I don't understand +EV or -EV

I see it all the time among these boards. If someone could explain a hand where you are -EV and +EV, it would be GREATLY appreciated.

+EV: Betting on the river when you have the nuts.

-EV: Calling on the river with queen high.

+EV (positive expected value) means that if you make the same play a 100 or 1000 times or whatever, that play will be profitable. It may not win this hand, but over the long haul it will show a profit.

-EV (negative expected value) means that if you make the same play a 100 or 1000 times or whatever, that play will cost you money. You may win this hand, but you will lose in the long run.

Less extreme examples of +EV and -EV:

+EV: Calling a $1 bet into a $10 pot on 4th street with the nut flush draw.

-EV: Calling a $10 bet into a $10 pot with a gutshot straight draw.

i think the words EV stand for evaluated value.
+ EV would be something that has a positive evaluated value.
-EV the opposite.

Examples of + and -EV can be found above.

EV = expected value. It is a term from the field of probability.

To compute EV, you take the probability of each event occurring and multiply it by the $ outcome if that event occurs. Then you add the products together and that is the EV.

It is difficult to calculate exactly because you don't know your opponent's holdings, but in most cases you can get pretty close.

For example, suppose you get to the turn holding 3s2s from the big blind. There are 4 big bets in the pot and the board is As10c 7sQd. You check, player to your immediate left bets (the pot is now 5 BB), and everyone else folds. It is your action. Is it EV to call?

There is no possibility that you are ahead. Assume by the action thus far that you are 100% certain that if you complete your flush you will win. Also assume that if you make your flush your opponent will not call a bet.

EV = (probability of win)*(bets you win) + (probability of loss)*(bets you lose)
EV = (9/46)*(5) + (37/46)*(-1) = 8/46 = 0.17

So calling a bet in this situation is slightly +EV. If there had been 4 BB or fewer in the pot, the call would be -EV.

Note that there are many factors that affect an EV calculation. For example, in the above scenario, your opponent may have higher spades than you some percentage of the time. He also may have a set or two pair, dirtying two of your outs. In some cases you may be ahead a portion of the time. Also you may win extra bets some percentage of the time if you make your draw.

Using pot odds at the table is a proxy for EV calculations. If you know how to do this, you basically understand EV.

Think of it as the average profit you are making on that hand\bet\situation. If a certain bet has an expected value of $10 it means that if you make the same bet a large number of times your average profit will be $10 (per bet).

If we flip a coin and I give you a $1 if its heads and you give me a $1 if its tails, then the expected value of that bet is $0. Why? Because if I win I make $1 profit and if I lose I lose $1. Since the probability of heads is 50% (as is tails) that means i will lose $1 50% of the time and I will win $1 50% of the time, 0.5*1 + 0.5*(-1) = 0

If I decide to give you $1.2 if its heads then I am not very clever, since the expected value of my bets is then 0.5*1 + 0.5*(-1.2) = -$0.1. So I can expect to lose 10 cents per bet on average. So if we do 100 bets I would expect to lose $10. I might lose more or I might lose less, heck I might even win but the larger the sample size (number of bets) is the closer your actual value will be to the expected value.

Thanks for the replies