|Posté le: Jeu 15 Oct - 01:50 (2009) Sujet du message: Expected Value - Learn to Calculate your Poker Hand EV
|Expected Value - Learn to Calculate your Poker Hand EV
With the rise of poker’s popularity over the last decade, a few terms have emerged describing various poker-related concepts that have proven especially helpful when it comes to discussing strategy and theory. “Expected value” (sometimes abbreviated as “EV”) is an example of one of those terms.
Expected Value - Defined
Put simply, expected value refers to what one expects to gain from a given situation, say, after having placed a bet. For example, let’s say you and I decided to bet $100 on a coin flip. Although only one of us is going to win the bet, we each have the same EV prior to the flipping of the coin. There is exactly a 50% chance of the coin landing heads, and 50% that it will land tails. That means we each have a 50% chance of winning $100 and 50% chance of losing $100.
You probably don’t need math to tell you your expected value is zero here, but we can nevertheless express this as an equation: 0.50(100.00) + 0.50(-100.00) = 0.
Now let’s say I offered you a different deal. Let’s say we again bet on a coin flip, but this time I will give you $100 if the coin lands on heads but you only have to give me $75 if it lands on tails. In this case, it perhaps isn’t obvious what exactly your expected value is, although you know it must be better than zero. So we do the math. Here’s how it looks from your side: 0.50(100.00) + 0.50(-75.00) = +12.50. And from my perspective: 0.50(-100.00) + 0.50(75.00) = -12.50.
You stand to gain an average of $12.50 every time we make this bet, while I stand to lose $12.50 (on average). It should be noted that not once will you win exactly $12.50. Rather, that’s what you expect to win on average should you repeatedly take this bet. Of course, it might not work out that way — I could get lucky on you — but it is nevertheless correct to say that is your “expected value” here.
Expected Value - Applied
How does this idea apply to poker? In fact, the idea of EV can be evoked to describe every single decision made at the poker table. There a few common situations, however, where one frequently hears references to expected value being made. One of those is with reference to pot odds.
Say we are playing a hand of no-limit hold’em. You raised big preflop with Ad-Ah from early position, I called you with Qc-Jc from the button, and everyone else folded. The flop came Ac-Ks-2c, and we both checked. The turn brought the Jh, and you pushed all in with your last $1,000, making the pot $1,500 total. I have enough chips to call your bet, but do I want to? Here is where I might think about my expected value before deciding what to do.
I don’t know what you are holding, but I am pretty sure my pair of jacks is not the best hand at the moment. I don’t think you would have made such a big bet without a big hand. Since you raised preflop from EP, I don’t believe you have queen-ten. In fact, I strongly suspect you have aces or kings in the hole and thus are holding a set. If that’s true, that means I have 11 outs to win the hand. Any ten is going to give me a straight (that’s four outs), and a club that doesn’t pair the board will give me a flush (that’s seven more outs, as we already counted the 10c).
The other clubs might be good for me, too, but let’s say I’ve read you correctly and know you have pocket rockets, so I can only really count on 11 clean outs to win. There are 44 unknown cards, so that means if I call I have exactly a 25% chance to win this hand, while you have a much better chance at 75%.
What is my expected value? Think back to the coin flip examples. It will cost me $1,000 to try to win the $1,500 in the middle. If I call, I have a 25% chance of winning $1,500, and a 75% chance of losing $1,000. Let’s do the math: 0.25(1500.00) + 0.75(-1000.00) = -375.00.
This is not such a good call for me. I have here what is called “negative expected value.” I stand to lose an average of $375.00 every time I call in this exact situation. Meanwhile, you have a “positive expected value” of $375.00, meaning that is what you stand to gain (on average) whenever I call in this spot. I think I’ll fold.
As you can see, expected value or “EV” can be brought up to assess any decision made at the poker table. Indeed, we might say my decision to call your preflop raise with Qc-Jc was probably “negative EV,” since your raise signaled to me that you likely had a stronger hand.
The idea, of course, is to try to make decisions that have “positive EV” more often than ones that have “negative EV.” You may lose some of those hands (indeed, you most definitely will). But on average, you should come out ahead if your decisions are consistently +EV.