Really Good Article
Not sure when it was written, but this definitely lets me know how far I still have to go in poker. Brings up some great concepts that I'm only beginning to realize exist, let alone understand them .
Bluff Magazine - bluffmagazine.com
By: Phil Galfond
Before I get going on this article, I want to stress that the following concept is one of the most important in poker. You will not meet a great player who doesnít understand this idea, whether he has put it into words himself or not. I havenít seen this concept explained well enough for the average player to understand, so Iím going to do my best here. It involves some boring math, but it will be worth it for your game if you can get through it. So pay attention.
In one or more of his many acclaimed books, David Sklansky introduced the term ďSklansky Dollars.Ē If you donít know what these are, you should pick up The Theory of Poker
and read it today, but Iíll touch on it briefly for the purposes of this article. Sklansky Dollars allow you to assess how youíre doing without your results being as affected by luck. To keep track of how many Sklansky Dollars you win, you look at the % chance you had to win the hand when money went into the pot, and multiply that by the money that goes in.
So, if you get all in pre-flop with A-A versus J-J for $10k and you lose, you lost $10k in real dollars; however you won about $6k in Sklansky Dollars because you should win that hand 80% of the time. As Sklansky explains, as long as you are making Sklansky Dollars, you will make money in the long run because luck evens out. In the ultimate long run, your Sklansky Dollars earned and real dollars earned will be the same. Itís a good way for you to keep calm and make the right decisions when facing the swings that inevitably come with poker. Itís a great concept.
I, however, am improving on it. And because Iím as egotistical as Sklansky, Iíll be naming my idea after me. Introducing ďGalfond DollarsĒ (G-Bucks for short):
First, I want to make sure you understand hand ranges. Letís say, for instance, you raise UTG in a 9-handed game with AhKh. Your hand is AhKh, but your range is so much more than that. Your range is every hand for which you would take the same action. So your range for raising UTG might be A-K offsuit, A-K suited, A-Q suited, and all pairs 9-9 and above. Letís say the button calls, and the flop is Q-6-5 rainbow with the queen of hearts. Now you bet 2/3 pot. Your hand is still AhKh, but letís say that you always (you probably donít always
do anything, but roll with it for the sake of simplification) check the flop with your smaller pairs, 9-9 to J-J, and you check your Q-Q half the time for deception. Now your range is A-K off-suit, A-K suited, A-Q suited, A-A, K-K, and half of your pocket queens.
Do you follow? Unfortunately, I canít hear your answer, so Iíll just keep going. Now, letís say the button calls and the turn is the 2h, putting two hearts on board. You bet 3/4 pot. Your hand is still AhKh, but your range has changed once again. Letís say that you give up with your non-heart A-K hands and you check A-Q suited for pot control. Now your range is AhKh, A-A, K-K, and half of your pocket queens. You following me? Okay.
The button calls and the river is the 2d. Tempted to bluff? Hold that thought. Weíll come back to this hand in a little while.
Now that you understand a range, letís talk about Galfond Dollars. The way that Galfond Dollars work is similar to the way Sklansky Dollars work. However, instead of taking your hand and seeing how it does against your opponentís hand, you take the entire range of your hand and see how it does against his hand. (The next level would be taking range versus range, but that gets very complicated mathematically.) So, letís go with a simple example:
Youíre playing $50-$100 No-Limit heads up. Your opponent has only $1k on the table and you have him covered. Youíre in the SB. You decide before the hand that you will shove all in with K-Q, J-J, Q-J suited, and 7-6 suited, and not push other holdings. (This shoving range is a bit far-fetched, but just go with it for this explanation.) Youíre dealt QsJs and, just as you planned, you go all in. Your opponent thinks for a bit and calls with Kc9d. The board comes Qh5s6dKh2h and you lose the $2k pot. Letís see how you did in real $, Sklansky $, and G$:
In real money, you lost $1,000.
In Sklansky Dollars, you lost $80 (Q-J suited is about 46% to win versus K-9 off-suit x $2k in pot = $920; $1k - $920 = $80).
Letís look at it in G-Bucks now...
