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Outcome counts, probabilities, dice, cards, combinations and expected-value models. 20 tools with purposes, formulas and worked examples.

Simple mode uses starting defaults for extra scenario controls. Advanced exposes those controls where available. Change an entry, then press Calculate.

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All 20 tools: purposes and formulas

Equally likely favorable probability — Use the labeled measurements to calculate equally likely favorable probability.
A ÷ B (A, B, C refer to the labeled entries)
Probability as percentage — Use the labeled measurements to calculate probability as percentage.
A × B (A, B, C refer to the labeled entries)
Complement event probability — Use the labeled measurements to calculate complement event probability.
A − B (A, B, C refer to the labeled entries)
Two independent event probability — Use the labeled measurements to calculate two independent event probability.
A × B (A, B, C refer to the labeled entries)
Expected success count — Use the labeled measurements to calculate expected success count.
A × B (A, B, C refer to the labeled entries)
Two-dice ordered outcome count — Use the labeled measurements to calculate two-dice ordered outcome count.
A × B (A, B, C refer to the labeled entries)
Two-stage independent draw choices — Use the labeled measurements to calculate two-stage independent draw choices.
A × B (A, B, C refer to the labeled entries)
Distinct ordered pairs without replacement — Use the labeled measurements to calculate distinct ordered pairs without replacement.
A × B (A, B, C refer to the labeled entries)
Unordered selections — Use the labeled measurements to calculate unordered selections.
n! / [r!(n−r)!] (A, B, C refer to the labeled entries)
Average game score — Use the labeled measurements to calculate average game score.
A ÷ B (A, B, C refer to the labeled entries)
Observed game win rate — Use the labeled measurements to calculate observed game win rate.
A ÷ B × 100 (A, B, C refer to the labeled entries)
Probability-weighted gross payout — Use the labeled measurements to calculate probability-weighted gross payout.
A × B (A, B, C refer to the labeled entries)
Expected net after stake — Use the labeled measurements to calculate expected net after stake.
A − B (A, B, C refer to the labeled entries)
Equal prize-pool split — Use the labeled measurements to calculate equal prize-pool split.
A ÷ B (A, B, C refer to the labeled entries)
Tokens used over rounds — Use the labeled measurements to calculate tokens used over rounds.
A × B (A, B, C refer to the labeled entries)
Whole rounds from token budget — Use the labeled measurements to calculate whole rounds from token budget.
floor(A ÷ B) (A, B, C refer to the labeled entries)
Game session length — Use the labeled measurements to calculate game session length.
A × B (A, B, C refer to the labeled entries)
Category share of deck — Use the labeled measurements to calculate category share of deck.
A ÷ B × 100 (A, B, C refer to the labeled entries)
Observed event frequency — Use the labeled measurements to calculate observed event frequency.
A ÷ B (A, B, C refer to the labeled entries)
Favorable-to-unfavorable count ratio — Use the labeled measurements to calculate favorable-to-unfavorable count ratio.
A ÷ B (A, B, C refer to the labeled entries)

Definitions and source references

Unit definitions and selected model references:

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