This is fun, we're having fun... Anyways "Bruce" and I were flying back from a recent playing trip. On the plane we of course brought a deck of cards to mess around and burn some time. At some point somehow the following question got brought up:
Given a completely random shuffled deck of cards. What are the odds you will draw ANY QUAD within the first half of the deck (re: 26 cards)? Not quads or better, no, just QUADS of any rank.
When we were younger we made up all kinds of card games. One of them we called "4 best." It's a 2 person poker variant. You randomly shuffle, get half the deck each, and make 4 five card poker hands. You set your hands and then compare one at a time, with each being worth different points. Hand 1 worth 1 point, 2 worth 2, etc, etc, up to Hand 4 worth 4 points. So clearly there was also strategy as to which points to go after (usually 4 and 2, but if someone knew that they could counter). During our fun of making this game up and playing it occurred to me that I almost always had a straight flush or quads. For some reason I feel like this might be influencing my rational, but none the less... I really wish I could remember more of the conversation and math we tossed back and forth, but it was unfortunately a couple weeks prior and I forgot to post this when we got home... as we made a bet on it =).
I figured since I've seen a bunch of these pop up as fun little math exercises I'd push it out to the masses to have some fun with. Please put any answers in spoilers, to not spoil the fun for others that want to take a guess and check back later!
Playing it correctly means you've already won.