Examples
Examples
Try the starting example
- Fair die sides
- 6
- Independent rolls
- 2
- Retain max or min
- max
- Retained result at least query
- 5
- At-least retained-result probability
- 0.555556
- Retained-result probability distribution
- 1: 0.0277777777778; 2: 0.0833333333333; 3: 0.138888888889; 4: 0.194444444444; 5: 0.25; 6: 0.305555555556
- Expected retained result
- 4.472222
- Retained-result variance
- 1.971451
Try another scenario
- Fair die sides
- 6
- Independent rolls
- 2
- Retain max or min
- min
- Retained result at least query
- 5
- At-least retained-result probability
- 0.111111
- Retained-result probability distribution
- 1: 0.305555555556; 2: 0.25; 3: 0.194444444444; 4: 0.138888888889; 5: 0.0833333333333; 6: 0.0277777777778
- Expected retained result
- 2.527778
- Retained-result variance
- 1.971451
Calculation method
Calculation method
At-least retained-result probability
Sum order-statistic counts at/above the target.
Retained-result probability distribution
For max use v^rolls−(v−1)^rolls; for min use (sides−v+1)^rolls−(sides−v)^rolls, all over sides^rolls.
Expected retained result
First moment of the exact retained-result distribution.
Retained-result variance
Exact second central moment; retain one result from all supplied rolls.
Symbols and units
- a
- Fair die sides
- b
- Independent rolls
- c
- Retain max or min
- d
- Retained result at least 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 repeated rolls, retaining exactly one maximum or minimum. This generalizes an advantage/disadvantage-style rule but does not infer a named game’s cancellation, tie or critical 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.