet on loss

2 doubles the bet after every loss

Balance

Losses in a row (N)

Payout2x50.50% chance to lose each roll

Losses your balance survives9The next bet after that many losses would not fit

Bankroll for 10 losses1,0232,047 to also place the next bet

Next bet after 10 losses1,024

Total lost after 10 losses1,0230.1079% (1 in 927) per fresh run

Minimum multiplier to recover2.0000xYour 2x recovers all losses on a win

Martingale table: bet, loss and odds by streak length

Rows stop at 25 losses or at the first streak your balance of 1,000 cannot pay for (shaded). Red next bets no longer fit in the balance.
N	Losing bet #N	Total lost	Next bet	Net if next wins	P(N losses in a row)
1	1	1	2	+1	50.50% (1 in 1.98)
2	2	3	4	+1	25.50% (1 in 3.92)
3	4	7	8	+1	12.88% (1 in 7.76)
4	8	15	16	+1	6.504% (1 in 15)
5	16	31	32	+1	3.284% (1 in 30)
6	32	63	64	+1	1.659% (1 in 60)
7	64	127	128	+1	0.8376% (1 in 119)
8	128	255	256	+1	0.4230% (1 in 236)
9	256	511	512	+1	0.2136% (1 in 468)
10	512	1,023	1,024	+1	0.1079% (1 in 927)

Bankroll needed to survive N losses, by multiplier

Base bet 1. Red cells are more than your balance.
N losses	x1.5	x2	x2.5	x3
5	13.1875	31	64.4375	121
8	49.2578	255	1,016.59	3,280
10	113.3301	1,023	6,357.16	29,524
12	257.4927	4,095	39,735.76	265,720
15	873.7878	32,767	620,881.05	7,174,453
20	6,648.51	1,048,575	60,632,979.45	1,743,392,200
Your balance survives	15 losses	9 losses	7 losses	6 losses

How the martingale calculator works

A martingale multiplies the bet by a fixed factor r after each loss and goes back to the base bet b after a win. After k losses the next bet is b × r^k, so the stake grows geometrically while the payout stays the same.

payout = (100 − house edge) / win chance

bet after k losses = b × r^k

total lost after N losses = b × (r^N − 1) / (r − 1)

losses survivable = floor( ln(1 + balance × (r − 1) / b) / ln r )

P(N losses in a row) = q^N, where q = 1 − win chance / 100

minimum recovery multiplier = 1 + 1 / (payout − 1)

The “net if next wins” column is the winning bet’s profit, b × r^N × (payout − 1), minus everything lost before it. When that number is negative, a win no longer gets the run back to even.

Worked example: doubling at 49.5%

Win chance 49.5%, house edge 1%, base bet 1, multiplier 2x, balance 1,000.

Payout is 2x and each roll loses with probability 50.50%.
The balance covers 9 losses in a row. Losing 9 times costs 511, and the next bet of 512 does not fit in what is left.
After 10 losses you would have lost 1,023 and the next bet would be 1,024.
The minimum recovery multiplier at this payout is 2.0000x, so doubling recovers every loss on a win. At 3x the same balance covers 6 losses instead of 9.
A run of 10 losses ends the session. One fresh run has a 0.1079% chance (1 in 927) of going that way, but over 10,000 rolls the chance of at least one such streak is 99.53%. On average it shows up once every 1,871 rolls.

Ten times the balance (10,000) covers 13 losses at 2x. The bankroll needed grows exponentially with N. With doubling, each extra loss you want to cover costs about as much as all the previous ones combined.

What this calculator does not tell you

The numbers describe one losing run at a time. They do not say how often such a run appears during a long session; for that, use the losing streak calculator, which gives the exact chance of a streak somewhere in T rolls. For a risk of ruin figure over a horizon and a bankroll projection, use the main crypto dice calculator.

The expected loss is the same as for flat betting per coin wagered. A martingale wagers more coins, so the house edge calculator shows a larger expected loss for it at the same number of rolls. The reasons betting systems cannot beat a fixed edge are covered in why betting systems fail.

FAQ

Martingale calculator questions

How much bankroll do I need for a martingale?

It depends on how many losses in a row you want to cover. With a base bet b and a multiplier r, covering N losses costs b × (r^N − 1) / (r − 1). Doubling from a base bet of 1, 10 losses cost 1,023, and placing the bet after them needs 2,047 in total.

How many losses in a row can my balance survive?

Find the largest N where the total of N losing bets still fits in the balance: N = floor(ln(1 + balance × (r − 1) / base) / ln r). With 1,000 and a base bet of 1 at 2x that is 9 losses. Ten times the balance only raises it to 13.

What multiplier do I need to recover my losses?

At least 1 + 1 / (payout − 1). At that multiplier a win after any streak pays back every earlier loss in the run and leaves one base-bet win as profit. At a 2x payout the minimum is 2.0000x. Lower multipliers leave part of the streak unrecovered.

Does a martingale change the house edge?

No. Every bet loses the house edge on average, whatever its size. A martingale raises the total amount you wager, so the expected loss in coins grows, and it trades many small wins for a rare large loss.

Is the probability in the table the chance of seeing that streak today?

No. The table shows the chance that one fresh run of bets loses N times in a row, q^N. Over many rolls the chance that such a streak happens somewhere is much higher: over 10,000 rolls at 49.5% the chance of at least one run of 10 losses is 99.53%. The losing streak calculator computes that number for any session length.