Examples
Examples
Try the starting example
- Independent dice
- 4
- Fair sides
- 6
- A roll succeeds at/above face
- 5
- Additional rerolls of FAILED rolls only
- 1
- At-least final successful dice query
- 3
- Final single-die success probability
- 0.555556
- Probability successful-dice count reaches query
- 0.400091
- Final successful-dice-count distribution
- 0: 0.0390184423106; 1: 0.195092211553; 2: 0.365797896662; 3: 0.304831580552; 4: 0.0952598689224
- Expected successful dice
- 2.222222
- Successful-dice-count variance
- 0.987654
Try another scenario
- Independent dice
- 4
- Fair sides
- 6
- A roll succeeds at/above face
- 5
- Additional rerolls of FAILED rolls only
- 0
- At-least final successful dice query
- 3
- Final single-die success probability
- 0.333333
- Probability successful-dice count reaches query
- 0.111111
- Final successful-dice-count distribution
- 0: 0.197530864198; 1: 0.395061728395; 2: 0.296296296296; 3: 0.0987654320988; 4: 0.0123456790123
- Expected successful dice
- 1.333333
- Successful-dice-count variance
- 0.888889
Calculation method
Calculation method
Final single-die success probability
1−(failure faces/sides)^(1+additional rerolls); successful dice stop rolling.
Probability successful-dice count reaches query
Binomial tail using exact rational final single-die probability.
Final successful-dice-count distribution
Exact binomial count weights for independent dice after each die’s permitted failure rerolls.
Expected successful dice
Dice count×final per-die success probability.
Successful-dice-count variance
Exact count variance, without assuming failed dice are rerolled indefinitely.
Symbols and units
- a
- Independent dice
- b
- Fair sides
- c
- A roll succeeds at/above face
- d
- Additional rerolls of FAILED rolls only
- e
- At-least final successful dice query
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Independent fair dice, rerolling each failed die up to the supplied additional limit and stopping it on first success. Reroll-all, exploding, shared reroll pools and success-counting-per-attempt are different rules.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.