I'm doing some Monte-Carlo simulations to evaluate equity in multiway pots in Texas Hold'em for a student project of mine. Think of it as roughly what PokerStove does only I need to code it on my own.

Right now it works for many cases but there are some special cases where I run into trouble, e.g., the equity of a specific hand vs. multiple opponents with wide ranges, for example:

Equity of AQ on a QJ3 board if four other players have ranges of 66+,A2s+,ATo+,KQo,KQs each.

The problem is that their range includes all the cards but still constitutes only about 12% of hands. Therefore, if I just take a random allocation of pocket cards more often than not it will not fit one or more of the ranges and I will have to discard that measurement, making the simulation extremely imprecise and/or slow.

Do you have any ideas on how that can be improved? Do you know how it is generally done in tools like PokerStove?

Any help (even if you just point me to some Monte-Carlo method variants/adaptations) will be much appreciated.

P.S. X-post w/ Software forum.

1) generate all possible hands
2) eliminate hands that use given hand's cards or dead cards
3) generate all remaining hands that fit the range(s)
4) pick randomly from those hands, making sure to eliminate hands with cards that have already been picked

You only have 1326 hands. After eliminating 5 cards, you're down to 1081. For each range, you can cut it down even more. Every additional card you use eliminates more hands. Just keep track of what cards have already been used, and you can then pick randomly from the hands instead of picking two cards.

yeah that makes sense; thanks, I will try it

There are a few ways to do this and here are some suggestions.

1) You can pre-define your seed and rng so you will always get the same cards and distrubution for say 1 million hands and you can work out the equity via this method according to different hand ranges.

2) You can do the same but fix the flop and use a seed to generate distrubution according to the flop. You can then iterate through the preflop range holdings to work out your ev this way.

3) You can use pre-simulation on the board initially or use a static mapping which knows the outcomes against board textures. E.g. Since you want to examine the board A Q 7 you can use an algorithm to work out all the possible turn river cards you can get on this board and the ev for this according to the 1326 possibily hand range (eliminating the turn and river card maps which have been used already)

This way you are just using a lookup map when you are evaluating the flop.

There are many ways to do monte carlo modelling it just depends really what you are wanting to analysis.