We develop a general approach to exploring how regret influences strategic interaction and risky choice. Regret is captured by the payoff gap between what a player actually gets and what he believes he would have gotten had he chosen differently. Ex post beliefs are critical to that evaluation, and the modeling therefore draws on tools from psychological game theory. Predictions depend in novel ways on the information structure across end-nodes and assumptions regarding the precise nature of Chance moves. Regret can have a powerful impact in a variety of economic settings including education, delegation, gambling, and market entry.