What is expected value?

In its simplest definition, expected value is an averaged-out result of a given action over time. As a reminder, expected value in poker is often referred to as the initialism, EV, but if a particular play is being analyzed, it’s going to be negative EV, or positive ev. Of course, your poker playing strategy should include as much positive EV as you can master.

Before we get to that, lets discuss a simple EV calculation that you can use to better understand more complex poker situations. Lets say you and your buddy always run this coin flip thing to see who buys the next round of beer. This time you chose tails, but it landed on heads so your buying. Man that looks good. You also lose the next time, and the next two times after that. Gheez what a bad run. In reality, you don’t really care though, because you know its going to even out right? We only had 4 flips here, but when you start adding beer after beer after beer, the probabilities of the coin flip are going to end up rather much close to a 50/50 result. Sure over 5 flips you might have to buy 4 beer, but over 500, or 5000 flips you guys are going to be even right?

You will never get the same result exactly, but averaged out, the results are going to be so close the two of you would consider this even odds or expressed 1:1, which is mathematically as accurate as you can be when it comes to probabilities. So the result is 1:1 of a given action (the coin flip) over time in this case, (5,000 times).

But wait, lets say your buddy feels bad for you losing 4 in a row and says “you know what Buddy, from now on, if I lose the toss I will also buy chips with our beer, and if you lose the toss, you just keep buying our normal 2 beers. Assuming you like chips, you instantly recognize this as a positive EV situation. Why? Well, lets do the numbers.

Since we know our coin flip is 1:1 and beer costs $4 bucks while the chips cost an extra buck, if we average it out over time, say 1,000 flips we will split the results between you and your friend. He buys 500 times for a total cost of $4,500, (WHAT, no tip?) and you buy 500 times for a total cost of $4,000. Now the total amount of value consumed by the both of you is 8,500, but you have only paid for 47% of it, while your buddy has paid for 53% of the chips and beer over time. Now that is a positive EV situation for you, if all you want from your buddy is more of his money.

What your friend failed to recognize is that EV is the expected value long term, so even though you bought 4 times in a row, he looked at the short term results, which can often be skewed. Remember it this way, short term results will normally vary, while long term results will invariably normalize. This short term situation is referred to as variance or well, just plain luck, which can go either way. Your friend felt for you because of your run of bad luck, and you made him feel better by accepting his +EV offer - Nice! With all this beer talk, you might have forgotten that we’re actually talking about poker, so lets look at and EV decision.

You limped into this pot with several others holding the 5 and 6 of spades and saw a promising flop of A5K. You missed on the turn and now its down to you and this other player who just bet $6 into your draw. So its $6 to call into a $24 pot which is exactly 4:1 pot odds. You count your outs as 9 spades but also think you can win with one of the 2 remaining 5s, or 3 remaining 6s. So altogether that is 14 outs, and we’ve since done this before so you should be able to instantly recognize that you are priced into call because your pots odds are 4:1 and the odds against you to win the hand are only 2.3:1, but lets extend that to EV in terms of money.

Over 1,000 beers, I mean hands, you will win that $21 pot 303 times and lose your $6 call 697 times when your draw does not come home for you. So even though you will lose the hand most of the time, you can see that you make money on this play because the pot odds are dictating that you call every time. Average that $2,181 over 1,000 hands and your +EV for this play $2.18 for every time you make the call. I hope you can you see how this works now because the more positive expectations you play in poker, the more likely it is that you will be a profitable player.

So are you curious as to what happened in this hand? Did your hand win or not? The answer is in the EV, and since you know this is a positive EV, then the answer is, IT really doesn’t matter if you won this time or not. The answer lies in you making a long term, positive EV play. Well, thanks for the beers, and to see more poker tutorials like this one, visit the poker school at Paddy Power poker.com