[WildTurkey]

The answer for fifty heads out of fifty coins is easy and you've already given it. One chance in 2**50. That is, impossible.

Hmm. You agreed that MY coin toss sequence had the same odds. Therefore it was "IMPOSSIBLE" for me to toss it but I did. I did the impossible, according to you.

[bvw]

Here stop the gedunken experiments -- which are perhsps too confusing for you. Report to the "Probability and Statistics 101" Lab right now! Bring some whiskey, food, pj's, a blankie and your favorite pillow. Don't forget the dental floss.

At the lab, take 20 coins, only 20 eh? I'm trying to keep this to your puny human lifetime. A favor it is!

Label them 1,2,3, through 20 so we can place them into that nice "HTHTH HTHTH ..." sequence you gave above. Now start tossing. Let us know when you hit the pattern. Okay?