Tight-Tight play problem

[MickeyHoldem]

Tight Timmy never plays or continues a hand if there is any chance that he is behind!! When Timmy takes a flop, what are the chances he continues to the turn? river? and showdown?

[XChamp]

Pretty slim he makes it to the river. Maybe 1/20,000 hands? Just an estimate. Figure he gets AA 1/221 hands and flops a set or quads 1/25 times. So about 1/8000 (estimate) hands he makes it to the turn. I dont really feel like factoring in straight or flush possibilities. This is a really hard problem.