MATHS, actually, that was me, that voted for two options, both Option 3 and 5. 5 may not be worded well. The probabilities in Chess rely on how likely it is that a player will see a particular move and act on it, as opposed to making another, less beneficial move. Chess is a combination of strategic moves and what we call "tempo moves". A "tempo move' is simply a move that keeps the game going, but adds nothing in the way of strategy to the board, and does not advance the game at all, as such.
So the likelyhood of whether a player will see a strategic move versus a tempo move and make it is what makes the game mathematical. Furthermore, as you are no doubt aware, computers are programmed to play Chess based on algorithmic formulae. I do not know the procedure, but there have been computers that have defeated reigning Chess Champions, and have been defeated by them. This would appear to indicate that the computer can be made approximately as strong as a human player.
There is yet more behind the whole math thing, but it gets very detailed, and FAR past the point of my comprehension. My maths skills probably aren't much better than about 9th Grade at this point. I always struggled with the subject.
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