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Expected Value (EV) in Poker, Explained
Poker is all about making money.
Poker is all about making money.
Unfortunately, even if you make all the right decisions over an entire session of poker, that doesn't ensure you'll book a win.
You can play great poker and still lose because poker is heavily influenced by luck - but mostly in the short term.
If you understand and deploy the concept of expected value (EV), though, you'll see you can control your profits in the long run. And it can go a long way toward helping you hone your play.
What is Expected Value in Poker?
Every decision you make at the table can be classified as Plus (+) EV or Negative (-) EV.
Simply put, +EV is a good choice -- one that will make you money in the long term.
Negative (-)EV is a bad move -- 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
The Math of Expected Value
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
- You would still only pay him $5 for every tails
The wager now becomes a +EV bet.
You'll still win 50% of all of the flips over the long term. But when you win you'll be paid double what you pay him when you lose.
So: 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.
Expected Value in Poker
You have 5♠ 6♠ on a 7♠ 8♠ A♣ board. Your opponent accidentally flips over his hand as he bets $10 into a $60 pot.
He has A♥ K♦ -- 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 non-spade fours and three non-spade nines.
That makes a total of 15 outs. You've 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 2-1. The pot odds are laying you 7-1 as you have to call $10 to win a $70 pot.
This bet is extremely +EV. On average you will win double your investment.
Why Expected Value is Crucial in Poker
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, will make money in the long run. Bad players will 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.
If You Make +EV Decisions, You Win Long Term
Think of poker as a continual, lifelong game. Your goal in this game is to make money in the long term. You may have losing days, weeks or even months, but as long as you make +EV decisions you will win in the long run.
You are "beating poker." Most beginners tend to look at one hand or one session and draw ridiculous conclusions from it. It's a mistake to react this way.
Let's say for example that you raise pre-flop on the button with K♦ K♣ and the new player calls from the big blind. The board comes K♠ J♦ 2♣; your opponent pushes all-in and you call.
He turns over the A♦ T♥. The turn comes 4♦ and the river Q♠. He starts gloating about how well he played the hand.
He feels that since he won the hand, his move was correct. Sometimes a novice player with KK will even question their call afterward just because they lost.
What you should do is look at your play and ask yourself whether it's profitable in the long run. That is, put whatever the actual outcome was out of your mind and look at it objectively.
In this case it's easy. You flopped top set, which is the stone-cold nuts on that board. Should you call his all-in? Absolutely - your call shows a positive expectation over the long term.
We always want make bets that show a positive expectation.
Always Look for the +EV Move!
What we should always try to do as poker players is look for the best move (the move with the highest expectation) at any given time. If you always make the best possible move, you'll always make money in the long term.
There will of course be times when you make the best move and still lose; that is inevitable, since poker is a game that is influenced by luck. Bad plays are going to get rewarded, but that doesn't all of a sudden make their moves good.
Put the short term completely out of your mind and focus only on making the best decision at any given time. Good results are destined to follow.
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