@tygxc, you act like you are playing casual chess whenever discussing anything. Try to read and understand what has been said rather than acting as if it is all the enemy!
Ramanujan's series, or even 4 * (1 - 1/3 + 1/5 - 1/7 + ...), permits you to find, say, the 1000,000th decimal digit of pi, with no uncertainty. A Monte Carlo estimation does not even achieve this, even for the first decimal digit.
That's a difference.
In the case of solving chess, a valid mathematical method will conclude the value of chess is some value from the set {0, 1/2, 1} with no uncertainty.
A hypothetical Monte Carlo method (none has been suggested) could only conclude that the value of chess is some value from the set {0, 1/2, 1} with probability p, where p is some value that is strictly less than 1.
Monte Carlo techniques can be the best tool when high confidence suffices (rather than certainty). When certainty is required, they are useless.
A Monte Carlo simulation can sometimes give answers with very high confidence. People are often willing to ignore a low probability of being wrong. Mathematical proofs are not one of those purposes: they require certainty.
@12609
Your Ramanujan series, or 4*arctan(1), or the Wallis product also only approximate pi for any finite number of steps.
actually no 4*arctan(1) is proven to be equal to pi.
you again mistake deductive equivalence with statistical estimation methods.
Do you agree that the number of possible chess games is at least 10^29241 according to a Monte Carlo simulation is a proof?
nobody agrees with that lmfao, not even the authors. thats why they called it an estimation and a simulation.