ListFan
Calculators · Free

Dice-pool success probability

Plan success thresholds for tabletop dice pools.

01Enter your values

Runs in your browser

Runs offline in your browser. Once the page and required files have loaded, processing needs no internet.

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Example
%

How it works

Plan success thresholds for tabletop dice pools.

P(S=s)=C(n,s)pˢ(1−p)ⁿ⁻ˢ; R|S=s ~ Binomial(min(n−s,r),p); X=S+R

Runs in your browser

Discovery source

Your data stays yours

Inputs are processed on this page and are never sent to a server.

About this tool

Plan success thresholds for tabletop dice pools.

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Use tool ↑

How to use it

  1. Enter your values

    Dice · Success per die · Required successes · Failed dice rerolled once, at most

  2. Calculate / generate

    Plan success thresholds for tabletop dice pools.

  3. Result

    At least the threshold: 50 % Exactly the threshold: 31.25 % Expected successes: 2.5

Calculation method

  1. Combine independent Bernoulli rolls, then condition on each initial success count.
  2. Reroll up to the chosen number of failed dice once.
  3. The table lists the full final distribution.
P(S=s)=C(n,s)pˢ(1−p)ⁿ⁻ˢ; R|S=s ~ Binomial(min(n−s,r),p); X=S+R
Example scenario

Dice-pool success probability

Dice
5
Success per die
50 %
Required successes
3
Failed dice rerolled once, at most
0
Result
At least the threshold: 50 %
Exactly the threshold: 31.25 %
Expected successes: 2.5

Frequently asked questions

Limits and key assumptions

Identical independent dice, fixed success chance, 1–200 dice. No exploding dice, repeated rerolls or game win prediction. Enter 50 for 50%, not 0.5.

Where does my data go?

Calculations run on your device. Form inputs are not sent to a server.

Terms and definitions

Enter your values

Dice

Reroll up to the chosen number of failed dice once.

Enter a whole number; fractional counts are not valid.

Minimum: 1 · Maximum: 200

Success per die

Combine independent Bernoulli rolls, then condition on each initial success count.

Enter a percentage, not its decimal fraction: 50 means 50%. Use the unit shown beside this field. %

Minimum: 0 · Maximum: 100 %

Required successes

Enter a whole number; fractional counts are not valid.

Minimum: 0 · Maximum: 200

Failed dice rerolled once, at most

Reroll up to the chosen number of failed dice once.

Enter a whole number; fractional counts are not valid.

Minimum: 0 · Maximum: 200

Result

Result

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

At least the threshold

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

Exactly the threshold

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

Expected successes

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

Value

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

Unit

Combine independent Bernoulli rolls, then condition on each initial success count. Reroll up to the chosen number of failed dice once. The table lists the full final distribution.

Calculated from your entries using the method below.

Common mistakes and quick fixes

Success per die

Mistake: Entering 0.5 when you mean 50%.

Fix: Enter 50 for 50%; 0.5 represents 0.5%.

Limits and key assumptions

Mistake: Treating a result as valid outside the described scope.

Fix: Identical independent dice, fixed success chance, 1–200 dice. No exploding dice, repeated rerolls or game win prediction. Enter 50 for 50%, not 0.5.

Limits and key assumptions

  • Identical independent dice, fixed success chance, 1–200 dice. No exploding dice, repeated rerolls or game win prediction. Enter 50 for 50%, not 0.5.
  • Displayed results may be rounded; rounding does not add measurement precision.

More tools

All tools