Dice odds · 1% house edge
90% dice odds: 1.1x payout, streaks and bankroll
Every number on this page is calculated for a 90% win chance at a 1% house edge unless a table says otherwise. A win pays 1.1x, you lose 10% of rolls, and a run of 4 losses in a row starts about once every 11,110 rolls.
Payout and targets
- Payout multiplier
- 1.1x
- 99 ÷ 90
- Roll under
- < 90
- Bet low wins below this
- Roll over
- > 10.00
- Bet high wins above 100 − 90
- Win / loss chance
- 90% / 10%
- House edge
- 1%
- Return per 1 unit bet
- 0.9900
- Average loss 0.0100 per unit
The payout is (100 − house edge) ÷ win chance, so the same 90% chance pays a little more on a site with a lower edge. The table compares three edges. Return per unit is the win chance times the payout, which works out to 1 minus the edge at any chance.
| House edge | Payout | Return per 1 unit |
|---|---|---|
| 0% | 1.1111x | 1.0000 |
| 1% | 1.1x | 0.9900 |
| 2% | 1.0889x | 0.9800 |
Losing streaks
Each row gives the chance that the next N rolls all lose, the average number of rolls between such streaks, and the chance of seeing at least one within 10,000 and 100,000 rolls (1 − e−T/E, where E is the average gap). At 90%, 2 losses in a row is 1 in 100, while 10 in a row is 1 in 10,000,000,000.
| Streak | Chance next N all lose | Odds | Avg rolls between | At least one in 10,000 | At least one in 100,000 |
|---|---|---|---|---|---|
| 2 in a row | 1% | 1 in 100 | 110 | over 99.99% | over 99.99% |
| 3 in a row | 0.1% | 1 in 1,000 | 1,110 | 99.99% | over 99.99% |
| 4 in a row | 0.01% | 1 in 10,000 | 11,110 | 59.35% | 99.99% |
| 5 in a row | 1.0e-3% | 1 in 100,000 | 111,110 | 8.61% | 59.34% |
| 6 in a row | 1.0e-4% | 1 in 1,000,000 | 1,111,110 | 0.896% | 8.61% |
| 7 in a row | 1.0e-5% | 1 in 10,000,000 | 11,111,110 | 0.09% | 0.896% |
| 8 in a row | 1.0e-6% | 1 in 100,000,000 | 111,111,110 | 9.0e-3% | 0.09% |
| 10 in a row | 1.0e-8% | 1 in 10,000,000,000 | 11,111,111,110 | 9.0e-5% | 9.0e-4% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 90% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 1.1x payout each win pays.
| Streak | Chance next N all win | Odds | Avg rolls between | At least one in 10,000 | At least one in 100,000 |
|---|---|---|---|---|---|
| 10 in a row | 34.87% | 1 in 2.87 | 19 | over 99.99% | over 99.99% |
| 20 in a row | 12.16% | 1 in 8.23 | 72 | over 99.99% | over 99.99% |
| 30 in a row | 4.24% | 1 in 24 | 226 | over 99.99% | over 99.99% |
| 50 in a row | 0.515% | 1 in 194 | 1,930 | 99.44% | over 99.99% |
| 75 in a row | 0.037% | 1 in 2,703 | 27,018 | 30.94% | 97.53% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 1.1x payout the smallest multiplier that does this is 11x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 0.1 base bets ahead, the same as a win on the first roll.
The table shows the bankroll, in base bets, needed to place every bet of an N loss streak, for 11x and for 2x. The last column is where the cycle stands if the win comes right after those N losses at 2x. Because 2x is below the minimum, a win after 1 or more losses leaves the cycle behind.
| Losses survived | Bankroll at 11x | Bankroll at 2x | Cycle result at 2x |
|---|---|---|---|
| 2 | 12 | 3 | -2.6 |
| 3 | 133 | 7 | -6.2 |
| 4 | 1,464 | 15 | -13.4 |
| 5 | 16,105 | 31 | -27.8 |
| 6 | 177,156 | 63 | -56.6 |
| 8 | 21,435,888 | 255 | -229.4 |
What this chance is used for
90% pays 1.1x at a 1% house edge, so each win adds a tenth of the stake and a single loss takes back about ten wins.
Sessions at this chance look smooth for long stretches. To win back a loss in one roll the bet has to grow elevenfold, so two or three losses in a row are enough to put a progression far beyond most balances.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 90% win chance pay in dice?
At a 1% house edge a 90% chance pays 1.1x (99 divided by 90). You win when the roll is under 90, or over 10.00 if you bet high. A 1 unit bet returns 0.99 units on average, so the expected loss is 1% of every bet.
How often do you lose 4 times in a row at 90%?
Any given 4 rolls all lose with probability 0.01% (1 in 10,000). Such a streak starts on average once every 11,110 rolls, so the chance of seeing at least one is 59.35% within 10,000 rolls and 99.99% within 100,000 rolls.
How much bankroll does martingale need at 90%?
To win back every loss at a 1.1x payout, the bet has to grow by at least 11x after each loss. Surviving 4 losses at that multiplier takes 1,464 base bets; at 2x it takes 15. The house edge still applies to every roll, so no multiplier makes the game profitable on average.