Texas Hold Em Combinatorics
Join Date: Nov 2010
Posts: 37
I am wondering if there is a good source for learning it... maybe a book or video. I know Tom Chambers does some for Omaha, but where is the Hold Em equivalent? I already use ProPokerTools but I think that is for something different.
EXAMPLE:
If I have A-K in a tournament, and two very tight players in front of me raise / reraise, if I know ahead of time exactly what their range is (A-K, some A-Q, paired 7's and up), then is there a calculation for how often I am going to run into two pocket pairs vs. at least one A-Q or A-K?
I suppose I could try to set this one up on pro poker tools.
Join Date: Nov 2010
Posts: 37
Another example would be heads up in a 6-max cash game:
If the flop has a jack, 7, and 3, with two suited cards.... and I could at least ballpark the range of hands someone has (suited connectors, most of the time playing suited one-gappers, every once in a while mix in a suited two-gapper, etc etc.)
In that case, is there a way to approximate how often he is going to have the jack in his starting hand vs. just the flush draw (like just a suited ace), and even be able to figure out how often he might have the low pair, possibly including some sort of flush or backdoor straight.
It may sound like a big task, but it's only a question of combinatorics. There is a limited number of ways you can deal out the pair of jacks to end up with that on the flop.
Join Date: May 2011
Posts: 128
I am sure there are books and videos that explain combinatorics of holdem, but I wouldn't spend money on any of them if all you're interested in is that. The stuff is simple enough to figure out on your own. And there's a shortcut called Flopzilla (you can find a thread about it in the commercial software subforum). If you absolutely have to spend your money, buy this program, it does all the job for you.
But the basics are very simple. Any pp is 6 combos. Any non-pair hand, e.g. AK, is 16 combos (4 Aces x 4 Kings). Any suited hand is 4 combos.
When the flop comes, a pair with a specific kicker (e.g. AK on AT8 flop) is 12 combos (have to subtract 4 combos of AK that contain the ace on the board). A particular set (e.g. a set of tens on AT8) is 3 combos. Two pairs (AT on AT8) is 9 combos, etc.
Good luck
Join Date: Apr 2011
Posts: 941
Join Date: Jul 2004
Posts: 3,166
IMO, the answer to this question is not going to be very helpful.
The questions that are useful are:
1. how often do one or both of these players fold if I shove (assuming they aren't all-in already).
2. how is my equity vs their getting-it-in range 3-ways (or HU).
Q2 can be easily answered (if your range assumptions are correct) using pokerstove or ppt.
