A Bayesian would take the opposite approach - roll the dice, and keep the one that rolls twenty twice in a row. Because no die is perfect, a die that rolled two twenties is has a slightly higher probability of being favourably loaded, and so his posterior probability of rolling twenties with the ‘twenty-rollers’ is a bit better than with all his other dice.

So theoretically, imperfections in the manufacturing of a particular 20 sided die could favor a specific number (or avoid rolling a 1, etc…). Of course, statistically speaking, you’d have to have a large sample set, and if you had 1000 dice, you’d have to do millions and millions of rolls before you figured out which ones didn’t roll a 1 very often.

The Gambler’s Fallacy is funny though, especially at the blackjack table. Good players know the basic strategy by heart and so when someone doesn’t play by basic strategy, they can still see what the next cards that come out are and will often blame the person not playing by basic strategy for losses. However, a person hitting or staying has just as much a chance of helping as hurting… I guess people just notice the bad results better.

that wiki entry you linked notes that there are some things that try ot trick you into thinking the Gambler’s Fallacy applies when in fact it does not. An example of this is the Monty Haul problem.

The short response is, “Lady Luck has no memory.”