Math and Hand Ranges
Currently reading Poker Math that Matters
by Owen Gaines and I'm a little stuck on his concept of establishing an opponent's hand range in relation to equity. The first part, Combinations, appears easy enough. He more or less states that you place your opponent on several possible hands and the different ways they can make a hand: if an opponent has pocket pairs (JJ, QQ) or a big gapped hand (AQ, KJ) he would have multiple combinations. For each pocket pair it would be six different combinations, and with the gapped hands you multiply the cards remaining, 4 aces x 4 queens = 16 combinations. In the above example there would be:
12 combinations for JJ and QQ together
32 combinations for AQ and KJ
44 total combinations
This is where it gets tricky, at least for me.
"Determining your equity against his range of hands is done in four steps:
1. Determine equity against each hand in his range
2. Multiply equity by the number of combinations
3. Add together the results from step 2 for each hand in the range
4. Divide the results from step 3 by the total combinations"
As an example
Hero: 10d 8h
Villain: JJ, QQ, AQ, KJ
Board: 10s 10h Jd Kc
Step 1: JJ (2%) QQ (88%) AQ (14%) KJ (90%)
Step 2: JJ (3 x 0.02 = 0.06) QQ (4 x 0.88 = 3.2) AQ (16 x .14 = 2.24) KJ (9 x .9 = 8.1)
Step 3: [.06 + 3.2 + 2.24 + 8.1 = 13.6]
Step 4: [13.6/32= 0.42]
An equity against this range would be 42%
To me, this seems like an overly complicated way to assess if you should make a call or not. I think it just seems easier to determine what hands you can beat and what hands you are a loser to, then make an educated guess based on how your opponent has played the hand to that point. My problem is, the rest of the book is dependent on applying this process to bluffing
, semi-bluffing, value-betting, and chunking.
So, how many of you out there understand and use this process? If so, how do you do it without busting out the calculator? (He does talk about an MS Method, but this still requires you to find all the possible combinations and the equity against them.)
If you don't do it, what's your process for determining your opponent's range of hands?
And finally, why does math have to suck so hard?
Any input would be great. Thanks in advance.