This is a discussion on Math and Hand Ranges within the online poker forums, in the Learning Poker section; 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 


#1




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, semibluffing, valuebetting, 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. 
#3




Quick example
Playing a 6 max game Villain that we have 650 hands on run 17/16 over all But UTG he plays a 4/4 that range looks like.99+,AQs+,AKo according to stove So if we have AKs our "pre flop EQ would be  287,667,072 games 0.000 secs 57,533,414,400 games/sec Board: Dead: equity win tie pots won pots tied Hand 0: 54.054% 44.17% 09.88% 127070076 28425114.00 { 99+, AQs+, AKo } Hand 1: 45.946% 36.06% 09.88% 103746768 28425114.00 { AKs }  But he steals 27% of the time from the button.That looks like 55+,A2s+,K6s+,Q8s+,J8s+,T8s+,98s,A7o+,K9o+,Q9o+,JT o Etc.. Just play around with stove 
#4




Wow, if that's what that book is like I'm glad I never bought it when I was considering it. That process seems so cumbersome and unweildy that I can't believe anyone actually works through all that mess while actually in a game.
JB is right; Pokerstove is the way to go. 
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Even though we use a pocket calculator we should still know how to add subtract, multiply and divide. Even though we have pokerstove you should understand how it works. 
#6




re: Poker & Math and Hand Ranges
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For example, I believe in space travel. I believe we landed on the moon. I have seen it. I don't need to know all the math behind it; even if I wanted to be an astronaut. Pokerstove is a wonderful tool. Use it. Understand the concept of ranges and equity against a range. Don't get bogged down in the concept of needing to know the math behind every calculation in creating that range and your equity against every individual hand in that range. As you mentioned, this isn't going to be used at the table anyway. So, if you can't do all this math dynamically, while involved in a game, it really comes back to almost rote memorization anyway. E.g., Ok I put villains UTG openraising range at 10,10+ AK, AQs.... I have JJ IP my equity against his range is approximately... number you pullout from your study of Pokerstove NOT a number you are able (unless you are a absolute math genius) to calculate on the fly. 
#7




The book is just trying to get you familiar with ranges and counting combo's, The more you practice that sort of thing the easier you can just come up with rough numbers when actually playing at the table. Im sure he does show you easier methods that get pretty close answers when at the table  good book

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For example, I have the Bill Chen book (title escapes me at the moment) and there is enough math in there to make anybody's head spin. Is it really practical to apply much of it at the table? Not the way he presents it in his book. The book does give some interesting concepts, but its stuff you just have to "know" from studying the book, not much you can actually workout while at the table. 
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Its similar to how, in chess you study patterns and tactics away from the game so that you recognize them quickly in game. One final note, the author is a member here and a really nice guy. I'm sure if you messaged him with a few of your questions he would discuss them with you. Qtip is his handle. 
#10




[quote=alaskabill;1891509]We agree on pokerstove (ldo ) and I wasn't suggesting getting bogged down in anything. I just think that having some understanding of how the game works mathematically will help you in the long run plus its interesting.[quote]
I really don't think anyone needs a book to help you with the maths of the game. 
#11




[quote=BlueNowhere;1891518][quote=alaskabill;1891509]We agree on pokerstove (ldo ) and I wasn't suggesting getting bogged down in anything. I just think that having some understanding of how the game works mathematically will help you in the long run plus its interesting.
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You can get most of the information online easily enough. I was simply responding to Big Rudy's assertion (if I understood him correctly) that you didn't need to understand the math in the game as long as you could use pokerstove. Its really not that big of a deal. Personally I like it if my opponent has no clue about the math of the game. 
#12




re: Poker & Math and Hand Ranges
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I call bullshit. Firstoff, that very precise equity calculation is inherently flawed as its based upon an ASSUMPTION or, at best, an EDUCATED GUESS about villains range. If you are off even slightly about your guess as to his range your corresponding equity is off as well, despite the "wall of math" you used to arrive at that conclusion. Secondly, do we ever really need to know that our equity is precisely 42%? I'm talking "realworld" here, not theorhetically. Knowing that your equity is approximately 40% is fine, and given that you can never know villains range with 100% accuracy anyway, may actually be closer to the truth that that big, long equity calculation. Estimating, imo, is a highly underrated and more valuable skill in poker applications than it is given credit for. As for the bit about Pokerstove, what I was trying to say was that when I punch in a range and PS spits out an equity of, say 42.6%, I just accept it and moveon. I see no need to do all the mathematical proofs to show that my equity is in fact what PS says it is. 
#13




I apologize for misunderstanding you. For practical purposes in a game I agree with you. I just don't think there is any harm and quite a bit of benefit from exploring some of the math (away from the table) in more detail. How much time we spend is obviously an individual choice.
I certainly would not go through and attempt to double check all of pokerstoves results anymore than I would constantly double check my calculator. I just think that it is useful to be understand the process it is using. Anyways, I meant no offence. 
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re: Poker & Math and Hand Ranges
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#19




I've read both of his books and they are pretty good.
I might be getting his books mixed up here.I know in one of them he talks about keeping notes on what you see villains show up at showdown. Lets say villain is 20/18 with a over all 3bet of 5%.His 3bet on the BTN is 7% Ok folds around, we are in the CO with KJo we raise 3x BTN 3bets to 10x SB folds,BB (45/7) calls,Hero folds Flop comes A57 two toned BB donks 1/2 pot ,BTN shoves,BB snap calls BB shows AJs,BTN shows A5s Now if i were to put 7%(which is what BTN 3bet% from the BTN is) it would look like. 88+,ATs+,KQs,AQo+ As you can see A5s is no were near the range stove gives us.Wemake a note. Now we know for a fact that BTN only raises 7% of hands on the btn.We know for a fact BTN showed he also can 3bet A5s.That leads us into thinking villains range is composed of weak hands that have some eq and only the strongest of hands AKo,AKs,AA,KK,QQ(aka polarized range) We could not know this by simply by using stove as stove only gives us a depolarized range. Most micro fish use a depolarized range though.So stove is awesome for us.One good thing you could do is play around with it one day with hands your not sure about. Get a note book wright down hands like 99,1010,JJ,AJs,AQo,AQs etc.Enter those hands in stove vs villains range in blocks of 5 up to around the 25 block.That way in game,If you not sure a 24/6 opens for a raise you have AQo you can look an see. AQo vs a 5% range which says we have ~40 eq Now thats just preflop eq if all the money goes in now.What it doesn't tell us is how often he folds to 3bets,how well we play ip etc. Damn sorry for the long winded response.. 
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#21




Hey, thanks for all the replies. I do think this book is really good, especially the first few chapters that cover odds, percentages, fractions, and just piecing it all together. This technical stuff just threw me because I was trying to get it down while I was playing. He does have an easier method which is the MS Method, but not being mathematically inclined, I still find it difficult to just keep track of the different percentages (you still have to figure out the number of combinations based upon the assumed hand range). But since I'm not playing live I'm definitely going to get pokerstove. It sounds very helpful.

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