Remember, we match our range up against his hand. So letís first see how likely we are to be dealt each hand in our range:
There are sixteen combinations of K-Q (KsQs, KhQc, KdQh, etc.), six combos of J-J, four combos of Q-J suited, and four of 7-6 suited. In total, there are thirty hand combinations we can have. Now we will see how each hand stacks up versus his K-9 off-suit:
K-Q versus K-9 off-suit - 74.0%
J-J versus K-9 off-suit - 72.0%
Q-J suited versus K-9 off-suit - 45.5%
7-6 suited versus K-9 off-suit - 41.0%
Next, you multiply each win percentage by how likely the hand is to be dealt. In other words, how many hand combinations make up that hand compared to how many hand combos you have in your entire range. The best way to do this is to multiply each winning percentage by the number of hand combos and then divide by the total number of hand combos.
K-Q J-J Q-J suited 7-6 suited Total hand combos
(.74 x 16 + .72 x 6 + .455 x 4 + .41 x 4) / 30 or
11.84 + 4.32 + 1.82 + 1.6 = 19.58
19.85/30 = .653
So, your range is 65.3% against K-9 off-suit, meaning that, on average, you win about $1,305 from the $2,000 pot when he calls your shove with K-9 off-suit. That makes your average profit $305. So, when K-9 off-suit called your Q-J suited shove, you made $305 G-Bucks!
Real Dollars -$1000
Sklansky Dollars: -$80
Galfond Dollars: +$305
The example was not very important to your poker game
, but I want to make sure the concept of G-bucks is entirely clear. Letís move on to more interesting hands.
How about the hand that we left off with up top? You have AhKh and have already fired two barrels after raising UTG and getting one caller. You missed your flush. Remember, the board read Qh6s5c2h2d, and we found that your range for raising pre-flop and then betting both the flop and turn was AhKh, A-A, K-K, and half of your pocket queens. We were deciding whether or not to bluff the river. Letís say in this spot your opponent has something like top pair or J-J or 10-10: a hand that is moderately strong but can only beat a bluff on this river. Letís say you bet the full pot with your AhKh, as well as with your entire range here once again. How much does your opponent make or lose when he calls?
We never gave the pot $ values, so letís just say thereís $5k in the pot. If you bet $5k and he calls, he makes $10k in real dollars and in Sklansky Dollars, since there are no more cards to be dealt. How does he do in G-Bucks?
Well, you have 14.5 hand combinations (three combos of Q-Q, so betting Q-Q half the time makes 1.5 hand combos), of which he beats only one. He loses $3,965.50 by calling your river bet versus your range. So, he would be making a terrible call if he had any idea of your range. An observant player would figure this out and would not pay you off here. Against weak players who call too much, almost always having the goods when you bet is a smart way to play. However, against higher level players, youíve made your game super exploitable by not bluffing enough. You have to think about manipulating your range so that you become more unpredictable and you put your opponents to tougher decisions. If, for instance, you could have 8-7 suited, AhJh, AhTh, and you followed through with half of your A-K off-suit hands, your opponentís decision would be closer on this river. In the example we gave, against half-decent players or better, you have to bet the river with your missed AhKh, otherwise you become even more predictable, since you actually are bluffing 0% of the time.
This is why, in tough games, you canít only raise 10-10 and above and A-K from UTG. Your smart opponents will be able to put you on a hand too easily when the flop hits. If the flop comes 7-6-5 rainbow, they know that you canít like it. Even with an overpair, you might have to fold if they play back hard at you, and because of your pre-flop raising range UTG, you could never have a set or a straight. In tough games, you canít only bet strong hands, and you canít give up every time you miss. You also have to learn to value bet thinner. Hereís an example of how value betting too tight can get you in trouble:
You are a solid, aggressive player. You put a lot of pressure on your opponents, which is a good thing. When you fire big bets on all streets, you can show up with a missed draw bluff sometimes, but you can also show up with the nuts. You arenít big on slowplaying. However, you are careful not to get stacked with one-pair type hands. On to the hand...
Everyone has $20k to start the hand.
You raise 9h8h to $700 on the button, and a smart optimistic player calls in the BB (I use the term optimistic to describe a poker player who is quick to put you on a hand he can beat if itís reasonable).
Flop is Qh10h5d ($1,500 in pot).
He checks and you bet $1,500. He calls.
Turn 4c ($4,500).
He checks and you bet $4,500. He calls.
River 5s ($13,500).
He checks and you go all in for your last $13,300. He insta-calls with AcJc. You look down at your 9h8h, think how bad of a call he just made, and that you would play Q-Q the exact same way, and muck. He gets the $40k pot.
