Originally Posted by Matthew Southall
Without doing any research, I'm going to guess #3.
I used to play chess a lot and I know that the number of possible games is tremendously high. I could be way off the margin here, but I think that there are about 10^50 possible chess games, since the average game lasts more than 50 moves and each additional move creates at least 10 possibilities.
I estimate that the number of grains of sand on the planet and the number of stars in the universe would both be around 10^15. Again, I could be way off the margin because I haven't done any research prior to answering this question, but that's just a rough guess.
I think that the poker all-in would be very close too. My estimate is that there are roughly 10^3 combos of hands that each player can have, so with 27 players and multiple all-in rounds, this could get very close with the chess one.
I give you the win, mostly because you are right in your thinking.
Actually, in theory, the poker scenario is the winner. It should yield roughly somewhere in the neighborhood of 15^220, and increase x 2.5^6 with each table. This of course is a rough estimate because the numbers are so large. The chess one has been said to be around 10^100 - 10^120. The truth is no one has every bothered to figure out the exact number because it is irrelevant and very time consuming. Now the poker scenario also did not take into consideration that sometimes the players will tie, and have to have more hands dealt, making the number even larger.
Sand is lowest, stars in 3rd, chess is 2nd, and poker is 1st (under 3 tables poker falls way behind chess).
With this in mind, does anybody still think there is a bot out there can can beat any better than average player? HIGHLY IMPROBABLE