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 doesn’t understand this idea, whether he has put it into words himself or not. I haven’t seen this concept explained well enough for the average player to understand, so I’m 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 “Sklansky Dollars.” If you don’t know what these are, you should pick up The Theory of Poker and read it today, but I’ll touch on it briefly for the purposes of this article. Sklansky Dollars allow you to assess how you’re 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 $8k 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. It’s a good way for you to keep calm and make the right decisions when facing the swings that inevitably come with poker. It’s a great concept.
I, however, am improving on it. And because I’m as egotistical as Sklansky, I’ll be naming my idea after me. Introducing “Galfond Dollars” (G-Bucks for short):
First, I want to make sure you understand hand ranges. Let’s say, for instance, you raise UTG in a 9-handed game with A♥K♥. Your hand is A♥K♥, 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 (Under the Gun) might be A-K offsuit, A-K suited, A-Q suited, and all pairs 9-9 and above. Let’s 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 A♥K♥, but let’s say that you always (you probably don’t 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 offsuit, A-K suited, A-Q suited, A-A, K-K, and half of your pocket queens.
Do you follow? Unfortunately, I can’t hear your answer, so I’ll just keep going. Now, let’s say the button calls and the turn is the 2♥, putting two hearts on board. You bet 3/4 pot. Your hand is still A♥K♥, but your range has changed once again. Let’s 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 A♥K♥, A-A, K-K, and half of your pocket queens. You following me? Okay.
The button calls and the river is the 2♦. Tempted to bluff? Hold that thought. We’ll come back to this hand in a little while.
Now that you understand a range, let’s 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 opponent’s 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, let’s go with a simple example:
You’re playing $50-$100 No-Limit heads up. Your opponent has only $1k on the table and you have him covered. You’re 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.) You’re dealt Q♠J♠ and, just as you planned, you go all in. Your opponent thinks for a bit and calls with K♣9♦. The board comes Q♥5♠6♦K♥2♥ and you lose the $2k pot. Let’s 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).
Let’s look at it in G-Bucks now…
Remember, we match our range up against his hand. So let’s first see how likely we are to be dealt each hand in our range:
There are sixteen combinations of K-Q (K♠Q♠, K♥Q♣, K♦Q♥, etc.), six combos of JJ, 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. Let’s move on to more interesting hands.
How about the hand that we left off with up top? You have A♥K♥ and have already fired two barrels after raising UTG and getting one caller. You missed your flush. Remember, the board read Q♥6♠5♣2♥2♦, and we found that your range for raising preflop and then betting both the flop and turn was A♥K♥, A-A, K-K, and half of your pocket queens. We were deciding whether or not to bluff the river. Let’s 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. Let’s say you bet the full pot with your A♥K♥, 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 let’s just say there’s $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 13.5 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 $3,889 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, you’ve 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, A♥J♥, A♥10♥, and you followed through with half of your A-K off-suit hands, your opponent’s 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 A♥K♥, otherwise you become even more predictable, since you actually are bluffing 0% of the time.
This is why, in tough games, you can’t 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 can’t 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 can’t only bet strong hands, and you can’t give up every time you miss. You also have to learn to value bet thinner. Here’s 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 aren’t 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 9♥8♥ 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 it’s reasonable).
Flop is Q♥10♥5♦ ($1,500 in pot). He checks and you bet $1,500. He calls.
Turn 4♣ ($4,500). He checks and you bet $4,500. He calls.
River 5♠ ($13,500). He checks and you go all in for your last $13,300. He insta-calls with A♣J♣.
You look down at your 9♥8♥, 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 don’t 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. Let’s 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, A♥5♥, 7-6, K-J, J- 9, A♥2♥ to A♥K♥, K♥9♥, J♥8♥, 9♥8♥, 8♥7♥, 9♥7♥.
I’m 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, let’s see how bad his river call was in G-Bucks. Since all the cards are out, GBucks 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 won’t go through the whole hand counting analysis again because it’s 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 A♣J♣ in your range, as he knows you cannot have the A♣ or the J♣.
I’m going to put the range into the program and see how often he has the best hand. If he’s right, he wins $26,800, and if he’s 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! That’s 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.
Let’s 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 opponent’s 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. Let’s 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 A♣J♣, 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 he’s 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 isn’t as good. I don’t 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:
• You’re out of position and there is some money left behind.
• The board is draw-heavy, and you don’t 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 don’t have hearts and a heart falls, you can bluff him off the best hand. Or you might hit a straight and he’ll 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 J♦10♦2♥. 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. You’re 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 opponent’s advantage on later streets because of the examples I gave above.
Let’s go back now to the A♣J♣ hand and talk about how you can make your turn and river play better. Remember the action looked like this:
Flop is Q♥10♥5♦ ($1,500 in pot). He checks and you bet $1500. He calls.
Turn 4♣ ($4,500). He checks and you bet $4,500. He calls.
River 5♠ ($13,500). He checks and you go all in for your last $13,300. He insta-calls with A♣J♣.
And we said that you would take this action with the following hands: Q-Q, 10-10, Q- 10, 5-5, 4-4, A♥5♥, 7-6, K-J, J-9, A♥2♥ to A♥K♥, K♥9♥, J♥8♥, 9♥8♥, 8♥7♥, 9♥7♥.
Now, his turn call is very close, as it would be with weak one-pair hands, so your turn play doesn’t need too much work, except for the fact that we need to tweak it a little to help your river range. So, let’s try checking behind on the turn with your ace-high flush draws besides A♥K♥ and A♥J♥. I like checking these a little bit better because we know where we stand when a heart hits, while we don’t if we check behind 9♥8♥ 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.
For the rest of the story visit our website at http://www.bluffmagazine.com/onlinefeature/gbucks.asp.