But what the smart player knows about you is that you donít bet hard enough with top-pair type hands, and you always bet hard with your draws. He knows that with K-Q or A-A, you would check behind on the turn to control the pot. So the only hands you bet for value on the turn are two pair and sets. You also bet with any open-ended straight draw on the turn and with any flush draw. Letís look at your range on the river and see how bad a call it was.
Your range for raising pre-flop and betting all three streets:
Q-Q, 10-10, Q-10, 5-5, 4-4, Ah5h, 7-6, K-J, J-9, Ah2h to AhKh, Kh9h, Jh8h, 9h8h, 8h7h, 9h7h.
Iím trying to get you to recognize how many hand combos make up a certain hand. For instance, when you think someone has a set, there are only three possible combos of each set, whereas there are twelve hand combos of top pair-top kicker. So, if someone takes a line where he has to have a set or a bluff, realize how unlikely it is that he has a set. Similarly, suited hands are much less likely than unsuited hands.
Anyways, letís see how bad his river call was in G-Bucks. Since all the cards are out, G-Bucks analysis is simply what % of your hands he can beat now. If it were earlier in the hand, we would also factor in % to improve to the best hand by the river.
I wonít go through the whole hand counting analysis again because itís as boring for me as it is for you. There are programs available online where you can input a range of hands and see how your hand does against that range, and it accounts for hand combinations. If you are so inclined, try this one by hand to see how often your opponent made a good call versus the range I gave above. Remember to account for his AcJc in your range, as he knows you cannot have the Ac or the Jc.
Iím going to put the range into the program and see how often he has the best hand. If heís right, he wins $26,800, and if heís wrong he loses $13,300; so he has to be right only about 33% of the time to make a call break even. Looking at the math, he has the best hand 70.5% of the time! Thatís way more than enough to call on the river. His call made him almost $15,000 Galfond dollars ($26,800 real dollars), and is clearly the right play against you.
Letís talk about a couple other aspects of the hand. First, his call on the turn. Second, how you can manipulate your range to make this a more difficult decision for him.
While your opponentís river call was very standard versus your range, his turn call was much shakier. River decisions are very simple in that they can be solved completely with numbers. Pre-river decisions are much more complicated. Letís look at his call on the turn from a Galfond Dollars perspective. When you bet the turn with that same range, and he calls with AcJc, he is 54% against your range of hands. Since he has to call $4,500 to try and win the other $9,000 in the pot, it might seem like heís making a good play. If your $4,500 bet put you all in, and your range was the same, his call would be making him $2,790 G-Bucks (see if you can get that number on your own). However, with a draw-heavy board, and being out of position with money still to go in, his call isnít as good. I donít have a clear-cut figure for you, but you should be folding spots that are marginally +G-Bucks when certain situations arise.
Here are some examples of times that you should fold when G-Bucks calculations are telling you otherwise:
- Youíre out of position and there is some money left behind.
- The board is draw-heavy, and you donít know which cards help your opponents.
- Your opponent is a strong aggressive player.
- Your hand has little chance to improve.
On the other side of things, there are some spots where you can call when G-Bucks calculations make a call seem slightly wrong:
- You are in position and there is some money left.
- The board is draw-heavy and you have a disguised draw (especially in position).
- Your opponent is very predictable ─ too loose or too tight ─ and you are a strong aggressive player.
- Your hand has outs to become very strong.
(These factors all increase in effect the deeper the stacks are.)
The reason your opponent should fold the AcJc if you are a competent player, in my opinion, is that you will make his life very difficult on the river. If you donít have hearts and a heart falls, you can bluff him off the best hand. Or you might hit a straight and heíll pay you off thinking you missed a flush draw. The main thing is that you have another street to act on where you have everything going for you. You should earn money on the river on average, if you are as good as your opponent or better, because of all of the factors above. So, he should give up a little bit of $ in value on the turn to make up for the value that you should gain on the river.
A good example that I like to give: same game, 100/200, $20k stacks. The button, a good aggressive player, raises to 600 and you call in the BB with 5-5. Flop is Jd10d2h. You check and the button bets $1,000, which he does with almost every hand he raised with. You usually have the best hand. But a fold is still correct. Think about that and make sure you understand. You likely have the best hand, definitely over 65% of the time, and you have over 2:1 pot odds
, but a fold is still clearly correct. First of all, you are an underdog to finish the hand ahead. Youíre about 44% against a reasonable button-raising range on that flop. Even with the pot odds
, which would make the call appear to net you some Galfond Dollars, you have to factor in your opponentís advantage on later streets because of the examples I gave above.
