Dice odds · 1% house edge
33% dice odds: 3x payout, streaks and bankroll
Every number on this page is calculated for a 33% win chance at a 1% house edge unless a table says otherwise. A win pays 3x, you lose 67% of rolls, and a run of 15 losses in a row starts about once every 1,228 rolls.
Payout and targets
- Payout multiplier
- 3x
- 99 ÷ 33
- Roll under
- < 33
- Bet low wins below this
- Roll over
- > 67.00
- Bet high wins above 100 − 33
- Win / loss chance
- 33% / 67%
- 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 33% 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% | 3.0303x | 1.0000 |
| 1% | 3x | 0.9900 |
| 2% | 2.9697x | 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 33%, 5 losses in a row is 1 in 7.41, while 30 in a row is 1 in 165,103.
| Streak | Chance next N all lose | Odds | Avg rolls between | At least one in 10,000 | At least one in 100,000 |
|---|---|---|---|---|---|
| 5 in a row | 13.5% | 1 in 7.41 | 19 | over 99.99% | over 99.99% |
| 8 in a row | 4.06% | 1 in 25 | 72 | over 99.99% | over 99.99% |
| 10 in a row | 1.82% | 1 in 55 | 163 | over 99.99% | over 99.99% |
| 12 in a row | 0.818% | 1 in 122 | 367 | over 99.99% | over 99.99% |
| 15 in a row | 0.246% | 1 in 406 | 1,228 | 99.97% | over 99.99% |
| 20 in a row | 0.033% | 1 in 3,010 | 9,117 | 66.61% | over 99.99% |
| 25 in a row | 4.5e-3% | 1 in 22,291 | 67,546 | 13.76% | 77.25% |
| 30 in a row | 6.1e-4% | 1 in 165,103 | 500,310 | 1.98% | 18.12% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 33% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 3x 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 |
|---|---|---|---|---|---|
| 3 in a row | 3.59% | 1 in 28 | 40 | over 99.99% | over 99.99% |
| 5 in a row | 0.391% | 1 in 256 | 380 | over 99.99% | over 99.99% |
| 8 in a row | 0.014% | 1 in 7,110 | 10,611 | 61.03% | 99.99% |
| 10 in a row | 1.5e-3% | 1 in 65,292 | 97,449 | 9.75% | 64.16% |
| 12 in a row | 1.7e-4% | 1 in 599,560 | 894,864 | 1.11% | 10.57% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 3x payout the smallest multiplier that does this is 1.5x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 2 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 1.5x and for 2x. The last column is where the cycle stands if the win comes right after those N losses at 2x.
| Losses survived | Bankroll at 1.5x | Bankroll at 2x | Cycle result at 2x |
|---|---|---|---|
| 5 | 13.19 | 31 | +33 |
| 8 | 49.26 | 255 | +257 |
| 10 | 113.3 | 1,023 | +1,025 |
| 15 | 873.8 | 32,767 | +32,769 |
| 20 | 6,649 | 1,048,575 | +1,048,577 |
| 25 | 50,500 | 33,554,431 | +33,554,433 |
What this chance is used for
33% pays 3x at a 1% house edge and is the default chance of the dynamic recovery script on DiceSim.
A 3x win covers two losing bets, so raising the stake by 50% after each loss is enough to win back a streak. Doubling at this chance also recovers, but the bankroll it needs grows much faster.
The house edge applies at every chance, so none of these settings has a positive expected return.
Scripts that default to 33%: Dynamic Recovery.
FAQ
What does a 33% win chance pay in dice?
At a 1% house edge a 33% chance pays 3x (99 divided by 33). You win when the roll is under 33, or over 67.00 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 15 times in a row at 33%?
Any given 15 rolls all lose with probability 0.246% (1 in 406). Such a streak starts on average once every 1,228 rolls, so the chance of seeing at least one is 99.97% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 33%?
To win back every loss at a 3x payout, the bet has to grow by at least 1.5x after each loss. Surviving 15 losses at that multiplier takes 873.8 base bets; at 2x it takes 32,767. The house edge still applies to every roll, so no multiplier makes the game profitable on average.