Dice odds · 1% house edge
1% dice odds: 99x payout, streaks and bankroll
Every number on this page is calculated for a 1% win chance at a 1% house edge unless a table says otherwise. A win pays 99x, you lose 99% of rolls, and a run of 300 losses in a row starts about once every 1,939 rolls.
Payout and targets
- Payout multiplier
- 99x
- 99 ÷ 1
- Roll under
- < 1
- Bet low wins below this
- Roll over
- > 99.00
- Bet high wins above 100 − 1
- Win / loss chance
- 1% / 99%
- 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 1% 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% | 100x | 1.0000 |
| 1% | 99x | 0.9900 |
| 2% | 98x | 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 1%, 50 losses in a row is 1 in 1.65, while 1,500 in a row is 1 in 3,525,398.
| Streak | Chance next N all lose | Odds | Avg rolls between | At least one in 10,000 | At least one in 100,000 |
|---|---|---|---|---|---|
| 50 in a row | 60.5% | 1 in 1.65 | 65 | over 99.99% | over 99.99% |
| 100 in a row | 36.6% | 1 in 2.73 | 173 | over 99.99% | over 99.99% |
| 200 in a row | 13.4% | 1 in 7.46 | 646 | over 99.99% | over 99.99% |
| 300 in a row | 4.9% | 1 in 20 | 1,939 | 99.42% | over 99.99% |
| 500 in a row | 0.657% | 1 in 152 | 15,120 | 48.39% | 99.87% |
| 700 in a row | 0.088% | 1 in 1,136 | 113,496 | 8.43% | 58.57% |
| 1,000 in a row | 4.3e-3% | 1 in 23,164 | 2,316,257 | 0.431% | 4.23% |
| 1,500 in a row | 2.8e-5% | 1 in 3,525,398 | 352,539,659 | 2.8e-3% | 0.028% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 1% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 99x 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 | 0.01% | 1 in 10,000 | 10,100 | 62.85% | 99.99% |
| 3 in a row | 1.0e-4% | 1 in 1,000,000 | 1,010,100 | 0.985% | 9.43% |
| 4 in a row | 1.0e-6% | 1 in 100,000,000 | 101,010,100 | 0.01% | 0.099% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 99x payout the smallest multiplier that does this is 1.0102x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 98 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 1.0102x and for 1.02x. The last column is where the cycle stands if the win comes right after those N losses at 1.02x.
| Losses survived | Bankroll at 1.0102x | Bankroll at 1.02x | Cycle result at 1.02x |
|---|---|---|---|
| 50 | 64.81 | 84.58 | +179.2 |
| 100 | 172.5 | 312.2 | +397.7 |
| 200 | 648.5 | 2,574 | +2,569 |
| 300 | 1,962 | 18,962 | +18,301 |
| 500 | 15,598 | 997,778 | +957,965 |
| 1,000 | 2,513,785 | 1.99e10 | +1.91e10 |
What this chance is used for
A 1% chance pays 99x at a 1% house edge, the highest payout on this list and the usual target for long-shot hunting with a flat bet.
The average gap between wins is 100 rolls, and a run of 300 losses comes around every couple of thousand rolls, so a balance needs room for hundreds of base bets before the first hit.
Scripts that raise the bet after losses at this chance use tiny steps of 1% to 2% per loss, because anything larger grows past the balance long before a 1,000 roll drought ends.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 1% win chance pay in dice?
At a 1% house edge a 1% chance pays 99x (99 divided by 1). You win when the roll is under 1, or over 99.00 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 300 times in a row at 1%?
Any given 300 rolls all lose with probability 4.9% (1 in 20). Such a streak starts on average once every 1,939 rolls, so the chance of seeing at least one is 99.42% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 1%?
To win back every loss at a 99x payout, the bet has to grow by at least 1.0102x after each loss. Surviving 300 losses at that multiplier takes 1,962 base bets; at 1.02x it takes 18,962. The house edge still applies to every roll, so no multiplier makes the game profitable on average.