Dice odds · 1% house edge
98% dice odds: 1.0102x payout, streaks and bankroll
Every number on this page is calculated for a 98% win chance at a 1% house edge unless a table says otherwise. A win pays 1.0102x, you lose 2% of rolls, and a run of 2 losses in a row starts about once every 2,550 rolls.
Payout and targets
- Payout multiplier
- 1.0102x
- 99 ÷ 98
- Roll under
- < 98
- Bet low wins below this
- Roll over
- > 2.00
- Bet high wins above 100 − 98
- Win / loss chance
- 98% / 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 98% 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% | 1.0204x | 1.0000 |
| 1% | 1.0102x | 0.9900 |
| 2% | 1x | 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 98%, 2 losses in a row is 1 in 2,500, while 8 in a row is 1 in 3.9e13.
| 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 | 0.04% | 1 in 2,500 | 2,550 | 98.02% | over 99.99% |
| 3 in a row | 8.0e-4% | 1 in 125,000 | 127,550 | 7.54% | 54.34% |
| 4 in a row | 1.6e-5% | 1 in 6,250,000 | 6,377,550 | 0.157% | 1.56% |
| 5 in a row | 3.2e-7% | 1 in 312,500,000 | 318,877,550 | 3.1e-3% | 0.031% |
| 6 in a row | 6.4e-9% | 1 in 15,625,000,000 | 15,943,877,550 | 6.3e-5% | 6.3e-4% |
| 7 in a row | 1.3e-10% | 1 in 781,250,000,000 | 797,193,877,550 | 1.3e-6% | 1.3e-5% |
| 8 in a row | 2.6e-12% | 1 in 3.9e13 | 4.0e13 | 2.5e-8% | 2.5e-7% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 98% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 1.0102x 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 |
|---|---|---|---|---|---|
| 50 in a row | 36.42% | 1 in 2.75 | 87 | over 99.99% | over 99.99% |
| 100 in a row | 13.26% | 1 in 7.54 | 327 | over 99.99% | over 99.99% |
| 200 in a row | 1.76% | 1 in 57 | 2,793 | 97.21% | over 99.99% |
| 300 in a row | 0.233% | 1 in 429 | 21,386 | 37.35% | 99.07% |
| 500 in a row | 4.1e-3% | 1 in 24,376 | 1,218,749 | 0.817% | 7.88% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 1.0102x payout the smallest multiplier that does this is 99x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 0.01 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 99x 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 99x | Bankroll at 2x | Cycle result at 2x |
|---|---|---|---|
| 2 | 100 | 3 | -2.96 |
| 3 | 9,901 | 7 | -6.92 |
| 4 | 980,200 | 15 | -14.84 |
| 5 | 97,039,801 | 31 | -30.67 |
| 6 | 9.61e9 | 63 | -62.35 |
What this chance is used for
98% pays about 1.0102x at a 1% house edge: tiny wins on almost every roll and a rare loss that takes back close to a hundred of them.
The balance moves slowly per unit wagered, so wagered volume piles up fast at this chance. The expected loss per unit wagered is the same 1% as at any other chance.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 98% win chance pay in dice?
At a 1% house edge a 98% chance pays 1.0102x (99 divided by 98). You win when the roll is under 98, or over 2.00 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 2 times in a row at 98%?
Any given 2 rolls all lose with probability 0.04% (1 in 2,500). Such a streak starts on average once every 2,550 rolls, so the chance of seeing at least one is 98.02% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 98%?
To win back every loss at a 1.0102x payout, the bet has to grow by at least 99x after each loss. Surviving 2 losses at that multiplier takes 100 base bets; at 2x it takes 3. The house edge still applies to every roll, so no multiplier makes the game profitable on average.