

Hi everyone,
its my first time posting on this forum but I watch many PSO replay videos. Recently ive been trying to figure out what +EV really is... I know it is expected value and I also know that it is only an indicator used when you are allin (right?) now I used HEM2 (Holdem manager 2) and i constantly see my EV in the negative, I even had EV on a AA vs KK hand, im so confused.. Preflop: Hero is UTG+2 with A of diamonds A of spades UTG+1 folds, Hero raises to $0.75, 6 folds, BB raises to $1.50, Hero raises to $2.25, BB raises to $12.12 and is allin, Hero calls $9.87 Flop: ($24.34) 6 of hearts Q of clubs 4 of clubs (2 players, 1 is allin) Turn: ($24.34) Q of hearts (2 players, 1 is allin) River: ($24.34) 2 of diamonds (2 players, 1 is allin) Results: $24.34 pot ($1.10 rake) Final Board: 6 of hearts Q of clubs 4 of clubs Q of hearts 2 of diamonds BB showed K of clubs K of hearts and lost ($12.12 net) Hero showed A of diamonds A of spades and won $23.24 ($11.12 net) Thanks for your help 




Hi Hylmnn,
Welcome to PokerSchoolOnline! Here is a link to help familiarize you with all the features and services available at PSO. Feel free to look around the forum and post any comments or questions you may have. You are invited to join the PokerSchoolOnline Community Home Games Club. Information on how to join the club may be found here. EV is a little bugger to understand, but it really is necassary to do so. Expected value should underline everything you do in poker. It's not just for when you're all in, you should be looking to make +EV bets everytime you make a decision at the tables. Expected value is the amount of money you would win or lose on average on your bet. So in poker you want to put yourself in a positon where you're making +EV bets all the time. As over the 'long run' (thousands and thousands of hands) you will show a profit from making that bet. Owen Gains explains Expected Value wonderfully in his book 'Poker Math that Matters' If you haven't got a copy I thoroughly recommend it. Good luck at the tables! Oliver 




Hi hylmnn!
EV is a mathematical term that is short for Expected value. When relating the math to gambling, we talk about whether taking a bet has a positive or negative expectation. A +EV bet is one that will make money in the long run. A EV bet is one that will lead to a monetary loss on average. You don't have to be all in to be making a +EV decision, however; it's only in tracking programs that EV is only calculated for called all ins. Betting with a flush draw will be +EV if a villain sometimes folds a better hand, for example. We might also say "I'm really tired today, so playing poker is not +EV". In tracking software, the various EV stats are there to show whether you are running above or below EV in called all in situations. To come up with the numbers, the software calculates your winning chances (your "showdown equity") when all the money went in the middle, works out how much you were "expected" to win or lose, and compares it to how much you actually won or lost. I'll give you an example similar to your hand, but with easier numbers. Imagine that you push allin preflop with pocket aces and a stack of $50, and you get called by pocket kings. Since you have a probability of winning of 82% against KK, your $EV is 82% x $100 = $82. Your equity in the pot is $82, but your Expectation is a profit of $32. Expected value is the amount you expect to gain or lose when making a bet, and in this case it is $32. Getting it in with AA vs KK in this spot will show an average profit of $32. That amount is your EV. Another way of putting it is EV = (equity * potential profit)  ((1equity) * potential loss) In this case, EV = (0.82 * $50)  (0.18 * $50) EV = $41  $9 = $32 In this situation, every time you get $50 in the middle with AA vs KK, you expect to make a profit of $32. So your EV is $32 with your 82% winning chance, but you either win 100% of the pot (aces hold), or you win 0% of the pot (aces get cracked by kings). If you win the pot, you make a profit of $50. This means winning the pot is 5032 = $18 above EV. (When you get it in as a big favourite and hold, you're only a litle bit above EV). If you lose the pot, you lose $50. This is $82 below EV. (When you lose as a big favourite, you're way below EV). Depending on which particular stat you are looking at in HEM, a negative EV number can mean you ran above EV. On your graph, an orange line (EV winnings) above your green line (actual winnings) means you're running below EV ("running bad"). The numbers for actual hands will tell you how much you ran above or below EV on that specific hand. The EV numbers add up to form the orange line on your graph. Since your aces held in your example hand, the number in the stat column will (counterintuitively) be negative. The number there will tell you how much the "actual winnings" need to be reduced by to get your "EV adjusted" number. I wouldn't pay much attention to that stat. It's just something the software uses when calculating how to plot your graph. Bracelet Winner





