Imagined Money Part 2: G-Bucks

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
Phil Galfond + G-bucks = WSOP bracelet.

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.

Calculating G-Bucks

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.

  • $600*0.38 = $228

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.

  • $228 - $250 = -$22

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
  • Set
  • Two pair
  • Open-ended
  • Overpair

Daniel Negreanu
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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Hag 2013-02-22 07:58:18

Should have double checked your results before posting that comment! Both methods provide exactly the same results. Feel free to delete the comment.

Hag 2013-02-22 07:48:25

The calculations aren’t entirely correct. You say:

‘You raise $50 pre-flop, and your opponent reraises you all-in for $300.’

The pot is currently $350. So we're calling $250 to win $350. Thus, it should be:

Win: $350*0.38 = $133

This is our expected profit. Our expected loss would then be: (1-0.38)*$250 = $155.

Our Expected Value (EV) would then be:
EV = $133 + (-$155) = -$22

Expected Value is calculated: (Probability of Winning)*(Pot We Win) - (Probability of Losing)*(Bet We Lose).

So we lose $22 every time we make this call, right? Or am I missing something?

rendalli 2009-02-24 22:32:00

Thanks for your explanation.

You are right, the concept is the same. It's just the point of view that changes. I just feel the point of view Galfond took is pretty creative, i.e. "i make money pushing a bluff into that guy even if he calls me - I just need to make sure my pushing range has a positive G-Bucks value against his call" (=enough value hands in pushing range).

But you are of course right, your point of view is also interesting ("i put him on a range and figure out the expectet value of my hand against his range") and the concept "Equity a Hand has vs a Range" stays the same.

Thx again

Sean Lind 2009-02-10 17:55:00

Hey Rendalli,
I actually flipped the G-Bucks on purpose. The concept is the same, just this makes more sense for the core of our readers.

The problem with evaluating your range vs their specific hand, is you can only ever do that post session. In the moment you will know your specific hand, and the range you put your opponent on. This allows you to use the concept in the moment.

Galfond wrote his article with the world's best players in mind. Most of the world's opponents aren't good enough to play against your range. Most amateurs will put you on the hand they want you to have, and play against that.

rendalli 2009-02-08 00:59:00

Sorry to say this, but you are not explaining G-Bucks as Galfond definied it imo.

You just put it the wrong way. You defined G-Bucks as "equity we have against his range".

But G-Bucks are: "Equity our range has against his hand"!

You should reread his article.

Just to make it clear the original definition from Galfond: " 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, [b] you take the entire range of your hand and see how it does against his hand.[/b]

Sean Lind 2009-01-17 18:55:00

- when you win a hand, you opponent might choose to muck. This means that your calculations will be biased towards loosing hands.

This is incorrect. Even after the player folds, meaning you know that he didn't have a hand that had you beat, those hands are still part of their possible range. You have to evaluate for the information you had at the time of your choice. Poker is not results based, if you're 99% to win and lose, you didn't play the hand wrong.

As for 4-5 players, you're correct that the calculations will get very in-depth and demanding. I doubt anyone in the world does it fully at the table. The idea is to do it enough on paper after your games to get a strong feel for the numbers, so when you think about their range, you'll know that it's somewhere around x%.

As for an easy way to do it, I just look for patterns and ways to cancel out options. For instance if I'm a 3-1 dog to hand A, and a 3-1 dog to hand B, I just remove both of them, as they cancel out to neutral EV. This way you can narrow down the range to making a pretty accurate guess of if the play is +EV or -EV, even if you dont' know the exact numbers.

mseng 2009-01-16 22:24:00

My comments:

- when you win a hand, you opponent might choose to muck. This means that your calculations will be biased towards loosing hands.

- the calculations will get extremely complicated and time-consuming when you have say, 4-5 opponents. Also, some of them might choose to muck at different stages of the hand.

- how can you do it in practice? I mean, for every hand you play you have to keep notes about your hand, the range you put your opponents in, the flop, turn and river, bets and opponents hands. Is there an easy way to do it?

Sean Lind 2008-12-10 19:28:00

Since updating this article, all previous comments are now obsolete, thus removed. Thanks again BrianaB for the feedback and discussion.

-Sean Lind