Explain Monte Carlo

Playing around with Pokerstove tonight before bed. What is the difference in the "Enumerate all" and "Monte Carlo"?

This a statistical type deal.


With enumarate all it will go through all possible boards and calculate your odds of winning. So it will actually create every board and evaluate your hand against it.

Monte Carlo means to take a sampling of boards and calculate your equity with just the sample. If you take enough samples the results will approach the true rate that the exhaustive solution (enumarte all) would take. The key is you can take many samples quicker and arrive at answers that are very very close to the true answer..

I hope this makes sense. Monte carlo type solutions are used when an exhaustive type solution would be very slow and a close enough answer is good enough.

Originally Posted by smoothdaddy

Monte carlo type solutions are used when an exhaustive type solution would be very slow and a close enough answer is good enough.

If you run the stove comparing 2 or more ranges against other ranges, the "enumerate all" option will attempt to crank through several hundred million possibilities - even billions, if the ranges are large enough and enough players are in the comparison.

My computer can run about 30 million combinations in 10 seconds, and that's enough to be within about .1% even on complicated comparisons.

Monte Carlo means setting up a matrix of the millions of comparisons possible and using a randomness function to choose which to do.

Originally Posted by Robb

Originally Posted by smoothdaddy

Monte carlo type solutions are used when an exhaustive type solution would be very slow and a close enough answer is good enough.

If you run the stove comparing 2 or more ranges against other ranges, the "enumerate all" option will attempt to crank through several hundred million possibilities - even billions, if the ranges are large enough and enough players are in the comparison.

My computer can run about 30 million combinations in 10 seconds, and that's enough to be within about .1% even on complicated comparisons.

Monte Carlo means setting up a matrix of the millions of comparisons possible and using a randomness function to choose which to do.

The gist of the previous answers is correct. Monte Carlo means that, instead of going through all the possible combinations, instead you draw samples from all the possibilities. With respect to poker, and any other card games, that means using a random number generator to "shuffle" the deck, and then evaluating the results.
I have actually written an Excel add-in that allows you to do these calculations (both enumeration and Monte Carlo) directly in a spreadsheet. You can check it out at pokeracle dot com - it's totally free, just go there and download it. If you think this is useful, or you have suggestions about what else could be done with it, please feel free to provide some feedback.