The following is a slightly modified version of a post I made on pokerpoker explaining EV to one of the members:

EV is an achronym that stands for Expected Value. The EV of a given play is a measure of the value of that play as its repetition tends towards infinity. In simple terms: EV answers the question, "If I make the same play in the same situation an inifinite number of times, how much money can I expect to win?". The equation I use for calculating EV is as follows:

As an example, let's look at the following hand:

It's easy to figure out P and C since they are right in front of you. To figure out W and L you either need to have memorized the odds for common situations, be really good at math, or at least be able to make a good estimate. I imagine that in a poker game of this caliber the pros are well aware of the odds for these situation and approximate the EV in their head pretty quickly. For discussion purposes, we can make use of a free online odds calculator provided by http://www.twodimes.net here's a breakdown of what this tool has to say about this situation.

The ouput looks like this:

http://twodimes.net/h/?z=1500056:

A link to the page where these odds are calculated

pokenum -h 9s 9h - ac jh -- 3c 7c 2c:

Tells you that the odds are being calculated for the hands: 9 of spades, 9 of hearts vs. Ace of clubs, Jack of hearts on a board of 3 of clubs, 7 of clubs, 2 of clubs.

Holdem Hi: 990 enumerated boards containing 7c 3c 2c:

Tells you that the game is holdem and that the tool has calculated 990 possible scenarios for the result of this hand if played to showdown.

cards win %win lose %lose tie %tie EV:

The header row of a table containing these columns left to right:

cards: the hole cards of each player

win: how many times that hand wins

%win: what percentage of the time that hand wins

lose: how many times that hand loses

%lose: what percentage of the time that hand loses

tie: how many times that hand ties

%tie: what percentage of the time that hand ties

EV: The %win expressed as a decimal so that it can be plugged into our euation as W and L.

So, after As bet:

the pot (P) is $117,700

the amount of times B will win (W) is 0.524

the amount of money B must call (C) is $86,100

the amount of times B will lose (L) is 0.476

the resulting equation is then:

This means that if B makes the same play an infinite number of times he can expect (in the long run) to win $20,691.20.

The same would hold true for any pair higher than 7s and lower than Jacks.

EV is an achronym that stands for Expected Value. The EV of a given play is a measure of the value of that play as its repetition tends towards infinity. In simple terms: EV answers the question, "If I make the same play in the same situation an inifinite number of times, how much money can I expect to win?". The equation I use for calculating EV is as follows:

(P * W) - (C * L) = EV

where:

P is the size of the pot before you call

W is the chance of you winning the hand

C is the amount you have to call

L is the chance of you losing the hand

and W+L = 1.

As an example, let's look at the following hand:

Game:

300/600 + 100 ANTE NL HOLDEM Cash Game

Stacks:

Player A: over $1,000,000

Player B: $106,100

Preflop:

A raises $1,400 to $2,200$ from the cut off with 9♠ 9♥,

B re-raises $7,800 to $10,000 from the button with A♣ J♥,

A calls.

Flop: 3♣ 7♣ 2♣

A checks,

B bets $10,000,

A raises $980,000 to $1,000,000,

B calls $86,100 and is all in.

Turn: 7♥

River: J♣

Result:

B wins $203,800 with a flush Ace high.

It's easy to figure out P and C since they are right in front of you. To figure out W and L you either need to have memorized the odds for common situations, be really good at math, or at least be able to make a good estimate. I imagine that in a poker game of this caliber the pros are well aware of the odds for these situation and approximate the EV in their head pretty quickly. For discussion purposes, we can make use of a free online odds calculator provided by http://www.twodimes.net here's a breakdown of what this tool has to say about this situation.

The ouput looks like this:

http://twodimes.net/h/?z=1500056

pokenum -h 9s 9h - ac jh -- 3c 7c 2c

Holdem Hi: 990 enumerated boards containing 7c 3c 2c

cards win %win lose %lose tie %tie EV

9s 9h 471 47.58 519 52.42 0 0.00 0.476

Ac Jh 519 52.42 471 47.58 0 0.00 0.524

http://twodimes.net/h/?z=1500056:

A link to the page where these odds are calculated

pokenum -h 9s 9h - ac jh -- 3c 7c 2c:

Tells you that the odds are being calculated for the hands: 9 of spades, 9 of hearts vs. Ace of clubs, Jack of hearts on a board of 3 of clubs, 7 of clubs, 2 of clubs.

Holdem Hi: 990 enumerated boards containing 7c 3c 2c:

Tells you that the game is holdem and that the tool has calculated 990 possible scenarios for the result of this hand if played to showdown.

cards win %win lose %lose tie %tie EV:

The header row of a table containing these columns left to right:

cards: the hole cards of each player

win: how many times that hand wins

%win: what percentage of the time that hand wins

lose: how many times that hand loses

%lose: what percentage of the time that hand loses

tie: how many times that hand ties

%tie: what percentage of the time that hand ties

EV: The %win expressed as a decimal so that it can be plugged into our euation as W and L.

So, after As bet:

the pot (P) is $117,700

the amount of times B will win (W) is 0.524

the amount of money B must call (C) is $86,100

the amount of times B will lose (L) is 0.476

the resulting equation is then:

($117,700 * 0.524) - ($86,100 * 0.476) = +$20,691.20 EV

This means that if B makes the same play an infinite number of times he can expect (in the long run) to win $20,691.20.

The same would hold true for any pair higher than 7s and lower than Jacks.

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