Dice Pool Odds & Minimum Pool Calculator
Enter your current dice pool and success rule to see the chance of meeting the target. The reverse result tells you the smallest starting pool that reaches your chosen chance.
Chance of enough successes47.18%
- Minimum dice for desired chance
- 9
- Expected successes
- 1.5
- Chance of exactly the required successes
- 30.87%
- Benefit of one additional die
- 10.8%
Success distribution
| Successes | Exactly this many | This many or more |
|---|---|---|
| 0 | 16.81% | 100% |
| 1 | 36.01% | 83.19% |
| 2 | 30.87% | 47.18% |
| 3 | 13.23% | 16.31% |
| 4 | 2.84% | 3.08% |
| 5 | 0.24% | 0.24% |
| 6 | 0% | 0% |
| 7 | 0% | 0% |
Assumes fair, independent dice. An explosion counts as one success, then rolls again without a limit.
How to use this calculator
- Enter the number of dice you have and choose the die size used for every die.
- Set the lowest face that counts as a success and the number of successes required.
- Choose whether failures reroll once and whether a maximum face explodes.
- Enter a desired chance to find the smallest pool that meets it.
How dice-pool success odds are calculated
A success-counting dice pool asks whether enough individual dice meet a threshold. With a d10 that succeeds on 8 or higher, each ordinary roll has a 3 in 10 chance of a success. For five dice needing two successes, the question is not about their total; it is whether at least two of the five results are 8, 9, or 10.
Let S be sides per die, T the success threshold, n the starting dice, and K the required successes. Before rerolls, failures have probability f = (T − 1) / S. With no explosion, successes have probability a = (S − T + 1) / S. With maximum-face explosions, ordinary successes have probability a = (S − T) / S and an exploding success has probability e = 1 / S.
If failures reroll once, each failed roll gets one identical second roll. The effective probabilities become f′ = f², a′ = a(1 + f), and e′ = e(1 + f). The probability-generating function for one starting die is G(z) = (f′ + a′z) / (1 − e′z). Raising it to the pool size gives Hₙ(z) = G(z)ⁿ. The coefficient of zᵏ is the exact chance of k successes, and the displayed target chance is 1 − Σ[zᵏ]Hₙ(z) for k from zero through K − 1.
What changes the result most
The threshold is usually the biggest lever because it changes every die's chance of success. Adding dice helps most when the current pool is close to the required number of successes; a die added to a pool that is already almost certain to pass has less room to help. A failure reroll is stronger when failures are common. Maximum-face explosions add a geometric tail, so a pool can score more successes than its starting number of dice.
How the minimum pool is found
The calculator evaluates starting pools from one through 500 and returns the first one whose cumulative chance is at least the desired percentage. It retains the full exploding tail when calculating each displayed count rather than treating an explosion as only one extra roll. If no pool through 500 reaches the request, the result says more than 500 instead of implying that a smaller pool works.
What this calculator leaves out
This model uses fair, independent dice of one size and a success-on-or-above threshold. It does not model botches, canceled or automatic successes, mixed dice, opposed pools, keep-highest rules, adding face values, or game-specific explosion triggers. Check your game's wording before treating its reroll or explosion rule as the one modeled here.
Worked example
With five d10s, a success on 8 or higher, no rerolls, and no explosions, each die succeeds with probability 0.3. The chance of at least two successes is 1 − [0.7⁵ + 5 × 0.3 × 0.7⁴], or 47.178%. The exact chance of two successes is 10 × 0.3² × 0.7³, or 30.87%.
For a 75% target under the same rule, eight dice give about 74.47%, while nine give about 80.47%. The minimum pool result is therefore nine dice.
Common questions
How many dice do I need for a 75% or 90% chance?
Enter the required successes and choose 75% or 90% as the desired chance. The calculator tests each starting pool from one upward and returns the first pool that reaches the target. The answer depends on the die size, success threshold, and whether rerolls or explosions apply.
What is the difference between counting successes and adding dice totals?
In a success-counting pool, every die at or above a threshold contributes one success, and only the number of successes matters. A total-based roll adds face values together instead, so it has a different distribution and needs a different calculator. An exploding success in this tool adds one success, not the face value of the die.
How do exploding successes change dice-pool odds?
A maximum face counts as a success and generates another full roll, which can itself explode. This creates an infinite but rapidly shrinking tail, so one starting die can produce several successes. The tool accounts for that chain rather than capping it at a fixed number of extra rolls.
How does rerolling failures once change the effective success chance?
A failure gets one additional chance, while a second failure stops. For a non-exploding die whose normal success chance is p, the effective success chance is p plus (1 − p) times p. The reroll also applies to a failed roll generated after an explosion, but never more than once to that roll.
Can an exploding pool score more successes than its starting number of dice?
Yes. Every maximum face adds a success and another roll, so even a one-die pool can continue producing successes. The chance becomes smaller for each additional success, but it never becomes exactly zero under an unlimited explosion rule.