Dice odds · 1% house edge
5% dice odds: 19.8x payout, streaks and bankroll
Every number on this page is calculated for a 5% win chance at a 1% house edge unless a table says otherwise. A win pays 19.8x, you lose 95% of rolls, and a run of 100 losses in a row starts about once every 3,358 rolls.
Payout and targets
- Payout multiplier
- 19.8x
- 99 ÷ 5
- Roll under
- < 5
- Bet low wins below this
- Roll over
- > 95.00
- Bet high wins above 100 − 5
- Win / loss chance
- 5% / 95%
- 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 5% 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% | 20x | 1.0000 |
| 1% | 19.8x | 0.9900 |
| 2% | 19.6x | 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 5%, 20 losses in a row is 1 in 2.79, while 250 in a row is 1 in 370,765.
| Streak | Chance next N all lose | 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% |
| 40 in a row | 12.85% | 1 in 7.78 | 136 | over 99.99% | over 99.99% |
| 60 in a row | 4.61% | 1 in 22 | 414 | over 99.99% | over 99.99% |
| 80 in a row | 1.65% | 1 in 61 | 1,191 | 99.98% | 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% |
| 200 in a row | 3.5e-3% | 1 in 28,529 | 570,550 | 1.74% | 16.08% |
| 250 in a row | 2.7e-4% | 1 in 370,765 | 7,415,279 | 0.135% | 1.34% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 5% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 19.8x 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 | 0.25% | 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% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 19.8x payout the smallest multiplier that does this is 1.0532x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 18.8 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 1.0532x and for 1.1x. The last column is where the cycle stands if the win comes right after those N losses at 1.1x.
| Losses survived | Bankroll at 1.0532x | Bankroll at 1.1x | Cycle result at 1.1x |
|---|---|---|---|
| 20 | 34.2 | 57.27 | +69.2 |
| 40 | 130.6 | 442.6 | +408.3 |
| 60 | 402.5 | 3,035 | +2,689 |
| 100 | 3,330 | 137,796 | +121,279 |
| 150 | 44,676 | 16,177,168 | +14,235,927 |
| 200 | 596,503 | 1.90e9 | +1.67e9 |
What this chance is used for
5% pays 19.8x, one win in 20 rolls on average.
A win covers 18.8 losing bets of the same size, so a progression can recover with about 5% added per loss, and the average wait for a win is a fifth of the wait at 1%. Runs of 100 losses still turn up every few thousand rolls.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 5% win chance pay in dice?
At a 1% house edge a 5% chance pays 19.8x (99 divided by 5). You win when the roll is under 5, or over 95.00 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 100 times in a row at 5%?
Any given 100 rolls all lose with probability 0.592% (1 in 169). Such a streak starts on average once every 3,358 rolls, so the chance of seeing at least one is 94.91% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 5%?
To win back every loss at a 19.8x payout, the bet has to grow by at least 1.0532x after each loss. Surviving 100 losses at that multiplier takes 3,330 base bets; at 1.1x it takes 137,796. The house edge still applies to every roll, so no multiplier makes the game profitable on average.