Dice odds · 1% house edge
9.9% dice odds: 10x payout, streaks and bankroll
Every number on this page is calculated for a 9.9% win chance at a 1% house edge unless a table says otherwise. A win pays 10x, you lose 90.1% of rolls, and a run of 50 losses in a row starts about once every 1,844 rolls.
Payout and targets
- Payout multiplier
- 10x
- 99 ÷ 9.9
- Roll under
- < 9.9
- Bet low wins below this
- Roll over
- > 90.10
- Bet high wins above 100 − 9.9
- Win / loss chance
- 9.9% / 90.1%
- 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 9.9% 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% | 10.1x | 1.0000 |
| 1% | 10x | 0.9900 |
| 2% | 9.899x | 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 9.9%, 10 losses in a row is 1 in 2.84, while 150 in a row is 1 in 6,184,169.
| 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 | 35.26% | 1 in 2.84 | 19 | over 99.99% | over 99.99% |
| 20 in a row | 12.43% | 1 in 8.04 | 71 | over 99.99% | over 99.99% |
| 30 in a row | 4.38% | 1 in 23 | 220 | over 99.99% | over 99.99% |
| 40 in a row | 1.55% | 1 in 65 | 644 | over 99.99% | over 99.99% |
| 50 in a row | 0.545% | 1 in 184 | 1,844 | 99.56% | over 99.99% |
| 75 in a row | 0.04% | 1 in 2,487 | 25,109 | 32.85% | 98.14% |
| 100 in a row | 3.0e-3% | 1 in 33,692 | 340,309 | 2.9% | 25.46% |
| 150 in a row | 1.6e-5% | 1 in 6,184,169 | 62,466,344 | 0.016% | 0.16% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 9.9% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 10x 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 | 0.98% | 1 in 102 | 112 | over 99.99% | over 99.99% |
| 3 in a row | 0.097% | 1 in 1,031 | 1,143 | 99.98% | over 99.99% |
| 4 in a row | 0.01% | 1 in 10,410 | 11,553 | 57.92% | 99.98% |
| 5 in a row | 9.5e-4% | 1 in 105,154 | 116,707 | 8.21% | 57.55% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 10x payout the smallest multiplier that does this is 1.1111x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 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 1.1111x 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 1.1111x | Bankroll at 1.2x | Cycle result at 1.2x |
|---|---|---|---|
| 10 | 16.81 | 25.96 | +29.77 |
| 20 | 65.03 | 186.7 | +158.4 |
| 30 | 203.3 | 1,182 | +954.5 |
| 50 | 1,737 | 45,497 | +36,407 |
| 75 | 24,316 | 4,340,732 | +3,472,594 |
| 100 | 338,829 | 414,089,868 | +331,271,903 |
What this chance is used for
9.9% is the chance that gives an even 10x payout at a 1% house edge, which makes the arithmetic easy: a win returns ten times the stake, so it covers nine losing bets of the same size.
Streaks of 50 losses in a row come up about once every 1,800 rolls at this chance, so a progression here has to stay gentle: about 11% more per loss is the least that recovers a run.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 9.9% win chance pay in dice?
At a 1% house edge a 9.9% chance pays 10x (99 divided by 9.9). You win when the roll is under 9.9, or over 90.10 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 9.9%?
Any given 50 rolls all lose with probability 0.545% (1 in 184). Such a streak starts on average once every 1,844 rolls, so the chance of seeing at least one is 99.56% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 9.9%?
To win back every loss at a 10x payout, the bet has to grow by at least 1.1111x after each loss. Surviving 50 losses at that multiplier takes 1,737 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.