Dice odds · 1% house edge
95% dice odds: 1.0421x payout, streaks and bankroll
Every number on this page is calculated for a 95% win chance at a 1% house edge unless a table says otherwise. A win pays 1.0421x, you lose 5% of rolls, and a run of 3 losses in a row starts about once every 8,420 rolls.
Payout and targets
- Payout multiplier
- 1.0421x
- 99 ÷ 95
- Roll under
- < 95
- Bet low wins below this
- Roll over
- > 5.00
- Bet high wins above 100 − 95
- Win / loss chance
- 95% / 5%
- 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 95% 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% | 1.0526x | 1.0000 |
| 1% | 1.0421x | 0.9900 |
| 2% | 1.0316x | 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 95%, 2 losses in a row is 1 in 400, while 10 in a row is 1 in 1.0e13.
| 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 | 0.25% | 1 in 400 | 420 | over 99.99% | over 99.99% |
| 3 in a row | 0.013% | 1 in 8,000 | 8,420 | 69.51% | over 99.99% |
| 4 in a row | 6.3e-4% | 1 in 160,000 | 168,420 | 5.76% | 44.77% |
| 5 in a row | 3.1e-5% | 1 in 3,200,000 | 3,368,420 | 0.296% | 2.93% |
| 6 in a row | 1.6e-6% | 1 in 64,000,000 | 67,368,420 | 0.015% | 0.148% |
| 7 in a row | 7.8e-8% | 1 in 1,280,000,000 | 1,347,368,420 | 7.4e-4% | 7.4e-3% |
| 8 in a row | 3.9e-9% | 1 in 25,600,000,000 | 26,947,368,420 | 3.7e-5% | 3.7e-4% |
| 10 in a row | 9.8e-12% | 1 in 1.0e13 | 1.1e13 | 9.3e-8% | 9.3e-7% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 95% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 1.0421x 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 |
|---|---|---|---|---|---|
| 20 in a row | 35.85% | 1 in 2.79 | 36 | over 99.99% | over 99.99% |
| 50 in a row | 7.69% | 1 in 13 | 240 | over 99.99% | over 99.99% |
| 75 in a row | 2.13% | 1 in 47 | 917 | over 99.99% | over 99.99% |
| 100 in a row | 0.592% | 1 in 169 | 3,358 | 94.91% | over 99.99% |
| 150 in a row | 0.046% | 1 in 2,195 | 43,882 | 20.38% | 89.76% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 1.0421x payout the smallest multiplier that does this is 24.75x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 0.04 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 24.75x 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 24.75x | Bankroll at 2x | Cycle result at 2x |
|---|---|---|---|
| 2 | 25.75 | 3 | -2.83 |
| 3 | 638.3 | 7 | -6.66 |
| 4 | 15,799 | 15 | -14.33 |
| 5 | 391,032 | 31 | -29.65 |
| 6 | 9,678,044 | 63 | -60.31 |
| 8 | 5.93e9 | 255 | -244.2 |
What this chance is used for
95% pays about 1.0421x at a 1% edge. Each win adds about 4% of the stake, and one loss costs as much as roughly 24 wins.
Recovering a single loss in one roll needs a bet about 24.75 times larger, which is why recovery systems at very high chances run out of room after two or three losses.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 95% win chance pay in dice?
At a 1% house edge a 95% chance pays 1.0421x (99 divided by 95). You win when the roll is under 95, or over 5.00 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 3 times in a row at 95%?
Any given 3 rolls all lose with probability 0.013% (1 in 8,000). Such a streak starts on average once every 8,420 rolls, so the chance of seeing at least one is 69.51% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 95%?
To win back every loss at a 1.0421x payout, the bet has to grow by at least 24.75x after each loss. Surviving 3 losses at that multiplier takes 638.3 base bets; at 2x it takes 7. The house edge still applies to every roll, so no multiplier makes the game profitable on average.