The Iowa Gambling Task is used to demonstrate our intuition with statistics and probability.
Essentially the subject sits in front of four decks. Each round, the participant can draw from any deck of her choosing. Each deck produces "wins" or "losses" along different probabilities. (Maybe the wins/losses vary in magnitudes, but let's simplify to the binary win/loss here). The goal is to maximize your wins (presumably by sampling from each deck to identify the deck with the best odds, then draw exclusively from that deck).
It's described more fully here: http://en.wikipedia.org/wiki/Iowa_gambling_task
One of the interesting things about this task is that most people fall into a pretty good intuitive strategy, even if they couldn't formalize what they're doing.
Just how hard is it to formalize an optimal approach here? Has anyone rigorously tackled this? (The research on the problem I can find so far is about childhood development and psychology, not mathematics, maybe it's been covered, I'm not sure.)
It's an interesting problem because seems to involve a few areas of mathematics, optimal stopping theory (for how long to sample): http://en.wikipedia.org/wiki/Optimal_stopping
And maybe something about statistical confidence. If you've drawn from one deck three times and it pays out 2/3, that should impact your decisions differently than if you had drawn from a deck 300 times and seeing it pay out 2/3.
Any ideas on ways to tackle this more rigorously?