Applied Math
Ways to count outcomes so odds can be worked out by hand.
Start here · Essential guide
Learn the basic counting rules behind game probabilities: the product rule, the sum rule, ordered and unordered selections, with worked dice and card examples.
See how Bayes rule turns evidence into updated beliefs about hidden cards or opponent types, with a worked example using natural frequencies you can check by hand.
Understand how revealed information shrinks the sample space and changes odds, using dice and card examples with every calculation shown.
Learn how the geometric distribution models waiting time for a rare event, including the expected number of tries and the chance of going long without a success.
Learn how to tell independent events like dice rolls from dependent ones like drawing cards without replacement, with side-by-side probability calculations.
Use Pascal triangle to count how many ways repeated trials can produce a given number of successes, with coin, dice and attack-roll examples.
Learn when order matters and when it does not, using card hands and draws to show how permutations and combinations differ and how to convert between them.
Learn the complement trick for the chance of one or more hits: work out the probability of none and subtract from one, with dice, loot and card examples.
Learn to list every possible outcome before assigning probabilities, and avoid the classic mistake of treating unequal results as equally likely.
See how probabilities multiply along a chain of steps, from three sixes on dice to upgrade attempts and card draws, with each calculation checked.
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