Question for BruceZ (or others) regarding streaks

[DougOzzzz]

A while ago you showed how to calculate the odds of getting 3 PP in a row any time during 1000 hands.

I'm interested in calculating the odds of getting X or more PP's in Y hands at any point over the course of Z hands. For example, use 14 as X, 100 as Y, and 1000 as Z. I know using the BINOM function in excel that the probability of getting 14 or more PP's in 100 hands is 0.002182578 or, about 458:1. How do I calculate the odds of this happening at any point over 1000 hands? 10000 hands? Etc.

Thanks.