Author Archives: possiblywrong

Another dice puzzle

Introduction The dice game craps is played by repeatedly rolling two six-sided dice, and making various wagers on the outcomes of the sequence of rolls. The details of the wagers don’t concern us here– instead, let’s consider just one particular … Continue reading

Posted in Uncategorized | Leave a comment

Tracking a card through a shuffled deck

Introduction Riffle shuffle a deck of cards once. What is the probability that the original top card ends up on the bottom of the shuffled deck (or vice versa)? This is very unlikely… but suppose that we shuffle again… and … Continue reading

Posted in Uncategorized | 4 Comments

A different sock matching problem

When I take a load of laundry from the dryer, there are socks mixed in with all of the other clothes. Suppose that there are pairs of socks, socks in total, that I match and fold by randomly drawing one … Continue reading

Posted in Uncategorized | 9 Comments

The hot hand

The wager described in the previous post was motivated by an interesting recent paper (Miller and Sanjurjo, reference below) discussing the hot hand, or the perception in some sports, particularly basketball, that a player with a streak of successful shots … Continue reading

Posted in Uncategorized | Leave a comment

Gambler’s fallacy fallacy?

The gambler’s fallacy is the belief that roulette wheels, dice, etc., have “memory,” so that, for example, having observed an unlikely streak of losses, the probability that the next outcome will be a win has increased, as a correction toward … Continue reading

Posted in Uncategorized | 10 Comments

Reproducing randomness

Introduction We often need “random” numbers to simulate effects that are practically non-deterministic, such as measurement noise, reaction times of human operators, etc. However, we also need to be able to reproduce experimental results– for example, if we run hundreds … Continue reading

Posted in Uncategorized | Leave a comment

The distribution of “roll and keep” dice

Introduction Some role-playing games involve a “roll and keep” dice mechanic, where you roll some number of dice, but only “keep” a specified number of them with the largest values, where the result of the roll is the sum of … Continue reading

Posted in Uncategorized | Leave a comment