Poker Math: What Are Sklansky Dollars and G-Bucks?

david sklansky 3218
David Sklansky, Inventor of Sklansky $ (ldo)

Some ideas and poker theories help your game while you're playing; others help you evaluate your play after the pot has been shipped.

One is no more important than the other. The No. 1 way every poker player improves is by looking back at the hands they've played and dissecting them - finding out what mistakes they made and where they left some value behind.

To be a great poker player you have to learn from all mistakes, big and small. Here are two great poker math tools to evaluate your game both during and after a poker session.

What are Sklansky Dollars?

For those few of you who don't know, David Sklansky is one of the all-time greatest mathematical poker minds.

David Sklansky poker
Sklansky dollars 4ever.

He wrote some of the first poker books which are still viewed as some of the most valuable ever written. His work has served as a building block for other players and theorists, making him truly legendary.

One of the concepts introduced by Sklansky is aptly named the Sklansky dollar. This concept is only useful for postgame analysis, but when used can give you valuable hints as to where you made mistakes, and how expensive the mistake was.

The Sklansky dollar is a simple but truly brilliant concept. Here's a basic example to get you acquainted with how it works:

You move all in with A A pre-flop for $100, and get called by K K.

Pot: $200

Board: Q T 2 K 7

In real money, you just lost $100 to a suck-out. Sklansky dollars work exclusively on the statistical probability of winning, ignoring the actual results.

Individual hand equity when the money went in:

A A - 83%

K K  - 17%

For the concept of Sklansky dollars, your equity percentage is equal to the same percentage of the total pot. This means 83% of the total pot is statistically yours, making your share $163.

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What Is Your Sklansky Dollar Amount?

With one final step, we can get our Sklansky dollars amount. You need to subtract your investment for the choice you're evaluating from the total pot. So $163 - $100 (your investment into the pot) = $63.

sklansky dollars poker
If only Sklansky dollars looked this sexy.

Even though you lost $100 in real money, you just made $63 in Sklansky dollars.

This concept is useful to evaluate in a dollar amount how profitable your action was statistically. Over a long enough sample of hands, your statistical profit will come to match your actual profit.

(The term "long enough" is deceptive, as this sort of math theory can require a sample size larger than a human can acquire in their lifetime. Meaning even though you play statistically perfect poker, it is possible, while not plausible, that you'll be a lifetime loser at the game.)

Another Sklansky dollars example:

Pot: $1,250

Board: A K J 4

Your hand: A K

Opponent's hand: Q Q

You move all in for your final $770 and your opponent decides you're bluffing and calls you. The river brings a ten, and you lose the pot.

To calculate your Sklansky dollars, first you need to get the equity of the hands when the money went in. You have an 86% chance of winning the pot.

Total pot: $1,250 + $770 +770 = $2,790

G-Bucks poker
G-Bucks not Gold bucks.

Total Share: $2,790*86% = $2,399.40

Minus your investment: $2,399.40 - $770 = $1,629.40 Sklansky dollars

You just lost a large pot in real money, but you made yourself a nice profit of Sklansky dollars. It almost helps lessen the sting of having to call for fresh chips.

This concept also works in reverse - you can use it to calculate how many Sklansky dollars you lost by making a bad play. In the same hand, let's calculate the Sklansky dollars of your opponent:

Total pot: $1,250 + $770 +770 = $2,790

Total Share: $2,790*14% = $390.60

Minus your investment: $390.60 - $770 = -$379.40 Sklansky dollars

Even though your opponent won a pot worth almost three grand, he lost $379.40 Sklansky dollars when he made the final call. He would have lost additional Sklansky dollars if you evaluate his play on the flop, and made only a small amount back for his slight pre-flop edge.

As you can see, with Sklansky dollars, they're not going to assist you in making the correct play in the moment, for it's simply not possible (other than in very rare scenarios) to put a player on an exact single hand. In the world of real poker you need to play exclusively against ranges, instead of single hands.

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What Are 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.

As we learned above, Sklansky dollars can put a dollar amount on the probable outcome of any poker scenario which is useful in evaluating your play post-session. The problem with Sklansky dollars is you can't really use them 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

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.

Phil Galfond
Aka G-Bucks

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.

Enter Phil Galfond and G-Bucks. G-Bucks use the same basic principles as Sklansky dollars, but pit your hand against your opponent's entire range.

How to Calculate G-Bucks

The way to calculate G-bucks is not quite as simple as Sklansky Dollars:

  • 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 calculate 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

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.

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Use G-Bucks Post-Session to Analyze Your Play

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.

Phil Galfond gbucks
G-Bucks before or G-Bucks after.

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.

Related Reading on Poker Math:

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amy 2014-07-12 22:31:25

damn...this guy sklansky was totally sitting at my poker table few days ago at mgm grand! I was beaten by a celebrity

Liam 2012-08-26 05:05:27

Why do you have an 86% chance on the second example when your opponent has 6 outs giving them a 12% chance? Or have I miscounted the outs?

Denisjkee 2011-09-01 09:36:33

Sorry.Why 63$, 66$ is not it?
Formula please, if I was wrong

Sean Lind 2010-03-29 22:56:21

etc.
Absolutely a typo, been fixed. Thanks.

-sl

etc 2010-03-29 22:11:01

Isn't there a typo in the 2nd example: you say you move in for your last $675, but yet in your calculation you add the pot (1250) + 770 + 770... ??

Kevin 2010-03-13 21:02:26

Is this the concept used for the Holdem Luck program?

Sean Lind 2009-04-25 20:19:00

Max, Expected Value (or EV) is typically only used as a red or black, (-EV or +EV). Sklansky dollars put a $ to the EV as you said.

max 2009-04-17 15:51:00

Great article. Sklansky dollars are very similar to the concept of expected value right? although more the actual dollars rather than percentages.

Sean Lind 2009-04-07 17:45:00

Hey Greg, the first two paragraphs of the article explain that Sklansky Dollars are for evaluating your plays post-hand, not during.

FUCK SLANKY DOLLARS 2009-04-06 00:11:00

FUCK SLANKY DOLLARS



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