Phil Galfond对Range的精辟阐述！（英文转载）

添哥 · 发表于 2012-12-6 16:42:28

这篇文章以NLHE举例，但是可以同样运用到PLO的分析中去。
如果大家完全理解了这篇文章里面的所有内容，那么我可以断定，你距离更上一层楼就不远了：）

“Range” is apretty powerful word in the poker community these days. I prOBably use italmost every time someone asks me about a hand he played. It seems likeeveryone who’s anyone knows about ranges. Ooooh. I have a fun idea. Let’s playsome “choose your own adventure”
Do you know whatrange is? (If you answered ‘no’, read the next paragraph. If you answered‘yes’, skip the next paragraph)
A range, inpoker, is basiCALLy the set of all hands a player can have at a certain pointin a hand, given the way he played it. So, if a tight player reraises pre-FLOPand bets every street strongly on an A♠Q♣4♥5♣A♥ board, you might be able to puthim on the range of hands including A-K, A-Q, A-A, Q-Q. Putting someone on arange of hands is a massive part of playing poker and an inexact science. It also gets much more complex thanthe above example. There has been plenty of discussion about it. I talked myhead off about ranges in my article “G-bucks” which can be found here:http://www.bluffmagazine.com/onlinefeature/gbucks.asp.
Great! I’m gladyou know about ranges, because I want to talk about weighting them. Whensomeone calls a raise pre-flop, check-raises the flop, and bets the turn intoyou, you should be analyzing and deducing his range the entire time. You thinkto yourself: What hands would he play like this? Let’s say you decide that hewould play a flush draw, two pair, or a set like this. (Don’t worry about theexact hand or the board for now.) So that’s his range. You can figure out howlikely he is to be dealt each of those hands, calculate your equity vs. each ofthem, and decide the best course of action.
Cool.
The problem withthis analysis is that it assumes your opponent will always play those hands inthis manner (or that he’s equally likely to take that line with each hand). Inreality, that’s not true. He might decide to just check-call with his flushdraws and sets some of the time, while always raising the two-pair hands. Nowwhen he raises, he’s more likely to have two pair than he was when we firstanalyzed his range. You need to adjust accordingly. That’s weighting a range.
Let’s jump into ahand example to show The idea of weighting:
You raise UTG6-handed (at $50/$100NL) to $350 with QsJs and a $19,000 stack. UTG+1 callswith $15,000, and everyone folds to the BB who calls with $15,000.
UTG+1 is a smart,tight aggressive player - almost definitely the best at the table. He iscapable of big bluffs and thin value when The time is right.
He views you asgood, smart, and a little loose.
Flop is Q♣T♣4♠($1100 in pot).
You bet $900, UTG+1 calls, BB folds.
Turn is the 5d ($2900 in pot).
You check, UTG+1 bets $2200, you call.
River is the 4h ($7300 in pot).
You check, UTG+1 bets $7300.
What should youdo? That’s easy: You should put him on a range of hands.
So you firststart with hands that would call pre-fl op and call the fl op, and then narrow
it down from there. You think he can have: A-Q, K-Q, Q-J suited, A-10 suited,K-10
suited, J-10 suited, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited, A-J.
You decide thathe wouldn’t slow-play a set or two pair on a fl op this drawy.
Now you check theturn and he bets. You decide that he would check behind with any 10 and withQ-J suited. That leaves: A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited,A-J.
Now the riverblanks and you’re faced with a bet. So you look at how many hand combos youbeat and how many beat you:
A-Q – 2 queensleft and 4 aces = 8 combos
K-Q – 8 combos
So that’s 16 combos that beat you.
9♣8♣, 8♣7♣, 7♣6♣ = 3 combos
K-J suited = 3 combos (you have the J♠ in your hand)
J-9 suited = 3 combos
A-J = 12 combos
That’s 21 combos you beat.
With that inmind, you make a no-brainer call with your 2:1 pot odds (you only have to beright 1 out of 3 times to break even).
You put in your$7300 and he shows KdKs and wins the pot. Oops, you missed that hand. Did youdo something wrong? Well, yes.
Justbecause you made the wrong decision doesn’t mean that you were actually wrongto call. However, you made your call based on some faulty range building.
Let’s go throughthe process and see what we missed. Well, first of all, as you can see, wemissed K-K and A-A. You assumed that UTG+1 would reraise those hands pre-fl op.
And you’re right, sort of. He usually would. From what you know about him, ourbest guess is that he calls with those hands about of the time and raises therest. So, how do we account for that? We weight those hands in his range. Solet’s take a look at our turn range again with these hands added: A-A (25%), K-K(25%), A-Q, K-Q, 9♣8♣, 8♣7♣,