I decided the best way to explain was with a simple example of flipping a coin. You take heads I take tails.
We're going to wager 10 O$ (Oliver dollars  original I know ) on every flip of the coin. The probability of you hitting heads is 50% or 0.5. The probability of me hitting tails is 50% or 0.5. So it's pretty intuative that the EV of this bet is zero since over the long run we will both win exactly 50% of the trials. But how about if I managed to convince you to pay my 20 O$ every time I hit tails. Well lets look at a little bit of math. One outcome of the flip is it comes heads, I lose 10 O$ when this happens. The other outcome is tails I win 20 O$ when this happens. So 50% of the time I'll win 20 O$ and the other 50% of the time I'll lose 10 O$. 20*(.5)  10*(.5) = 10  5 = 5 This means that on average I'm making 5 O$ every time we flip the coin, thus I'll how a positive expectation from the wager and the bet is +EV for me. Unfortuantely that means it's EV for you. 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 and running them thousands of times. Obviously the probabilities don't converge right away, I'm sure you've flipped a coin and got 3 heads in a row, right? Well that's were variance comes in and I'll leave that one for another day. 




funny you mention it Oliver ive been looking for that book but i cant find anyone who ships to canada lol, amazing has some but theyre going at like 60$ for a used book..
And thanks for the replies guys I appreciate it, its crazy how much math Ive forgotten since highschool i feel like an idiot when having to use math now lol. 




right. so getting +EV has to do with making the right decisions based of pot odds, implied pot odds, etc.. right?





Generally speaking, yes. Making a +EV play is one that is likely to make money for you in the long run. Often, your profit comes from betting when you have the best hand, but sometimes it's +EV to call with a draw, because the pot lays profitable odds to do so. Occasionally, betting as a bluff is also +EV, because you'll win the pot a certain amount of the time when villain folds. For example, if villain folds to a half pot bet more than a third of the time, then it's profitable (i.e. +EV) to make a halfpot bluff.
For some real numbers on bluffing... Let's say the pot is $100, and you are considering making a bet of $50 as a total bluff. You're risking $50 to win $100. Since every time your bluff gets called, you lose your $50, and every time the bluff works, you gain the $100 pot, then your total EV is calculated as follows: (How much you win * how often it happens)  (How much you lose * how often it happens) = ($100 * How often villain folds)  ($50 * how often villain calls) It turns out that if villain folds one third of the time, then this half pot bluff will break even, because (100 * .33)  (50 * .66) = 33  33 = 0. If villain folds to your bluff anything more than a third of the time, this bluff is +EV. Bracelet Winner





Hi Arty,
So applying this concept to a real game using a HUD, we want to look at the Cbet fold stat (or a similar stat) to get an indication on how often this opponent folds. But, how do we try to work out what size bet is likely right for this cbet fold stat, and so to make a +EV bluff; is there a stat for that, process, or is it down to just good observation. Also, if I am the villain, what is likely to be the best move, and turn this is a +EV situation for me. Would it something like... Look at a particular stat based on an opponent that indicates his when he is reraised his fold percentage, and look for a postive EV that way, e.g. folds 60% of the time to reraise, etc Apologies if I talk nonsense  trying to think outside the box. Cheers, pullin1988 




Chances are I think, that you probably won't have a reliable stat on what I described above.
Cheers, pullin 




