[bachfan]

[ QUOTE ]

Under monte carlo, once the code is fast enough, it doesn't really matter too much if you make it twice as fast. You'll get close to the exact value quickly, but you'll never get the exact value. Said another way, doubling the number of evals won't double the convergence of the result. There are also issues of what sort of RNG you use, and equally important how you use it. Getting the RNG problem wrong can mean that your monte carlo simulations converge to the wrong result.

[/ QUOTE ]

I'd just like to echo that an elaborate a bit. While computing exact results is very satisfying (and has a certain "gee whiz" appeal), in my case generating a fast exhaustive algorithm was a lot easier than generating a fast monte-carlo algorithm. Fortunately, it doesn't matter a lot in practice, at least not for me, because in almost all cases it is pretty easy to converge on a useful result.

There's another point I'd like to raise here - perhaps some other programmer types have some thoughts.

In developing propokertools, one of the biggest challenges has been generating random hands for monte carlo simulations such that the results correctly approach the same results from an exhaustive simulation. Now, I am fairly confident my algorithms work, and I have automated tests to "prove" it, but there are some situations (most of them academic and not useful in practice) where the random hand generation gets really bogged down. I don't want to get into too many technical details as that isn't my point (get to it, bachfan!). My point is, there may be a tradeoff to be made in certain situations between "correctness" and speed. In fact, you can think of monte-carlo as just such a tradeoff. There may well be some psycho-fast algorithm out there that is almost-but-not-quite-entirely-correct that, for purposes of mass generation (ie, for creating a bot using neural networks or whatever), might be the right way to go.

Just a thought, (babbling now)
bachfan