Dice odds · 1% house edge
24.75% dice odds: 4x payout, streaks and bankroll
Every number on this page is calculated for a 24.75% win chance at a 1% house edge unless a table says otherwise. A win pays 4x, you lose 75.25% of rolls, and a run of 20 losses in a row starts about once every 1,188 rolls.
Payout and targets
- Payout multiplier
- 4x
- 99 ÷ 24.75
- Roll under
- < 24.75
- Bet low wins below this
- Roll over
- > 75.25
- Bet high wins above 100 − 24.75
- Win / loss chance
- 24.75% / 75.25%
- 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 24.75% 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% | 4.0404x | 1.0000 |
| 1% | 4x | 0.9900 |
| 2% | 3.9596x | 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 24.75%, 5 losses in a row is 1 in 4.14, while 50 in a row is 1 in 1,495,116.
| 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 | 24.13% | 1 in 4.14 | 13 | over 99.99% | over 99.99% |
| 10 in a row | 5.82% | 1 in 17 | 65 | over 99.99% | over 99.99% |
| 15 in a row | 1.4% | 1 in 71 | 284 | over 99.99% | over 99.99% |
| 20 in a row | 0.339% | 1 in 295 | 1,188 | 99.98% | over 99.99% |
| 25 in a row | 0.082% | 1 in 1,223 | 4,936 | 86.81% | over 99.99% |
| 30 in a row | 0.02% | 1 in 5,068 | 20,471 | 38.64% | 99.24% |
| 40 in a row | 1.1e-3% | 1 in 87,044 | 351,690 | 2.8% | 24.75% |
| 50 in a row | 6.7e-5% | 1 in 1,495,116 | 6,040,867 | 0.165% | 1.64% |
Exact counts over a fixed number of rolls are on the loss streak calculator.
Winning streaks
The same math with the 24.75% win chance. Positive progressions such as Paroli depend on these streaks, and the house edge is already inside the 4x 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 | 6.13% | 1 in 16 | 20 | over 99.99% | over 99.99% |
| 3 in a row | 1.52% | 1 in 66 | 86 | over 99.99% | over 99.99% |
| 4 in a row | 0.375% | 1 in 267 | 353 | over 99.99% | over 99.99% |
| 5 in a row | 0.093% | 1 in 1,077 | 1,430 | 99.91% | over 99.99% |
| 6 in a row | 0.023% | 1 in 4,351 | 5,780 | 82.27% | over 99.99% |
Martingale recovery
A recovery progression multiplies the bet after each loss so that one win pays back the run. At a 4x payout the smallest multiplier that does this is 1.3333x, which is 1 + 1 ÷ (payout − 1). With it, a win after any number of losses ends the cycle 3 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 1.3333x 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 1.3333x | Bankroll at 1.5x | Cycle result at 1.5x |
|---|---|---|---|
| 5 | 9.64 | 13.19 | +9.59 |
| 10 | 50.27 | 113.3 | +59.67 |
| 15 | 221.5 | 873.8 | +439.9 |
| 20 | 943 | 6,649 | +3,327 |
| 30 | 16,796 | 383,500 | +191,753 |
| 40 | 298,309 | 22,114,663 | +11,057,334 |
What this chance is used for
24.75% is the 4x chance at a 1% edge, a win roughly one roll in four.
It is a middle ground for progression players: a win covers three losing bets, so the minimum recovery multiplier is about 1.33, and a loss streak of 15 is much less common than at the 5x chance.
The house edge applies at every chance, so none of these settings has a positive expected return.
FAQ
What does a 24.75% win chance pay in dice?
At a 1% house edge a 24.75% chance pays 4x (99 divided by 24.75). You win when the roll is under 24.75, or over 75.25 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 24.75%?
Any given 20 rolls all lose with probability 0.339% (1 in 295). Such a streak starts on average once every 1,188 rolls, so the chance of seeing at least one is 99.98% within 10,000 rolls and over 99.99% within 100,000 rolls.
How much bankroll does martingale need at 24.75%?
To win back every loss at a 4x payout, the bet has to grow by at least 1.3333x after each loss. Surviving 20 losses at that multiplier takes 943 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.