Examples
Examples
Try the starting example
- Mutually exclusive turn outcomes: name, probability, then resource yields in declared label order
- None,0.5,0,0 Wood,0.25,2,0 Mine,0.25,0,1
- Resource labels in yield-column order, joined by |
- Wood|Ore
- Independent identical turns
- 4
- Expected resources after supplied turns
- Wood: 2; Ore: 1
- Resource variances after supplied turns
- Wood: 3; Ore: 0.75
- Distinct resource-pair covariances after supplied turns
- Wood/Ore: -0.5
- Expected sum of resource units
- 3
- Variance of summed resource units
- 2.75
Try another scenario
- Mutually exclusive turn outcomes: name, probability, then resource yields in declared label order
- None,0.5,0,0 Wood,0.25,2,0 Mine,0.25,0,1
- Resource labels in yield-column order, joined by |
- Wood|Ore
- Independent identical turns
- 8
- Expected resources after supplied turns
- Wood: 4; Ore: 2
- Resource variances after supplied turns
- Wood: 6; Ore: 1.5
- Distinct resource-pair covariances after supplied turns
- Wood/Ore: -1
- Expected sum of resource units
- 6
- Variance of summed resource units
- 5.5
Calculation method
Calculation method
Expected resources after supplied turns
Turns×sum(outcome probability×resource yield), using exact six-decimal integer moments.
Resource variances after supplied turns
Turns×(E[y²]−E[y]²), evaluating the difference with exact integer numerators before conversion.
Distinct resource-pair covariances after supplied turns
Turns×(E[yi×yj]−E[yi]E[yj]); mutually exclusive turn outcomes may create negative covariance.
Expected sum of resource units
Sum resource means, only meaningful as a count when units are comparable.
Variance of summed resource units
Sum every covariance-matrix entry, including off-diagonal terms twice.
Symbols and units
- a
- Mutually exclusive turn outcomes: name, probability, then resource yields in declared label order
- b
- Resource labels in yield-column order, joined by |
- c
- Independent identical turns
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- A supplied finite mutually exclusive resource-outcome model repeated independently across turns. Probabilities and yields use at most six decimal places. Covariance is retained; no actual board layout, player strategy or resource prices are 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.