Thanks again for the response Arty.
@pullin, I am no expert but depending on the range you put your opponent on and how often he opens a pot and cbets then im sure you can use stats against him. For example, I play 25NL zoom and when I have a decent sample on a player (normally 200+ hands I think is enough to pull this off), if a player is playing 23/18, with a cbet ratio of 80 then I find it highly profitable to either float the flop or even raise it up and take it down right there.. Not sure if this makes any sense, but ive been playing 25NL zoom for about 3 months now after beating the 10NL stakes and this move has proven to be quite profitable.. Maybe arty can elaborate on this more or tell me if im being a donk hahaha 




Quote:
bet size / (current pot + bet size) So if you bet 50 into 100, you need villain to fold 50/(100+50) = 50/150 = 1/3 of the time. You can pretty much just memorize these numbers for when you're considering a bluff: If you bet 50% of pot, you need villain to fold 33% of the time. If you bet 60% of pot, you need villain to fold 37.5% of the time. If you bet 70% of pot, you need villain to fold 41% of the time. If you bet 80% of pot, you need villain to fold 44% of the time. If you bet 90% of pot, you need villain to fold 47% of the time. If you bet full pot, you need villain to fold 50% of the time. As you may have noticed from your HUD, villains tend to fold to cbets more than 40% of the time. This means that it's mathematically profitable to bet 60% of pot on every single flop if villain is folding 40% of the time. Barry Greenstein obviously knows the math, because he has cbets 100% of the time when he raised pre. But cbetting 100% of flops doesn't necessarily maximise your EV, however. On some flops, where your fold equity is minimal, it's far better to checkfold when you have air. Bracelet Winner





Wow, fantastic as always.
Cheers pullin 




I feel that cbetting wide has the danger of being floatbluffed/checkraise bluffed out of a better hand. For example, what will you do if you cbet bottom pair 50% of pot on a standard board, lets say 6 9 K 2tone and opponent calls with air and bets into you on the turn or river?
You could say that you need 30% folds to profit when you have nothing, but that time you had the better hand and will loose 150% of the pot if you fold vs a float bluff! Of course, you can call the float bluff, but the problem is that you are now on a marginal bluffcatcher situation and your opponent can have enough value hands that your call vs his bet on later streets is break even or unprofitable, so your opponent will always have the advantage (I think you average 20% EV or so as the bluffcatcher vs a polarized range between GTO players, but not sure). I do understand doing this to mix up your ranges though. Also what will your checking back range be? Thinking opponents will likely perceive your checking back range as either air or polarized (checking back a polarized range is very far from game theory optimal I think). Playing loose and cbetting wide can be a problem too? I think Barry is tight preflop relative to the insane geniuses that he is playing with, so he can cbet wider, but I don't watch too many live games. What average cbetting percentage do you think is game theory optimal? What if you and your opponent have the same range on the flop, what cbetting percentage then? Do you think that percentage changes by flop texture? Also I'm pretty sure Adonis112 doesn't call cbets that wide based on a sample of games I watched, but nobody cbets 100% into him. 




To further illustrate my point, you need 60% folds to break even on a 50% pot cbet if you are going to fold a call or checkraise 100% of the time.





Most people that I run into have above 50% folding to cbets.
As with everything, adapt your play per opponent. Some opponents will be floating a lot and you need to adapt to that. Usually by a combination of less frequent cbetting against this opponent and when you cbet, be prepared to double barrel. And as Arty pointed out, Cbet smart. Some spots are just horrible to cbet. Like in a multi way pot with a flop of Js 10c 3s. If you don't have a part of it, don't cbet. If you are in position and it checks round on the turn, you could take a stab if you think you could get away with it, but that should be the limit of your investment usually. 




I'm currently writing a very long article all about cbetting the flop. In fact, I'll probably post it in 3 parts on my blog.
I'll reiterate the math of cbetting, give advice on standard lines to take with typical hand strengths, and provide a wide array of flop textures, explaining why some are "good flops to cbet" and why some are "bad". Quote:
50/(100+50) = 1/3 Bracelet Winner



