The most important poker article you'll ever read
Expected Value is the amount of money we stand to win or lose on average in a particular situation. It's often abbreviated as "EV."
EV is an absolutely key concept in poker. Once you understand it, your poker game should improve dramatically. Now that we've looked at pot odds and the odds of winning a hand, we can focus on EV.
Let’s look at an example:
We play 7♥ 8♥.
On the turn, the board reads: A♠ T♥ 3♥ 4♦.
The pot is $5,000.
Our opponent moves all-in with his last $2,500.
We’re convinced he has Ace-King, so we’re sure that if we hit our flush – i.e all hearts - we win the hand. Should we call? Let’s run the numbers…
There are 9 hearts left in the deck, giving us 9 outs.
There are (52 – 6) 46 possible outcomes on the river.
Our odds of hitting the flush are 37/9, roughly 4/1 against us.
The pot, after our opponent moves all-in, contains $7,500. We need to call $2,500 if we want to stay in the game – making the pot odds 7,500/2,500, or 3/1.
We know this is a losing proposition since the pot-odds are smaller than the odds of hitting our hand. But how much do we stand to lose, on average? In other words, what is our expected value?
Here’s how we calculate EV:
- Multiply the potential profit by the number of successful events
- Multiply the potential loss by the number of unsuccessful events
- Deduct the potential loss from the potential profit
- Divide the profit minus loss by the total number of events.
Have a look at this formula:
(Profit * Successful events) - (Loss * Unsuccessful events)
EV = ---------------------------------------------------------------------------------
Total number of events
Let’s put in the numbers from our example:
(7,500 * 1) - (2,500 * 5)
EV = ----------------------------------------
6
which works out as
7,500 - 12,500
EV = ----------------------------------------
6
which works out as
- 5,000
EV = ----------------------------------------
6
That means:
EV = - 833,33
So, in this example, this means that every time we call the $2500, we can expect to lose an average of $ 833,33.
So our expected value is negative. Bad news. We can classify this situation as –EV. If it had been profitable, we would say the situation was +EV.
Poker is all about finding the +EV situations and playing them. When you know you’ve made a positive EV play, yet you still lose the hand, you shouldn’t worry.You know you’ve done the right thing and if you keep making these plays, in time, the odds will even out and you will make a profit.
This is an incredibly important point so if you feel you need to go back re-read what we’ve covered so far, please do so! It will make a massive difference to your poker game.
Let’s look at another example:
We’re playing against one opponent and we are dealt A♠ A♥.
After some raising and re-raising, we’re all-in against K♦ K♣.
With all the chips in the middle, the pot is $10,000.
The odds of us winning are roughly 4/1. How much do we expect to win, on average? Let’s calculate the EV:
4 out of 5 times, we will win $5,000 off our opponent.
1 in 5 times, we will lose our $5,000.
Let’s calculate the EV:
(5,000 * 4) - (5,000 * 1)
EV = ----------------------------------------
5
20,000 - 5,000
EV = -----------------------------------
5
15,000
EV = --------
5
EV = $3,000
So, more often than not, you will pick up a $5000 profit. Sure, sometimes you'll lose your $5000, but, on average, you stand to win $3000 in this situation.
Cool, huh?
Hopefully, you can now see that is a extremely useful concept in poker. That's why we say that this is the most important article about poker you'll ever read.
In our final article on maths, we’re going to look at the concept of implied odds. And if you want to read more about EV, check out David Sklansky's book: 'The Fundamental Theory of Poker.'
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