Phil Galfond (known online by the handle OMGClayAiken) took the Sklansky dollars concept and built on it to make it applicable to the concept of ranges as opposed to just a single hand.
In part one of this two-part strategy series, which looked at Sklansky dollars in detail, we learned how to put a dollar amount on the probable outcome of any poker scenario. This concept is useful in evaluating your play post-session, giving you a statistical dollar amount you can directly compare with the real-money dollar amount.
The problem with this theory is its inability to be used in the moment. For example:
You raise $50 pre-flop, and your opponent reraises you all-in for $300. You have a strong read and are 100% sure that your opponent is holding a top pocket pair; you hold A♣ K♣.
|Versus Hand ||Your Equity ||Your Sklansky Dollars|
|A♥ A♦ ||12% ||-$178|
|K♥ K♦ ||34% ||-$46|
|Q♥ Q♦ ||46% ||$26|
|J♥ J♦ ||46% ||$26|
Phil Galfond + G-bucks = WSOP
As you can see, if you rely only on the concept of Sklansky dollars, you're unable to decide how to play until you know exactly which hand your opponent has. If they have JJ you'll make Sklansky money by calling, but if they have AA you're losing Sklansky money.
In the real world of poker, you can only put your opponent on a range, and use any information you pick up to narrow that range. G-bucks use the same basic principles as Sklansky dollars, but pit your hand against your opponent's entire range.
The way to calculate G-bucks is not quite as simple as Sklansky Dollars, but let me walk you through it:
- First, you have to get the equity of your hand versus every hand in their range. For this example, we'll use the chart above. Because G-bucks calculates the value of the range, we have to use the equity for the versus hands, meaning:
- A♥ A♦ = 88%
- K♥ K♦ = 66%
- Q♥ Q♦ = 54%
- J♥ J♦ = 54%
- Second, you have to figure out how likely you are to be dealt each hand in that range. For example, there are 16 different combinations of A-K including suited and offsuit, and only six combinations for any pocket pair. NOTE: These figures do not take into account your hand. If you're calculating the G-bucks of a range against a specific hand, you would use these figures. For calculating the G-bucks of a hand vs. a range, we must remove the duplicate permutations. (leaving three combinations for aces, and three combinations for kings)
- Next, you need to multiply every hand's equity by the number of hand combos each hand has:
- A♥ A♦: 0.88*3 = 2.64
- K♥ K♦: 0.66*3 = 1.98
- Q♥ Q♦: 0.54*6 =3.24
- J♥ J♦: 0.54*6 =3.24
- Now, add all of those together, and divide them by the total number of hand combinations in the range:
- (2.64 + 1.98 + 3.24 + 3.24) / (3 + 3 + 6 + 6)
- 11.1 / 18 = 0.616
0.616 is the percentage of the range versus your hand. Since we want to calculate the G-bucks of our hand, and not the range, subtract 62% from 100% to give us our hand's equity of 38%.
Now that we know our equity, we can calculate our G-bucks for making the call. Remember, pot = $600 and it costs us $250 to call.
Our share of the total pot is $228; subtract our investment of $250 (we would have to pay $250 to call the bet) and we have our final G-bucks.
According to G-bucks, every time we make this call, we're losing $22.
As you can see, calculating G-bucks can be a lot of work, especially when you have your opponent on a wide range, such as:
- Any hand with two hearts
- Two pair
The range Daniel Negreanu
can put a player on is ridiculously small, even for a pro.
When you have over 20 hands in your opponent's range, for instance, it can be a lot of work to get all the calculations done. There are some poker equity calculators out there that will give you the equity of your hand versus an entire range, but even with those it takes a little effort.
Getting the exact G-bucks is a phenomenal post-session exercise for evaluating your session performance. When you're at the table, you can use the G-bucks concept to get a vague idea of whether your call is going to be +EV or -EV.
For our example, you would know that you're about a coin flip to both JJ and QQ, and you're a 2-1 dog to KK and 8-1 to AA. If you don't know those exact numbers, you'll be aware that you're really behind AA, far behind KK and a coin flip to QQ and JJ. Since you're only getting 1.4-1 on your money, it would seem to you that you're not getting enough odds to make up for being so far behind half of the range.
The more time you spend doing the calculations on paper, and running the numbers after your sessions, the closer your guesses of the numbers will be at the table. You don't have to be great at doing math to be a solid math player at poker. You just have to spend the time working with the numbers to afford yourself a strong feel for them.
If you can put them on a range of five hands, and you can only beat one of those, chances are you should fold. There are situations where the range you put your opponent on will be so weak that you can afford a call with a garbage hand, simply because your hand beats enough of their range to make it profitable.
There are times where your opponent will have the one or two hands that will beat you, but if you're evaluating your ranges accurately and consistently, you will make money in the long run by playing against the entire range. Almost never put your opponent on just the one hand you can beat, or just the one hand that beats you.
Use G-bucks and Sklansky dollars to figure out where your game is making or losing the most money. You should be running these numbers after winning sessions as well as losing sessions. Your short-term real-money results are not an accurate representation of the strength of your game; G-bucks are.
PS. This article was updated thanks to feedback and discussion with reader Briana. Keep the feedback coming, comments are always appreciated.
More strategy articles from Sean Lind:
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