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Expected Value (EV) Calculations

Expected Value Calculations Part 5 - SklanskyBucks and Gbucks

6,959 Views on 27/4/15

In Part 5 of our Expected Value Calculations Series, we look at G-Bucks - A different way of looking at EV.

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With thepokerimage intense calculation out of the way, we are going to think about the relevance of Expected Value and the various ways it can be measured.

True Expected Value (EV)

In this series we have been attempting to calculate “true EV”. In reality this will be completely impossible in the large majority of situations. Why?

In order to calculate “true EV” we need to take into account every possible event that might occur. There are two main problems with this -

1. The permutations are endless – Not only would we need to take into account every possible action and bet size, we'd also need to take into account extra-game occurrences that could effect play. Perhaps your opponent is watching a film in another window and will mis-click with an increased frequency. Perhaps he has a pizza in the oven and will suddenly leave the table mid-hand when he realizes it is burning. It may sound crazy, but if we are talking about “true EV”, this is what it involves, absolutely everything. 

2. We don't have all the relevant information – Even if we had an infinite amount of time to think of all the possible outcomes of a certain situation, we would still be limited by not having access to all the relevant information. We can never know with 100% accuracy how often someone will fold in a certain situation.

If we knew our opponent was having trouble with his ISP and would disconnect 40% of the time during a certain hand, it could have a dramatic effect on our “true EV”. In reality we'd almost never have access to this information, and couldn't use it in our calculations even if we wanted to. 

We can see then that in most (if not all) situations, calculating your “true EV” is an ideal. We can still make good estimates based on the most relevant factors and most likely outcomes. In the pre-ceding articles we have broken our EV calculations down into a number of simple scenarios, rather than considering every possible alternative. In practice this is how EV calculations must be done; they are simply estimates after all. 

You could include 1000 possible outcomes in an advanced EV calculation, but if your estimates regarding your "">fold-equity are inaccurate, the overall calculation will be inaccurate whether you considered 5 variables or 1000.

Allin-EV/Sklansky Bucks

Computers have a hard time calculating true-EV. They usually are not programmed with the ability to estimate fold-equity, or the knowledge to ascertain the most relevant factors to use in EV calculations. They are however, able to calculate with accuracy a specific type of EV known as “all-in EV”.

All-in situations allow you to calculate EV almost perfectly, because aside from a stray meteor hitting the room, there are no real variables to consider; the money is already in the middle and no further actions will be taken.

Imagine you shove all-in pre-flop with AA for $100. Your opponent calls $100 with his KK. (There are no blinds). Your opponent spikes a king, and you lose your $100. In reality you've just lost $100, but your all-in EV will be positive. This can also be referred to as making “Sklansky bucks” coined after the famous player and author David Sklansky.  Assuming AA has roughly 82% equity, we could calculate that the all-in expected-value was $64.

(0.82 * $100) – (0.18 * $100) = $64

In reality we've just lost $100, but we could say that we've made 64 Sklansky bucks. This is the amount we expect to make on average every time we get AA v KK in this spot.

Many poker players typically put a lot of emphasis on their all-in EV. You will see plenty of graphs posted on the forums where players are complaining how unlucky they've been because they are many buyins below their allin-EV. But have they really been unlucky? Possibly. There is a chance they haven't though; there are huge limitations to how useful all-in EV actually is.

Limitations of All-in EV

1. Only takes into account equity at the time of all-in. In other words, with 100bb effective stacks, we could get 99b in the middle when we have top-set and our opponent has a gutshot. On the river, our opponent hits and shoves all-in for his last 1bb and we call. According to all-in EV we just got the money in drawing-dead, and it won't be profitable for us. In reality seeing as we got 99% of the stacks in with an equity edge, of course this will profitable for us in terms of our “true EV”.

2. Doesn't take into account fold-equity. Perhaps we 5bet shove A5s as a bluff after our opponent 4bets us pre-flop. According to all-in EV we just got the money in with 33.6% equity. In reality we expect to generate some fold equity with both our 3bet and our 5bet, so our true EV will be a lot higher than our all-in EV suggests.

3. Doesn't take into account our opponents range. Perhaps we get bottom set all-in on the flop against our opponents top set. According to all-in EV we just got the money in almost drawing dead. If our opponent's range actually contains a whole bunch of draws and 1pair hands we expect our all-in to be profitable even though we got shown a better hand on this occasion. 

So, is all-in EV actually useful?

Not really. It'spokerimage an indication of how well you are running in one specific type of situation (I.e all-ins), but it's certainly not a good indication of whether you are running above or below your true EV. You might be below your all-in EV but running way above your true-EV.

If you are repeatedly hitting 8% rivers after you already committed most of your stack, can you really complain that you are “running bad” when you lose a few coin-flips? Or if you've coolered your opponent 5 times in a session, can you really complain when he catches a couple of flush-draws against your top-pair?

All-in EV is one of those statistics that players like to check purely out of interest, but is essentially useless. If your all-in EV line is tilting you, switch it off.

G-Bucks

G-bucks, coined by the legendary Phil Galfond, is a far more useful version of Sklansky Bucks. Rather than considering the expected-value against of your specific hand at the point of all-in, you consider the EV of your range against your opponent's specific hand.

To take a very simple example, imagine our shoving range in a certain pre-flop situation is TT+,AQ+. For simplicities sake we'll imagine we shove $100 into a dry pot as before. In one particular hand we wake up with TT, the bottom of our shove range. We shove for $100, our opponent calls and tables JJ.

In terms of Sklansky bucks, we've just made a loss. We got our $100 in with 18% equity.

(0.18 x $100) – (0.82 x $100) =  -$64 Sklansky Bucks

In terms of G-bucks we expect to make some profit, because against our entire range JJ is a slight underdog and has only 47% equity. 

(0.53 x $100) – (0.47 x $100) = $6 Galfond Bucks

The next stage would be to think about the EV of our range vs our opponent's range. After all, our opponent may have JJ in this instance, but if his calling range is JJ+/AK it wouldn't really be accurate to suggest we made G-bucks just because our opponent's specific hand was behind our range.

Using Galfond bucks allows us to more accurately determine the EV of situations by considering ranges rather than specific hands. Intuition possibly tells you that getting all-in with bottom set 50bb deep on a rainbow board is going to be profitable. When your opponent does show up with top-set in these situations, you still make G-bucks, because you know your opponents range is much wider than top set.

Unfortunately tracking software will not be able to help you calculate G-bucks. This is because commercially available software is not capable of putting players on ranges.  Use poker-stove to calculate the equity of one range vs another range to help you work out your G-bucks.

Make sure to read all of the Expected Value Calculation articles in our EV Series here on PokerVIP and make sure to understand poker rules before embarking into a more advance level! Rules are always 90% of every good strategy.

Author

w34z3l

I am of British nationality and go by the online alias w34z3l. I am considered one of the top consultants in the field for technical analysis (i.e. database work) and application of game theory concepts to various card games. I make a ... Read More

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