I've just stumbled upon an interesting article on the Gamasutra website, which discusses the differences between probability (the chance that something will happen in the future) and statistics (comparing data about things that have already happened). One page in the article - and it's a quick read - discusses the "Gambler's Fallacy," which is when people conflate/confuse the two different concepts. Specifically, it's thinking that independent and related events are the same thing when in fact they're quite different.
Page 3 discusses how to calculate probability, while page 4 discusses the Gambler's Fallacy.
http://www.gamasutra.com/view/feature/130218/statistically_speaking_its_...
I figure this would be useful reading, along with the rest of the article, for those of us who enjoy creating games that use shuffled cards or thrown dice (which, I can PREDICT, is a lot of us).
Hope this is useful info! :)
EDIT: Oh, nice. Another of Tyler Sigman's probability articles, which uses a specific board game example to demonstrate calculations.
http://www.gamasutra.com/view/feature/131908/plundering_the_seas_of_prob...
