Imagined Money Part 1: Sklansky Dollars
Some ideas and poker theories help your game while you're playing, while 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.
This article describes the first of two mechanisms that will help you do so: a tool to evaluate your game after the hand or session is long over.
For those few of you who don't know, David Sklansky is one of the all-time greatest mathematical poker minds. 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♣.
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.
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.
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:
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
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 $379.40 Sklansky dollars when he made the final call. He would have lost additional Sklansky dollars if you evaluate his play on the flop, and made only a small amount back for his slight pre-flop edge.
As you can see, with Sklansky dollars, they're not going to assist you in making the correct play in the moment, for it's simply not possible (other than in very rare scenarios) to put a player on an exact single hand. In the world of real poker you need to play exclusively against ranges, instead of single hands.
Phil Galfond (known online by the handle OMGClayAiken) took the Sklansky dollars concept and built on it to incorporate the concept of ranges as opposed to a single hand. In the spirit of naming concepts and theories after yourself, Galfond named his concept "Galfond dollars" or G-bucks for short.
The second half of this article will explain G-bucks - how they work, and how you can use them to evaluate the quality of your play post-session, as well as to assist you in making the most profitable decisions in the moment.
More strategy articles from Sean Lind:
- Poker Books: Putting Their Advice to Use
- Tracking Your Records: Excel-ent Practice
- Taking One Shot at the Big Time
- Anti-Outs and Money Cards
Why do you have an 86% chance on the second example when your opponent has 6 outs giving them a 12% chance? Or have I miscounted the outs?
Sorry.Why 63$, 66$ is not it?
Formula please, if I was wrong
Absolutely a typo, been fixed. Thanks.
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... ??
Is this the concept used for the Holdem Luck program?
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.
Great article. Sklansky dollars are very similar to the concept of expected value right? although more the actual dollars rather than percentages.
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
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
THE CONCEPT OF SLANSKY DOLLARS IS RIDICULOUS
WHAT THE HELL IS WRONG WITH YOU PEOPLE