Examples
Examples
Try the starting example
- Pool A dice
- 1
- Pool A sides
- 6
- Pool B dice
- 1
- Pool B sides
- 6
- Tie treatment: draw or a-wins
- draw
- Resolved A-win probability
- 0.416667
- Resolved draw probability
- 0.166667
- Resolved B-win probability
- 0.416667
- Expected A-sum minus B-sum
- 0
- Intrinsic equal-sum probability before tie treatment
- 0.166667
Try another scenario
- Pool A dice
- 1
- Pool A sides
- 6
- Pool B dice
- 1
- Pool B sides
- 6
- Tie treatment: draw or a-wins
- a-wins
- Resolved A-win probability
- 0.583333
- Resolved draw probability
- 0
- Resolved B-win probability
- 0.416667
- Expected A-sum minus B-sum
- 0
- Intrinsic equal-sum probability before tie treatment
- 0.166667
Calculation method
Calculation method
Resolved A-win probability
Convolve each fair sum distribution and compare every weighted outcome pair; include ties only in a-wins mode.
Resolved draw probability
Equal-sum probability in draw mode, otherwise zero.
Resolved B-win probability
Strict B-sum>A-sum probability.
Expected A-sum minus B-sum
Difference between the two exact sum means.
Intrinsic equal-sum probability before tie treatment
Probability of equal raw sums, reported independently of tie resolution.
Symbols and units
- a
- Pool A dice
- b
- Pool A sides
- c
- Pool B dice
- d
- Pool B sides
- e
- Tie treatment: draw or a-wins
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 SUM pools with the explicit tie rule. This is not an opposed success-count, keep-highest or exploding-pool model; bonuses and strategic choices are not inferred.
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.