Another article from Phil Galfond

Wait, Weight
January 2008 | Phil Galfond
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“Range” is a pretty powerful word in the poker community these days. I probably use it almost every time someone asks me about a hand he played. It seems like everyone who’s anyone knows about ranges. Ooooh. I have a fun idea. Lets play some “choose your own adventure”

Do you know what range is? (If you answered ‘no’, read the next paragraph. If you answered ‘yes’, skip the next paragraph)

A range, in poker, is basically the set of all hands a player can have at a certain point in a hand, given the way he played it. So, if a tight player reraises pre-fl op and bets every street strongly on an A♠Q♣4♥5♣A♥ board, you might be able to put him on the range of hands including A-K, A-Q, A-A, Q-Q. Putting someone on a range of hands is a massive part of playing poker and an inexact science. It also gets much more complex than the above example. There has been plenty of discussion about it. I talked my head off about ranges in my article “G-bucks” which can be found here: http://www.bluffmagazine.com/onlinefeature/gbucks.asp.

Great! I’m glad you know about ranges, because I want to talk about weighting them. When someone calls a raise pre-flop, check-raises the flop, and bets the turn into you, you should be analyzing and deducing his range the entire time. You think to yourself: What hands would he play like this? Let’s say you decide that he would play a flush draw, two pair, or a set like this. (Don’t worry about the exact hand or the board for now.) So that’s his range. You can figure out how likely he is to be dealt each of those hands, calculate your equity vs. each of them, and decide the best course of action.
Cool.

The problem with this analysis is that t assumes your opponent will always play those hands in this manner (or that he’s equally likely to take that line with each hand). In reality, that’s not true. He might decide to just check-call with his flush draws and sets some of the time, while always raising the two-pair hands. Now when he raises, he’s more likely to have two pair than he was when we first analyzed his range. You need to adjust accordingly. That’s weighting a range.

Let’s jump into a hand example to show The idea of weighting:

You raise UTG 6-handed (at $50/$100NL) to $350 with QsJs and a $19,000 stack. UTG+1 calls with $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 is capable of big bluffs and thin value when The time is right.

He views you as good, 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 you do? That’s easy: You should put him on a range of hands.

So you first start 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 that he wouldn’t slow-play a set or two pair on a fl op this drawy.

Now you check the turn and he bets. You decide that he would check behind with any 10 and with Q-J suited. That leaves: A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited, A-J.

Now the river blanks and you’re faced with a bet. So you look at how many hand combos you beat and how many beat you:

A-Q – 2 queens left and 4 aces = 8 combos
K-Q – 8 combos
So that’s sixteen 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 in mind, you make a no-brainer call with your 2:1 pot odds (you only have to be right 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 you do something wrong? Well, yes.

Just because you made the wrong decision doesn’t mean that you were actually wrong to call. However, you made your call based on some faulty range building.

Let’s go through the process and see what we missed. Well, first of all, as you can see, we missed 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, our best guess is that he calls with those hands about of the time and raises the rest. So, how do we account for that? We weight those hands in his range. So let’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, he probably also can have A-K along with a few other hands, and he will reraise or fold 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 my point)

There we go. Did we 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 J-9 for fear of getting it in vs. a higher flush draw. So the chances that he just calls the flop with the hands are (our best 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 that he’d bet the turn with these hands, which is reasonable. The problem is, the range you made had the built-in assumption that he’d bet all of these hands with 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 of simplicity, 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 bet some of the hands than others.

Now we get to the river 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-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%)] - 75%

The river is where you made your biggest mistake. You check-called the turn, meaning you almost definitely have a made hand, likely mid-pair or so in your opponent’s eyes. You check to him on a board that is very drawy and completely blanked off. He reads you as a little bit loose. My point? This is not a good spot for your 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 if he misses his draw. Most of the time he will give up and check behind, figuring that you’ll call his bet with any pair. So, we should give every bluff in his range a 25% chance of firing again on the river. That might sound low, but it’s very, very reasonable. Think about what you’d do in his spot, against a loose-ish player, with J♠9♠. I would hope you’d usually check.

So we give those hands a 25% chance of firing again, yet we keep the value hands at 100%, since he will always value bet strong pair hands when you check the river.

His final range then 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 it into 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 decided that he only bets the turn 75% of the time with these hands, so we take our total and tweak it: 18.9(75%) = 14.175 hand combos

Then we take our 14.175 hand combos, and weight it to account for the fact that he will only bluff about 25% of the time on the river. 14.175 (25%) = 3.544 hand combos

So after weighting our range, we go from being ahead of his range (21 to 16) to being way behind (3.5 to 19) and we have a clear fold on the river.

The example was extreme and simplified, but it should get some points across; and it hopefully taught you how to weight a range.

The number one problem people run into when putting opponents on a range is that they forget to weight the bluffs. If your opponent is representing the nuts, when you check to him on the river, he may or may not bluff, but he ALWAYS will bet with the nuts. The fact that the value portion of his range is so strongly weighted makes a big difference when you’re deciding to make a hero call. Don’t underestimate the likelihood of your opponent to just give up on his bluffs.

When you’re facing a player you know very little about, that doesn’t mean you can’t weight his range. In fact, it’s actually more important that you weight his range since you’re so unsure about a lot of his tendencies. You have to keep a lot of hands in his range and weight them as best you can, taking the estimated chances of him playing hands certain ways, from street to street, and using them together to find a good estimated range for him. This is basically the way that Bayes’ Theorem applies to poker. (If you’re interested, studying Bayesian probability is great for your poker game.)

Good luck.

假设可以抛开经济因素,如果让我在这世界上所有牌手中任选一人来成为我长期扑克导师的话,我会毫不犹豫的选择Phil Galfond(无论是HLHE还是PLO).

Phil Galfond不仅牌打得好,各种教学内容也是绝对的大师级,人品牌品亦是令人信服(这一点我个人觉得很重要,为人师表应该有为人师表的样子,在牌桌上曾经有过各种乱来行为的人,还是不要当教练比较好).

我相信同等条件的假设之下,和我是同样选择的人应该不在少数

raythetruth 发表于 2011-11-21 10:51
假设可以抛开经济因素,如果让我在这世界上所有牌手中任选一人来成为我长期扑克导师的话,我会毫不犹豫的选择 ...

相当同意！  

我看过一个视频，应该是Phil Galfond刚才茅庐时打Cash Game的，稚嫩模样，遇到难题，他一转身取出Gallon水罐儿，仰头就灌下去，一下子让我回忆起学生时代。。。

好复杂，这样的计算要能那么快算准确吗？打牌的时候