Expected Value

When you make important decisions the expected value is important

Making the right decisions in poker is as important as getting a good poker rakeback deal.

The ignorant may say that poker is a game of luck; that outcomes are based entirely on “how the cards fall”, and since nobody has any control over this, it is deemed that luck is the main determinant of a hand outcome. Whilst this is a false statement, it does bear some truth. In the short term, the outcome of any poker hand is mostly determined by luck. However, poker is a game about the long-term. It is about making the correct decisions over a large sample, so that the luck aspect dissipates, and outcomes fall back onto the mathematical basis upon which the game is built. This is known as expected value.

So what exactly is expected value (EV for short)? Simply put, expected value is the amount of money that one should win when two or more unique hand combinations face off in an all-in situation. Note that EV can only be calculated in all-in situations, as prior to that opponent’s exact hole-cards are unknown, and thus we cannot work out one’s own holdings fare against them. Although the use of calculating EV has the same application in both cash games and tournaments, it is tended to be more of a cash game calculation. In a cash poker game, one can assign a real money number to their EV, as you are winning and losing actually money in each hand. Whereas in a tournament, although the calculations are exactly the same, a real money figure cannot be assigned to an EV calculation, as tournament chips have no monetary value, and the calculation does not take into account the distance from the money bubble or payout structure.

Let’s run through a simple example. In a live 1/2 NL game, you hold Ks Kd. Both you and an opponent 100BB’s deep proceed to get the money all-in pre-flop. When the cards are turned over, your opponent reveals As Qd. In this match up, KK is expected to win 71.96% of the time. This is called your equity – the frequency at which one hand should win over another over an infinite sample. Now how does the calculation work? Assuming both you and your opponents were the blinds, there is $400 in the pot. Over a sample of 100 occurrences, KK should win that $400 72 times, and AQ should win the $400 28 times. So, for the player holding KK, their expected value is (200×72 – 200×28)/100 = 8,800/100 = 88. Thus our EV for this situation is $88 – we are expected to win $88 in profit every time this exact situation arises. Of course, due to short term luck, this may not be the exact case. One could lose 4 such hands in a row before one is actually won. This is why EV is a long-term calculation.

In the example above, we calculate the expected value once we know our opponent’s hand. In real games, you don’t know your opponent’s hand and you want to calculate if it’s positive expected value to move all-in on the spot, so you must put your opponents on a “range” instead of just a fixed hand. Knowing their playing style will allow you to put them on a more accurate range of hands. Let’s say that he is a loose aggressive player and {JJ-AA,ATs+,ATo+,KQs} is his assumed shoving range preflop. KK has a 68% equity against this range so it would be +EV to call the all-in. The easiest way to calculate the chance of winning against a range of hands is to use an odds calculator such as Calculatempro when away from the tables. That way you can calculate if its a positive expected value play on the spot, which is common when playing against short stack players who are looking to move all-in preflop.

David Sklansky pioneered this concept in his book “The Theory of Poker”. He coined the term “Sklansky dollars”, which equates to the intangible EV amount that one should win over an infinite sample. More recently, Phil Galfond took this idea of EV further by introducing the term “G-Bucks”. This is an EV calculation done by comparing one’s holdings to your opponent’s entire range based on prior action, and is significantly more complicated. Unlike normal EV calculations, there does not have to be an all-in situation for “G-Bucks” to be calculated.

So what does this mean for a poker player? Essentially, to be a profitable winning poker player, one has to make the most positive expected value (+EV) decisions possible. If you have a read that your opponent only goes all-in holding AA, and you decide to call with KK, you have made an -EV decision – one that will lose you money over a long period of time if repeated. Making a +EV decision repeatedly requires a lot of practice and concentration, but once firmly entrenched in one’s mind, it sets that person up for a profitable poker career. So don’t worry if your AA loses to a maniac who decided to shove 37o pre-flop – know that over the long-term, you’ve made a +EV decision which will equate to profits. Now that we are talking about profit. Are you getting poker rakeback? If not, then you could be missing out on thousands of dollars every month. We offer the best rakeback deals and rake races, so open a rakeback account here. If you dont know what poker rakeback is, then please start with our article on poker rakeback.