Letís go back now to the AcJc hand and talk about how you can make your turn and river play better. Remember the action looked like this:
Flop is Qh10h5d ($1,500 in pot).
He checks and you bet $1500. He calls.
Turn 4c ($4,500).
He checks and you bet $4,500. He calls.
River 5s ($13,500).
He checks and you go all in for your last $13,300. He insta-calls with AcJc.
And we said that you would take this action with the following hands: Q-Q, 10-10, Q-10, 5-5, 4-4, Ah5h, 7-6, K-J, J-9, Ah2h to AhKh, Kh9h, Jh8h, 9h8h, 8h7h, 9h7h.
Now, his turn call is very close, as it would be with weak one-pair hands, so your turn play doesnít need too much work, except for the fact that we need to tweak it a little to help your river range. So, letís try checking behind on the turn with your ace-high flush draws besides AhKh and AhJh. I like checking these a little bit better because we know where we stand when a heart hits, while we donít if we check behind 9h8h and a flush comes, and also because our ace outs might be good, and I would hate to get check-raised off of a hand with that many outs on the turn.
We also need to add some more one-pair hands to our range. Remember our opponent is smart and optimistic, so on a board this draw heavy, he is going to call down light quite often. In addition, itís unlikely that he would only call your flop bet with a hand like a set of fives or Q-10 when so many scary cards could come on the turn. Thereís no reason for you to think that a hand like A-Q is beat here. So, letís also pot the turn with K-Q, A-Q, J-Q, K-K, and A-A. Weíll stop there and not bet Q-9 because he can have K-Q or Q-J often, and he could check-shove the turn with a draw and you might have to fold the best hand.
Letís look at your new range: Q-Q, 10-10, Q-10, 5-5, 4-4, A-A, K-K, A-Q, K-Q, Q-J, 7-6, K-J, J-9, AhKh, AhJh, Kh9h, Jh8h, 9h8h, 8h7h, 9h7h.
Iím certain now that his turn call is bad against this range.
Letís see how good his AcJc river call is against your new range, assuming you bet all of these on the river. Running the numbers... he still has the best hand 43.3% of the time, making his call correct and netting him some G-Bucks. Since heís kind of a calling station, we want to make his call incorrect. At the very least, we want to make it a tougher decision. So letís try to get his hand down to 30% against you. This means we have to check behind with some of our bluffs on this river. Well, for starters we should check behind A-K and A-J of hearts, even though they actually arenít bluffs versus his hand. We should check them behind if weíre going to check any more hands behind because they can sometimes win the pot without betting. How about we check behind with open-ended straight draws? So K-J and J-9. We give up with those hands, so now we are betting: Q-Q, 10-10, Q-10, 5-5, 4-4, A-A, K-K, A-Q, K-Q, Q-J, 7-6, Kh9h, Jh8h, 9h8h, 8h7h, 9h7h.
Running the numbers once again, it looks like his A-J is only good 26.6% of the time now, so we made his call a bad one. So, now, when we bet this river and he calls with A-J (or Q-J or A-10 or 8-8), whether we have a full house or nine-high, he loses G-Bucks and we make G-Bucks. That means that in the long run we will earn money if he keeps making that call. To be exact, that river call cost him $2,633 Galfond Dollars, and earned you the same amount.
Why, you ask, should we just not bluff this river? Then heíd be extremely wrong to call, right? Definitely a good question. If you are up against a very loose, very unintelligent player, you should probably bluff this river close to 0% of the time. The problem with doing it against good players, even if they are loose, is that theyíre smart enough to catch on. Theyíll notice that you arenít bluffing enough and theyíll not give you any action. Remember the AhKh example up top where we werenít bluffing enough? Your goal is to make the most money on average, not necessarily on the present hand. You have to bluff sometimes against smart players in order to get paid off other times when you have a big hand. So, if you are only going to play five minutes against this player, and you think he will almost always call the river Ė sure, donít bluff. But if you play against him often, you have to occasionally bluff so that he doesnít figure you out and start to play correctly against you.