probability is hard

"Every time you shuffle a deck of playing cards, it's likely that you have come up with an ordering of cards that is unique in human history."

an old (1877) mechanical device that calculates bayesian inference with bins of beads

describes the Elo and TrueSkill competitive ranking systems

"Given two games, each with a higher probability of losing than winning, it is possible to construct a winning strategy by playing the games alternately."

quasi-random sequences are more reliably spread out than truly random ones, and this is useful aesthetically and for monte carlo integration. closer to what people usually want when they say 'random'.

"Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes. Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope. You must now guess whether the number in the other, closed envelope is larger or smaller than the one you’ve seen.

Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?"

cards for calculus, linear algebra, abstract algebra, real analysis, probability, topology, mechanics, thermodynamics, statistical mechanics, electrodynamics, quantum mechanics.

guy presents an imperative algorithm for producing random sequences for games. instead of just zero-memory picking items, you return a shuffled sequence of items, and when that's done, reshuffle that sequence and return those.

intuitive venn diagrams

a nice visualization