Examples
Examples
Try the starting example
- Participants: ID, whole initiative bonus, unique tie-priority number, smaller first
- A,0,1 B,0,2
- Fair die sides, same for every participant
- 6
- Probability each participant acts first
- A: 0.583333333333; B: 0.416666666667
- Expected finishing position by participant
- A: 1.41666666667; B: 1.58333333333
- Exact position distributions by participant
- A: 1=0.583333333333 / 2=0.416666666667; B: 1=0.416666666667 / 2=0.583333333333
Try another scenario
- Participants: ID, whole initiative bonus, unique tie-priority number, smaller first
- A,0,1 B,1,2
- Fair die sides, same for every participant
- 6
- Probability each participant acts first
- A: 0.416666666667; B: 0.583333333333
- Expected finishing position by participant
- A: 1.58333333333; B: 1.41666666667
- Exact position distributions by participant
- A: 1=0.416666666667 / 2=0.583333333333; B: 1=0.583333333333 / 2=0.416666666667
Calculation method
Calculation method
Probability each participant acts first
Condition on each possible own roll and count opposing rolls that act before it under score and supplied tie priority.
Expected finishing position by participant
Sum rank×probability for each participant, with first position numbered one.
Exact position distributions by participant
For each own roll convolve independent before/after indicators of other participants; sum exact integer outcome counts.
Symbols and units
- a
- Participants: ID, whole initiative bonus, unique tie-priority number, smaller first
- b
- Fair die sides, same for every participant
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 initiative rolls with fixed integer bonuses and unique supplied tie priorities. It computes position probabilities without assuming ties disappear or inferring a named game’s initiative policy.
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.