Mark  Poker Articles, Poker Mathematics
This article is a part of the Poker Mathematics series.
This article is number 3 in a series of 3 articles covering the (in my opinion) most important mathematical aspects of poker:
 Calculating pot odds: see Poker pot odds; all you need to know
 Calculating poker probabilities: see Poker probabilities; all you need to know
 Calculating expected value: see +EV poker; making the winning plays
Having explained how to calculate poker pot odds and poker probabilities in my two previous articles we now move on to applying these concepts to improve your poker game by making the winning plays every time. The concept you will need to learn is EV, which is short for expected value.
In poker, EV is a measure of how much you will be payed back on average on a 1$ bet:
 EV < 1 – If you always play hands with an EV of less than 1 you will lose on average
 EV = 1 – If you always play hands with an EV equal to 1 you will break even on average
 EV > 1 – If you always play hands with an EV of more than 1 you will win on average
Needless to say it should be the goal of any poker player to make plays that always belong to the EV > 1 category.
When it comes to calculating your EV for any given poker hand that the European decimal odds system, which I favor, excels.
Simply multiply the decimal pot odds you are given by the probability that you will win the hand, and you have your EV. Simple as that.
When using the European decimal odds system it is also easy to calculate either the pot odds or probability needed to break even (EV = 1) from the following relationships:
 pot odds = 1/Probability
 probability = 1/pot odds
Here are some examples of how these calculations work in real situations:
 You have 15 outs on the turn to win the hand and you have to call 700 into a 1500 pot. What is your EV for the given situation? Well the probability for winning the hand is (15*2+1)% = 31% = 0,31 using the easy rule of thumb. Your decimal pot odds are (1500+700)/700 = 3,14. This gives an EV of 3,14*0,31 = 0,97. Therefore you will on average lose 3 cents for every dollar you bet by making this call.
 In the example from above, what decimal pot odds do you need to break even? The answer is 1/0,31 = 3,23.
 You are holding a pair of eights and the flop is high cards. To win the hand you need to hit a set on either the turn or the river. What pot odds do you need on the turn and the river in order to break even? Again using the easy rule of thumb the probability of hitting your set on the turn is (2*2+1)% = 0,05, so you need a pot odds of 1/0,05 = 20 in order to break even. The same applies to the river.
Even though these calculations are straightforward you will need some practice to be able to perform them fast enough at the poker tables. Therefore you might want to make a set of guidelines to memorize. The list below will get you started:
 If your single opponent bets the pot on the flop your pot odds are 3 for calling to see the turn card. Therefore you need a probability better than 33% to make the call and win in the long run. This corresponds to approximately 16 outs.
 If your single opponent bets half the pot on the flop your pot odds are 4 for calling to see the turn card. Therefore you need a probability better than 25% to make the call and win in the long run. This corresponds to approximately 12 outs.
 When you flop a flush draw and want to see a turn card you need pot odds 5,2 to break even.
For those of you using the fractional odds system I would recommend that you convert your pot odds to the decimal system when calculating your EV values. For conversion between the European decimal odds system and the UK fractional odds system see poker pot odds; all you need to know.
Having now covered the basics of the poker mathematics essentials I will move on to the more advanced concepts of implied and reverse implied odds in later articles. The combination of a sound understanding of poker mathematics with bankroll management for poker should give you an edge against many opponents at lower limits.
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9 Comments to Poker ev; calculating the winning plays
I will start practising right away:)
September 16, 2011
In the first practice example I am coming up with a positive EV. The pot odds are 1500:700 = 2.14:1 and the odds against making your hand on the river with 15 outs are 31:15 = 2.07:1. My understanding is that whenever the pot odds are greater than your hand odds it is + EV to make the call.
November 24, 2011
indeed Craig this blog is full of bullshit
November 25, 2011
Hi Craig
I believe the odds against making your hand on the river is 32:15 = 2,13:1. There are 47 unseen cards left in the deck on the turn when you subtract your two hole cards and the three cards on the flop. But you’re right that with this more exact calculation of the odds against making your hand on the river, the call is actually +EV (barely though). The mistake I made was to use the easy rule of thumb to calculate poker probabilities, which isn’t exact.
Thanks for your feedback!!!
November 25, 2011
@Mike: What makes you say that? Is there anything you would change?
November 26, 2011
Mark,
I don’t find anything wrong with your method. By and large it works fine on all but the closest calls. I think most math minded players do a lot of quick and dirty math at the table, at least I do.
In the above example, my thought process is “I know 1500:700 is a little over 2:1 and I know 15 outs with one card to come is a little over 2:1, so I can either call or fold without making too much of a mistake.” I do have to point out though that on the turn there are 46 unseen cards left (you forgot about the turn card).
November 26, 2011
@Craig: Thanks for your comments. In my example the turn card hasn’t been dealt yet, so I am going to stick to 47 cards
Otherwise I agree totally with your thoughts!
March 11, 2012
WTF 46 and 47 cards? I hold 2 Cards, oponent hold 2 Cards, thats 4 and next 3 card are on flop…527 is 45 Cards unseen, dude
March 11, 2012
Hey…if you know a method by which you can see your opponent’s cards please tell us about it. Otherwise you cannot count your opponent’s cards as seen.
/M
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