Race Odds Math: Rolls to Expect
What this page helps you decide: How many rerolls to budget before you start hunting a specific race, and whether that budget is realistic against your actual reroll income.
Every race has a published draw rate, and every draw is an independent trial, which means three questions have exact answers rather than opinions: how many rerolls it takes on average, how many give you an even chance, and how many make failure unlikely. The average is one divided by the rate. The even-odds figure is about 0.69 divided by the rate. The 90% figure is about 2.30 divided by the rate. For Human at 25.40% that is 3.9, 3 and 8 rerolls. For Lucifer at 0.20% it is 500, 347 and 1,151. Those three multiples of one over the rate are the whole model, and this page works them out for all 13 races so you can compare a hunt against your real reroll income before you commit to it.
The formulas, written out
For a draw rate p, the average number of rolls until the first hit is 1/p. This is the mean of a geometric distribution, and it is the only one of the three numbers most guides ever quote. The chance of having hit at least once in n rolls is 1 minus (1 minus p) to the power of n. Set that equal to 0.5 and solve for n and you get n equals ln(0.5) divided by ln(1 minus p), which for small rates is very close to 0.69 divided by p. Set it to 0.9 instead and you get 2.30 divided by p. Round up, because you cannot spend a fraction of a reroll. All three scale with one over the rate, which is why the whole table below is one shape repeated at different sizes.
Why the average is the most misleading of the three
The average rolls figure sounds like a target but behaves like a coin flip. At any rate, the chance of having hit by the time you reach the average is about 63%, which means roughly one hunter in three is still empty-handed at the number everyone quotes. The even-odds column is the honest planning figure: it is always smaller than the average, about 69% of it, and it is the point where your chances have genuinely tipped. The 90% column is the one to look at before committing real money or a whole season of rerolls, because it is 2.3 times the average and it is where most people find out that a 0.20% hunt is not a weekend project.
What a season of rerolls buys you
A full Battle Pass is 28 rerolls. Against the live pool, that is enough to make a common effectively certain and to give you an 80.7% chance at epic or better, since epic, legendary and mythical together make up 5.70% of the pool. It gives a 22.4% chance at any of the four mythicals, whose rates combine to 0.90%, and a 5.5% chance at one named 0.20% race. Compare that to the even-odds column: a single named mythical needs 347 rerolls, which is more than twelve seasons of pass rewards. That comparison, not a tier list, is what should decide whether you hunt a specific race or take the best thing the pool hands you.
The one number the arithmetic proves
Add all 13 published rates and you get 101.00%, which no live pool can produce. Remove Dragoon, the single race the official table itself marks Season 1, and the other 12 sum to exactly 100.00%. That is not a rounding coincidence at two decimal places across twelve figures. It is the strongest available evidence that Dragoon is out of circulation, and it is the reason every roll budget on this site is computed against a 12-race pool rather than a 13-race one.
Step-by-Step
- Take the published rate for the race you want and convert it to a decimal. Sorcerer at 2.10% becomes 0.021.
- Divide one by that number for the average rerolls. One divided by 0.021 is 47.6, so a Sorcerer hunt averages about 48 rerolls.
- Multiply the average by 0.69 for the even-odds point, the roll count at which you are as likely to have hit as not. For Sorcerer that is 33 rerolls.
- Multiply the average by 2.30 for the 90% point, where fewer than one hunter in ten is still empty-handed. For Sorcerer that is 109 rerolls.
- Multiply the average by three if you want the race at three stars, because a star ceiling of three means landing the same draw three times. Sorcerer at three stars averages 143 rerolls.
Data Tables
| Race | Rarity | Draw rate | Average rolls | Even odds | 90% sure | To three stars |
|---|---|---|---|---|---|---|
| Human | Common | 25.40% | 3.9 | 3 | 8 | 12 |
| Orc | Common | 25.40% | 3.9 | 3 | 8 | 12 |
| Goblin | Common | 24.50% | 4.1 | 3 | 9 | 12 |
| Undead | Uncommon | 13.00% | 7.7 | 5 | 17 | 23 |
| Dragonkin | Rare | 6.00% | 16.7 | 12 | 38 | 50 |
| Sorcerer | Epic | 2.10% | 47.6 | 33 | 109 | 143 |
| Fairy | Epic | 1.70% | 58.8 | 41 | 135 | 176 |
| Dragoon | Epic | 1.00% (Season 1) | 100.0 | 69 | 230 | 300 |
| Archdruid | Legendary | 1.00% | 100.0 | 69 | 230 | 300 |
| Angel | Mythical | 0.30% | 333.3 | 231 | 767 | 1,000 |
| Night Elf | Mythical | 0.20% | 500.0 | 347 | 1,151 | 1,500 |
| Demon | Mythical | 0.20% | 500.0 | 347 | 1,151 | 1,500 |
| Lucifer | Mythical | 0.20% | 500.0 | 347 | 1,151 | 1,500 |
Draw rates and rarity bands from the official Template:Races. The four right-hand columns are our arithmetic on those rates: 1/p, ln(0.5)/ln(1-p) rounded up, ln(0.1)/ln(1-p) rounded up, and 3/p. Dragoon is highlighted because the table only sums to 100.00% once it is removed.
| Band | Races | Combined rate | Average rolls for the band |
|---|---|---|---|
| Common | Human, Orc, Goblin | 75.30% | 1.3 |
| Uncommon | Undead | 13.00% | 7.7 |
| Rare | Dragonkin | 6.00% | 16.7 |
| Epic | Sorcerer, Fairy | 3.80% | 26.3 |
| Legendary | Archdruid | 1.00% | 100.0 |
| Mythical | Angel, Night Elf, Demon, Lucifer | 0.90% | 111.1 |
Dragoon excluded as Season 1. The six band rates sum to exactly 100.00%.
Tips & Notes
- Round the even-odds and 90% figures up, never down. A fraction of a reroll does not exist, and rounding down quietly understates every hunt.
- The three-star column assumes a locked slot. With the slot unlocked, a different race replaces yours and the count starts again.
- These numbers describe the pool, not your luck. Half of all hunters beat the even-odds figure and half do not, by definition.
FAQ
How many rerolls does a mythical race take in Iron Soul: Dungeon?
For a 0.20% race, 500 rerolls on average, 347 for an even chance and 1,151 before failure drops under 10%. Angel is easier at 0.30%: 333, 231 and 767.
Why do the published race odds add up to 101%?
Because Dragoon is included and it is marked Season 1. Remove it and the remaining 12 races sum to exactly 100.00%, which is the case for treating Dragoon as retired.
Does hitting the average number of rolls mean I should have the race by now?
No. At the average, about 63% of hunters have hit and 37% have not. The even-odds column, roughly 69% of the average, is the point where it becomes more likely than not.
How many rerolls to take a race from one star to three?
Two more copies, which averages twice the single-hit figure: 8 more rolls for a common, 1,000 more for a 0.20% mythical, on top of the first hit.
Sources
- Official Official Iron Soul Roblox Wiki - Template:Races — Source of all 13 draw rates and rarity bands in the tables above, and of the Season 1 marking on Dragoon. Every derived column is our own arithmetic on those rates.
- Community Iron Soul Wiki - Race Rolling — Source of the star ceiling of three and the locked-slot behaviour assumed by the three-star column.