Dice odds · 1% house edge
10% dice odds: 9.9x payout, streaks and bankroll
Every number on this page is calculated for a 10% win chance at a 1% house edge unless a table says otherwise. A win pays 9.9x, you lose 90% of rolls, and a run of 50 losses in a row starts about once every 1,930 rolls.
Payout and targets
- Payout multiplier
- 9.9x
- 99 ÷ 10
- Roll under
- < 10
- Bet low wins below this
- Roll over
- > 90.00
- Bet high wins above 100 − 10
- Win / loss chance
- 10% / 90%
- 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 10% 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% | 10x | 1.0000 |
| 1% | 9.9x | 0.9900 |
| 2% | 9.8x | 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 10%, 10 losses in a row is 1 in 2.87, while 150 in a row is 1 in 7,305,057.
| Streak | Chance next N all lose | 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% |
| 40 in a row | 1.48% | 1 in 68 | 667 | 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% |
| 100 in a row | 2.7e-3% | 1 in 37,649 | 376,476 | 2.62% | 23.33% |
| 150 in a row | 1.4e-5% | 1 in 7,305,057 | 73,050,556 | 0.014% | 0.137% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 10% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 9.9x 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 |
|---|---|---|---|---|---|
| 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% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 9.9x payout the smallest multiplier that does this is 1.1124x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 8.9 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 1.1124x and for 1.2x. The last column is where the cycle stands if the win comes right after those N losses at 1.2x.
| Losses survived | Bankroll at 1.1124x | Bankroll at 1.2x | Cycle result at 1.2x |
|---|---|---|---|
| 10 | 16.91 | 25.96 | +29.15 |
| 20 | 65.97 | 186.7 | +154.5 |
| 30 | 208.2 | 1,182 | +930.8 |
| 50 | 1,818 | 45,497 | +35,497 |
| 75 | 26,160 | 4,340,732 | +3,385,780 |
| 100 | 374,885 | 414,089,868 | +322,990,106 |
What this chance is used for
A round 10% chance pays 9.9x at a 1% edge, slightly under the 10x that 9.9% pays.
The two settings are close enough that the streak numbers barely differ; pick 10% when you want the win rate to be a round one in ten, and 9.9% when you want the payout to be round.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 10% win chance pay in dice?
At a 1% house edge a 10% chance pays 9.9x (99 divided by 10). You win when the roll is under 10, or over 90.00 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 50 times in a row at 10%?
Any given 50 rolls all lose with probability 0.515% (1 in 194). Such a streak starts on average once every 1,930 rolls, so the chance of seeing at least one is 99.44% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 10%?
To win back every loss at a 9.9x payout, the bet has to grow by at least 1.1124x after each loss. Surviving 50 losses at that multiplier takes 1,818 base bets; at 1.2x it takes 45,497. The house edge still applies to every roll, so no multiplier makes the game profitable on average.