Dice odds · 1% house edge
2% dice odds: 49.5x payout, streaks and bankroll
Every number on this page is calculated for a 2% win chance at a 1% house edge unless a table says otherwise. A win pays 49.5x, you lose 98% of rolls, and a run of 200 losses in a row starts about once every 2,793 rolls.
Payout and targets
- Payout multiplier
- 49.5x
- 99 ÷ 2
- Roll under
- < 2
- Bet low wins below this
- Roll over
- > 98.00
- Bet high wins above 100 − 2
- Win / loss chance
- 2% / 98%
- 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 2% 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% | 50x | 1.0000 |
| 1% | 49.5x | 0.9900 |
| 2% | 49x | 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 2%, 25 losses in a row is 1 in 1.66, while 750 in a row is 1 in 3,805,776.
| 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 | 60.35% | 1 in 1.66 | 33 | over 99.99% | over 99.99% |
| 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% |
| 400 in a row | 0.031% | 1 in 3,233 | 161,587 | 6% | 46.14% |
| 500 in a row | 4.1e-3% | 1 in 24,376 | 1,218,749 | 0.817% | 7.88% |
| 750 in a row | 2.6e-5% | 1 in 3,805,776 | 190,288,753 | 5.3e-3% | 0.053% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 2% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 49.5x 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 | 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% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 49.5x payout the smallest multiplier that does this is 1.0206x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 48.5 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 1.0206x and for 1.05x. The last column is where the cycle stands if the win comes right after those N losses at 1.05x.
| Losses survived | Bankroll at 1.0206x | Bankroll at 1.05x | Cycle result at 1.05x |
|---|---|---|---|
| 25 | 32.28 | 47.73 | +116.5 |
| 50 | 86.06 | 209.3 | +346.8 |
| 100 | 324.8 | 2,610 | +3,768 |
| 200 | 2,825 | 345,832 | +492,859 |
| 300 | 22,071 | 45,479,903 | +64,808,910 |
| 500 | 1,310,557 | 7.86e11 | +1.12e12 |
What this chance is used for
At 2% the payout is 49.5x, so one win covers 48.5 base bets of losses.
Players who find 1% too slow often move here: wins come about every 50 rolls on average, half as long a wait, while dry spells of a few hundred rolls still happen many times in a long session.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 2% win chance pay in dice?
At a 1% house edge a 2% chance pays 49.5x (99 divided by 2). You win when the roll is under 2, or over 98.00 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 200 times in a row at 2%?
Any given 200 rolls all lose with probability 1.76% (1 in 57). Such a streak starts on average once every 2,793 rolls, so the chance of seeing at least one is 97.21% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 2%?
To win back every loss at a 49.5x payout, the bet has to grow by at least 1.0206x after each loss. Surviving 200 losses at that multiplier takes 2,825 base bets; at 1.05x it takes 345,832. The house edge still applies to every roll, so no multiplier makes the game profitable on average.