You guys aren't allowed to use logic... that's not fair [:D]
ORIGINAL: Shades of Grey
As HansBolter state below, not a sure assumption. Warranties on computer parts are not that long and not many old computers around. And assuming unlimited time for plotting moves somewhat assumes that the players will be around when it is their turn.
Otherwise every turn based game would reduce to who lives longer, ie refuse to move
and wait for victory.
I guess my point is simply that a brute force algorithm that can explore all possible moves, then all possible counter moves, then all possible counter counter moves, etc. etc. will have the ability to pick the 'best' move on each turn of a game.
For a simple game, a human would be able to tie against this computer. Take, Tic-Tac-Toe, for example. I can write an unbeatable AI for it -- though it will tie most games against a competent human opponent.
If you allow me to do the same for chess, I can create a program that is unbeatable -- worst case a tie (let's just ignore the black vs. white thing for now.) The problem with chess, however, is that the combinations are huge compared with tic-tac-toe, so a brute force algorithm won't work unless you are willing to wait a very long time (given today's computing power.)
Tin Soliders is actually (from a combinational perspective) more complex than Chess because I move all of my pieces each turn instead of just 1. Again, if you allow me to write a brute force algorithm (randomness of dice aside), I can write an AI that is guaranteed to at least tie (or at least perform to the highest possible level given the setup, etc.)
If my PC today can process enough moves to make brute force possible for Tic-Tac-Toe, perhaps in 100 years, I can write a chess algorithm that can do the same in an acceptable amount of time. Maybe 100 years after that, I can do the same for Tin Soldiers.
Computing power has continued to double every 18 months. If that trend continues, eventually, that will all be possible.
And yes, a human could *potentially* have resources that match a computer. But, realistically, the day will come when a simple PC will have more computing resources available than a human brain. (According to Kurzeil, that should occur around 2029, I believe.) And, only 18 months later, there will be a new model with 2x that capacity. And, in just 50 years later, a computer with 2^50 (1,125,899,906,842,624) that capacity -- a combined computing power greater than all the humans that have ever lived.
Deride
P.S. I think human 'computing' capacity doesn't double every 18 months. Perhaps that should have been on my list instead. [8D]
P.P.S. There are several computers that still run after hundreds of years including Babbage's difference engine, several Chinese abacuses, etc. Though, those would all probably find WitP a bit difficult to deal with [;)]
P.P.P.S. If infinity is so huge, how come it isn't even in the class of numbers that are bigger? [X(]
