Dice odds · 1% house edge
3.35% dice odds: 29.55x payout, streaks and bankroll
Every number on this page is calculated for a 3.35% win chance at a 1% house edge unless a table says otherwise. A win pays 29.55x, you lose 96.65% of rolls, and a run of 100 losses in a row starts about once every 871 rolls.
Payout and targets
- Payout multiplier
- 29.55x
- 99 ÷ 3.35
- Roll under
- < 3.35
- Bet low wins below this
- Roll over
- > 96.65
- Bet high wins above 100 − 3.35
- Win / loss chance
- 3.35% / 96.65%
- 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 3.35% 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% | 29.85x | 1.0000 |
| 1% | 29.55x | 0.9900 |
| 2% | 29.25x | 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 3.35%, 25 losses in a row is 1 in 2.34, while 300 in a row is 1 in 27,507.
| Streak | Chance next N all lose | Odds | Avg rolls between | At least one in 10,000 | At least one in 100,000 |
|---|---|---|---|---|---|
| 25 in a row | 42.66% | 1 in 2.34 | 40 | over 99.99% | over 99.99% |
| 50 in a row | 18.2% | 1 in 5.49 | 134 | over 99.99% | over 99.99% |
| 75 in a row | 7.76% | 1 in 13 | 355 | over 99.99% | over 99.99% |
| 100 in a row | 3.31% | 1 in 30 | 871 | over 99.99% | over 99.99% |
| 150 in a row | 0.603% | 1 in 166 | 4,921 | 86.89% | over 99.99% |
| 200 in a row | 0.11% | 1 in 911 | 27,171 | 30.79% | 97.48% |
| 250 in a row | 0.02% | 1 in 5,007 | 149,418 | 6.47% | 48.79% |
| 300 in a row | 3.6e-3% | 1 in 27,507 | 821,073 | 1.21% | 11.47% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 3.35% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 29.55x 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 | 0.112% | 1 in 891 | 921 | over 99.99% | over 99.99% |
| 3 in a row | 3.8e-3% | 1 in 26,599 | 27,520 | 30.47% | 97.36% |
| 4 in a row | 1.3e-4% | 1 in 794,000 | 821,520 | 1.21% | 11.46% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 29.55x payout the smallest multiplier that does this is 1.035x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 28.55 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 1.035x and for 1.04x. The last column is where the cycle stands if the win comes right after those N losses at 1.04x.
| Losses survived | Bankroll at 1.035x | Bankroll at 1.04x | Cycle result at 1.04x |
|---|---|---|---|
| 25 | 38.96 | 41.65 | +34.47 |
| 50 | 131.1 | 152.7 | +50.24 |
| 100 | 864.1 | 1,238 | +204.4 |
| 150 | 4,962 | 8,948 | +1,300 |
| 200 | 27,877 | 63,744 | +9,086 |
| 300 | 872,353 | 3,220,612 | +457,644 |
What this chance is used for
3.35% pays about 29.55x at a 1% edge and is the default chance of the delayed escalation script on DiceSim. That script bets the base amount through a preroll of 50 losses, then raises the bet by 4% per loss until a win.
The idea behind that style is to skip the start of a dry spell, but every roll is independent, so a preroll changes when you bet more and leaves the odds of the next roll as they were.
Losing runs of 100 or more are routine here, which is why scripts at this chance raise the bet by only a few percent per loss.
The house edge applies at every chance, so none of these settings has a positive expected return.
Scripts that default to 3.35%: Delayed Escalation.
FAQ
What does a 3.35% win chance pay in dice?
At a 1% house edge a 3.35% chance pays 29.55x (99 divided by 3.35). You win when the roll is under 3.35, or over 96.65 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 100 times in a row at 3.35%?
Any given 100 rolls all lose with probability 3.31% (1 in 30). Such a streak starts on average once every 871 rolls, so the chance of seeing at least one is over 99.99% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 3.35%?
To win back every loss at a 29.55x payout, the bet has to grow by at least 1.035x after each loss. Surviving 100 losses at that multiplier takes 864.1 base bets; at 1.04x it takes 1,238. The house edge still applies to every roll, so no multiplier makes the game profitable on average.