The answer is 25. Almost nobody got it on the intuitive guess, but more than half of you got it after doing the math. I screened a couple of comments at first, since they gave the answer away, but I'll unscreen them now-- they give a good description of how it works. If you're not pretty well versed in probability, the answer is completely non-intuitive.
This was slightly reworded from a problem on rec.gambling.poker. My first guess was 24.