7♣6♣, K-J suited, J-9 suited, A-J.
(In reality, heprobably also can have A-K along with a few other hands, and he will reraise orfold some other hands that we assumed he always called with some % of the time.All of that just going to complicate things further, and it won’t help mypoint)
There we go. Didwe fix everything? Not yet. There are a couple other things you forgot.
First, UTG+1 will raise the flop most of the time with AcJc, KcJc, and Jc9c.He’s less likely to raise the Jc-9c for fear of getting it in vs. a higherflush draw. So the chances that he just calls the flop with the hands are (ourbest guess): A♣J♣ (20%), K♣J♣ (20%), J♣9♣ (50%).
So now we have:A-A (25%), K-K (25%), A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited
(KcJc 20%), J-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%).
You decided thathe’d bet the turn with these hands, which is reasonable. The problem is, therange you made had the built-in assumption that he’d bet all of these handswith equal frequency on the turn. Some of the time, UTG+1 would check behind,take his free card, and hope to hit on the river. However he would almost never(let’s say never) check behind with the top pair + hands. For the sake ofsimplicity, we’ll just assume he checks behind with all the nonmade hands 25%of the time, and bets them 75%. In reality, he’s probably more likely to betsome of the hands than others.
Now we get to theriver with our new range of:
A-A (25%), K-K (25%), A-Q, K-Q, [9♣8♣, 8♣7♣, 7♣6♣, K-J suited (K♣J♣ 20%), J-9suited (J♣9♣ 50%), A-J (A♣J♣ 20%)] - 75%
The river iswhere you made your biggest mistake. You check-called the turn, meaning youalmost definitely have a made hand, likely mid-pair or so in your opponent’seyes. You check to him on a board that is very drawy and completely blankedoff. He reads you as a little bit loose. My point? This is not a good spot foryour opponent to bluff!
He’s smart so he knows that.
Because of this,we can figure he will bluff this river when checked to only 25% of the time ifhe misses his draw. Most of the time he will give up and check behind, figuringthat you’ll call his bet with any pair. So, we should give every bluff in hisrange a 25% chance of firing again on the river. That might sound low, but it’svery, very reasonable. Think about what you’d do in his spot, against aloose-ish player, with J♠9♠. I would hope you’d usually check.
So we give thosehands a 25% chance of firing again, yet we keep the value hands at 100%, sincehe will always value bet strong pair hands when you check the river.
His final rangethen is: A-A (25%), K-K (25%), A-Q, K-Q, {[9♣8♣, 8♣7♣, 7♣6♣, K-J
suited (K♣J♣ 20%), J-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%)] - 75%}-25%
So let’s break itinto combos again:
A-A, K-K = 12 combos (25%) = 3 combos
A-Q = 8 combos
K-Q = 8 combos
That’s 19 combos that beat you.
9♣8♣, 8♣7♣, 7♣6♣ = 3 combos
K-J suited = K♥J♥, K♦,J♦ = 2 combos
K♣J♣(20%) = .2 combos
J-9 suited = J♥9♥, J♦9♦ = 2 combos
J♣9♣ (50%) = .5 combos
A-J = 11 combos + A♣J♣ (20%) - 11.2 combos
That totals 18.9 hand combos.
Then we decidedthat he only bets the turn 75% of the time with these hands, so we take ourtotal and tweak it: 18.9(75%) = 14.175 hand combos
Then we take our14.175 hand combos, and weight it to account for the fact that he will onlybluff about 25% of the time on the river. 14.175 (25%) = 3.544 hand combos
Soafter weighting our range, we go from being ahead of his range (21 to 16) tobeing way behind (3.5 to 19) and we have a clear fold on the river.
The example wasextreme and simplified, but it should get some points across; and it hopefullytaught you how to weight a range.
Thenumber one problem people run into when putting opponents on a range is thatthey forget to weight the bluffs. If your opponent is representing the nuts, when you checkto him on the river, he may or may not bluff, but he ALWAYS will bet with thenuts. The fact that the value portion of his range is so strongly weightedmakes a big difference when you’re deciding to make a hero call. Don’tunderestimate the likelihood of your opponent to just give up on his bluffs.
When you’refacing a player you know very little about, that doesn’t mean you can’t weighthis range. In fact, it’s actually more important that you weight his rangesince you’re so unsure about a lot of his tendencies. You have to keep a lot ofhands in his range and weight them as best you can, taking the estimatedchances of him playing hands certain ways, from street to street, and usingthem together to find a good estimated range for him. This is basically the waythat Bayes’ Theorem applies to poker. (If you’re interested, studying Bayesianprobability is great for your poker game.)

Good luck.