Expected Value (EV) Explained
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Expected Value (EV) Explained
By: Daniel Skolovy
Poker is all about making money. Unfortunately, making all the right decisions doesn't ensure you'll book a win.
You can play great poker and still lose, because poker is heavily influenced by luck in the short term.
However, understanding and using the concept of expected value (EV) can go a long way toward helping you hone your play.
Expected Value: What Is It?
Every decision you make at the table can be classified as +EV or EV.
Simply put, +EV is a good choice  one that will make you money in the long term. Negative ()EV is a bad move, or one that will lose you money in the long run.
Wikipedia has this to say about expected value:
"In probability theory the expected value of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).
"Thus, it represents the average amount one 'expects' as the outcome of the random trial when identical odds are repeated many times."
What that means in English: expected value is the amount of money you would win or lose on average on your bet.
If you and a friend were to bet on the outcome of a coin flip and agree that you would be paid $5 for every time it came heads and you would pay him $5 every time it came tails, you would win half the time and he would win the other half of the time.
That would make the bet a neutral EV bet.
Let's say, though, that your opponent decided he would pay you $10 for every heads but you would still only pay him $5 for every tails.
The wager now becomes a +EV bet.
You're still going to be winning 50% of all of the flips; however, when you win, you're getting paid double what you pay him when you lose.
Your expected value on every flip is now $2.50.
Let's look at the math. One outcome of the flip is it comes tails ($5); the other outcome is heads (+$10).
So 50% of the time you'll win $10 and the other 50% of the time you'll lose $5. $10 (.5)  $5 (.5) = +$2.5.
In poker this means you only want to make bets that show a positive expectation and avoid ones with a negative expectation.
This is where your money comes from  making bets that only show a positive expectation.
An example from the felt:
You have 5♠ 6♠ and the board is 7♠ 8♠ A♣. Your opponent accidentally flips over his hand as he bets $10 into a $60 pot.
He has A♥ K♦. He has top pair aces with the best kicker.
You have a straight draw and a flush draw. You can only win if a spade falls or if a 9 or a 4 comes.
There are nine spades left in the deck plus three nonspade fours and three nonspade nines.
That makes a total of 15 outs.
You have seen 7 of the 52 cards in the deck leaving 45 remaining, meaning 15/45 cards win it for you.
The odds against you hitting your hand are 21. The pot odds are laying you 71 as you have to call $10 to win a $70 pot.
This bet is extremely +EV. On average you will win double your investment.
Conclusion
Expected value is crucial in poker because the game will have fluctuations.
In the short term, whether you play good poker or bad poker, you will win and you will lose.
Good players, however, are going to make money in the long run. Bad players are not.
That's because good players discipline themselves to make only +EV wagers, whereas bad players play with reckless disregard.
Do yourself a favor and become a good player: look for bets that show a positive expectation.
Poker is all about making money. Unfortunately, making all the right decisions doesn't ensure you'll book a win.
You can play great poker and still lose, because poker is heavily influenced by luck in the short term.
However, understanding and using the concept of expected value (EV) can go a long way toward helping you hone your play.
Expected Value: What Is It?
Every decision you make at the table can be classified as +EV or EV.
Simply put, +EV is a good choice  one that will make you money in the long term. Negative ()EV is a bad move, or one that will lose you money in the long run.
Wikipedia has this to say about expected value:
"In probability theory the expected value of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).
"Thus, it represents the average amount one 'expects' as the outcome of the random trial when identical odds are repeated many times."
What that means in English: expected value is the amount of money you would win or lose on average on your bet.
If you and a friend were to bet on the outcome of a coin flip and agree that you would be paid $5 for every time it came heads and you would pay him $5 every time it came tails, you would win half the time and he would win the other half of the time.
That would make the bet a neutral EV bet.
Let's say, though, that your opponent decided he would pay you $10 for every heads but you would still only pay him $5 for every tails.
The wager now becomes a +EV bet.
You're still going to be winning 50% of all of the flips; however, when you win, you're getting paid double what you pay him when you lose.
Your expected value on every flip is now $2.50.
Let's look at the math. One outcome of the flip is it comes tails ($5); the other outcome is heads (+$10).
So 50% of the time you'll win $10 and the other 50% of the time you'll lose $5. $10 (.5)  $5 (.5) = +$2.5.
In poker this means you only want to make bets that show a positive expectation and avoid ones with a negative expectation.
This is where your money comes from  making bets that only show a positive expectation.
An example from the felt:
You have 5♠ 6♠ and the board is 7♠ 8♠ A♣. Your opponent accidentally flips over his hand as he bets $10 into a $60 pot.
He has A♥ K♦. He has top pair aces with the best kicker.
You have a straight draw and a flush draw. You can only win if a spade falls or if a 9 or a 4 comes.
There are nine spades left in the deck plus three nonspade fours and three nonspade nines.
That makes a total of 15 outs.
You have seen 7 of the 52 cards in the deck leaving 45 remaining, meaning 15/45 cards win it for you.
The odds against you hitting your hand are 21. The pot odds are laying you 71 as you have to call $10 to win a $70 pot.
This bet is extremely +EV. On average you will win double your investment.
Conclusion
Expected value is crucial in poker because the game will have fluctuations.
In the short term, whether you play good poker or bad poker, you will win and you will lose.
Good players, however, are going to make money in the long run. Bad players are not.
That's because good players discipline themselves to make only +EV wagers, whereas bad players play with reckless disregard.
Do yourself a favor and become a good player: look for bets that show a positive expectation.
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