In the complex question fallacy a question is asked that assumes or implies something that will benefit the questioner’s argument, but which has not been agreed to generally. A rhetorical technique often used in interrogation, a classic example is, “So, when did you stop beating your wife?”
Named after a common mistake made by gambler’s in thinking about probability, the gambler’s fallacy refers to the misleading idea that separate, independent events are causally related, such that the likelihood of one is increased by the occurrence of the other. For example, “The roulette wheel has landed on black twice in a row now, it’s more likely now to land on red.”
Example: Bill is playing against Doug in a WWII tank battle game. Doug has had a great “streak of luck” and has been killing Bill’s tanks left and right with good die rolls. Bill, who has a few tanks left, decides to risk all in a desperate attack on Doug. He is a bit worried that Doug might wipe him out, but he thinks that since Doug’s luck at rolling has been great Doug must be due for some bad dice rolls. Bill launches his attack and Doug butchers his forces. (via Nizkor)
A hasty generalization fallacy is committed when some conclusion is drawn based on a very limited or unfounded basis. For example, one could draw the conclusion from recent uprisings against dictatorial regimes that all countries that don’t have democratic, representative rulership structures are violent, oppressive, and need to be changed. While there may be some truth to the idea, the evidence given is not nearly strong enough to support the conclusion.