[quote name=\'clemon79\' post=\'255348\' date=\'Jan 22 2011, 08:45 PM\']The guy could have answered every question right and controlled where all of the cards went. I think you would be extremely hard pressed to find a shuffle of the cards which, if one player gets to draw and assign every card (save for the first three, of course), can't be assigned in such a way that the player ends up winning the round, if indeed such a permutation exists. (And if it does, your next task is to prove to me that there are enough of them so as to be statistically significant...say, convince me that it could happen 0.01% of the time, making it likely to happen in at least one round of a 65-episode season.)[/quote]

I got bored while watching the Steelers mop the floor with the Jets on Sunday evening and wrote a monte carlo simulator. After numerous tweaks of the strategy during the week, I got up to a 99.7% win rate. For one run with 10,000 simulations, 9 of the 29 losses were the result of one or both opponents starting with an ace followed by multiple face cards off the top of the deck (a scenario which is impossible to win AFAICT), so that gives a conservative estimate of 0.1% of games that were unwinnable. I'm reasonably sure that at least some of the others couldn't be won either, but I didn't feel like sorting through all the possibilities. The rest looked like cases of bad luck - the algorithm made the right move for the situation, but that move turned out to be a bad idea in hindsight.

If you use the 0.29% loss rate I found and 130 rounds a season with three players, that works out to one game every 2.65 seasons where a person with a very good strategy and 100% skill on the buzzer won't win a game.