Dice odds · 1% house edge
19.8% dice odds: 5x payout, streaks and bankroll
Every number on this page is calculated for a 19.8% win chance at a 1% house edge unless a table says otherwise. A win pays 5x, you lose 80.2% of rolls, and a run of 20 losses in a row starts about once every 412 rolls.
Payout and targets
- Payout multiplier
- 5x
- 99 ÷ 19.8
- Roll under
- < 19.8
- Bet low wins below this
- Roll over
- > 80.20
- Bet high wins above 100 − 19.8
- Win / loss chance
- 19.8% / 80.2%
- 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 19.8% 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% | 5.0505x | 1.0000 |
| 1% | 5x | 0.9900 |
| 2% | 4.9495x | 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 19.8%, 5 losses in a row is 1 in 3.01, while 50 in a row is 1 in 61,842.
| 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 | 33.18% | 1 in 3.01 | 10 | over 99.99% | over 99.99% |
| 10 in a row | 11.01% | 1 in 9.08 | 41 | over 99.99% | over 99.99% |
| 15 in a row | 3.65% | 1 in 27 | 133 | over 99.99% | over 99.99% |
| 20 in a row | 1.21% | 1 in 83 | 412 | over 99.99% | over 99.99% |
| 25 in a row | 0.402% | 1 in 249 | 1,251 | 99.97% | over 99.99% |
| 30 in a row | 0.133% | 1 in 749 | 3,780 | 92.9% | over 99.99% |
| 40 in a row | 0.015% | 1 in 6,808 | 34,379 | 25.24% | 94.55% |
| 50 in a row | 1.6e-3% | 1 in 61,842 | 312,327 | 3.15% | 27.4% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 19.8% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 5x 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 | 3.92% | 1 in 26 | 31 | over 99.99% | over 99.99% |
| 3 in a row | 0.776% | 1 in 129 | 159 | over 99.99% | over 99.99% |
| 4 in a row | 0.154% | 1 in 651 | 810 | over 99.99% | over 99.99% |
| 5 in a row | 0.03% | 1 in 3,286 | 4,096 | 91.3% | over 99.99% |
| 6 in a row | 6.0e-3% | 1 in 16,596 | 20,692 | 38.32% | 99.2% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 5x payout the smallest multiplier that does this is 1.25x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 4 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 1.25x and for 1.5x. The last column is where the cycle stands if the win comes right after those N losses at 1.5x.
| Losses survived | Bankroll at 1.25x | Bankroll at 1.5x | Cycle result at 1.5x |
|---|---|---|---|
| 5 | 8.21 | 13.19 | +17.19 |
| 10 | 33.25 | 113.3 | +117.3 |
| 15 | 109.7 | 873.8 | +877.8 |
| 20 | 342.9 | 6,649 | +6,653 |
| 30 | 3,227 | 383,500 | +383,504 |
| 40 | 30,089 | 22,114,663 | +22,114,667 |
What this chance is used for
19.8% pays exactly 5x at a 1% house edge, about one win every five rolls.
A 5x win covers four losing bets of the same size, so a loss multiplier of 1.25 is enough to recover a streak. That is a much gentler climb than the doubling a 2x bet needs, but streaks of 20 or 30 losses come up regularly over a long session.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 19.8% win chance pay in dice?
At a 1% house edge a 19.8% chance pays 5x (99 divided by 19.8). You win when the roll is under 19.8, or over 80.20 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 20 times in a row at 19.8%?
Any given 20 rolls all lose with probability 1.21% (1 in 83). Such a streak starts on average once every 412 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 19.8%?
To win back every loss at a 5x payout, the bet has to grow by at least 1.25x after each loss. Surviving 20 losses at that multiplier takes 342.9 base bets; at 1.5x it takes 6,649. The house edge still applies to every roll, so no multiplier makes the game profitable on average.