Poker Math: Understanding Expected Value in Online Poker

What is Expected Value (EV)?
In essence, “expected value” is a concept used to describe the average outcome of a given scenario that hinges on an uncertain probabilistic event.

We use expected value to determine if a move or play is the correct one by balancing risk versus what we get in return (the reward).

Is there an Expected Value formula?
Oh you bet. And we break it all down for you in our guide: Expected Value Explained: Understanding EV in Online Poker

We cover scenarios and formulas for limit and no-limit hold'em, as well as tips for applying EV in real-time poker situations.

Do you make it a practice to apply Expected Value to your game?

For my logical thinking i've got this simple math, if i am playing against one opponent i use this logic, and my plan is to go on until i can make a good analysis on when to bet. I will make a guideline post with future discoveries.




>80% = AA,KK; >70% = QQ,JJ,TT,99; >65% = 88,AK's,77,AQ's; >60% = AK,AJ's,AT's,AQ,77,AJ,KQ's,AT,A9's,KJ's,KQ,A8's,KT 's

Hi. I just had a question regarding the explanation of EV.




Why do we use 2.50 to do the calculation and where does this come from?

with math I have a very tight, but ruined flashpro it turns out I think 80 percent. expectations that will reach, makes us spend a lot of chips. it makes me think of a coin with three sides.

Interesting stuff. This shows why it's so unfair to use poker tracker because with large enough hand history sample against particular player it can show exact ev to every situation automatically.

Does that mean it's also unfair to manually track hands? Yes the software makes it easier but it's essentially the same thing. If you were watching all the players very closely you would be able to get to point where you know how player reacts in a given spot and you could fine the most +EV play. No one who is decent in poker is going through and playing a hand as if no other hand has happened before it so whether you use a HUD or not you're still going to be doing the same thing that's why you watch other players and take notes. All the HUD does is pay better attention and do the math for you but it never tells you "This is the most plus EV play do this and only this right now", the player still has to take the information and figure out how to use it.

WOW , this is way to much for me to do while playing ! If I am just working on math for something like my income taxes , or Wayyyy back when I was in school - then I would be able to do it .
But to sit and figure this out during my PLAY Time !!! ???
I do try to keep track of the cards coming out , and make an educated guess as to what the odds are if other have them in their hand or if they will be dealt out , but to sit there and try to do all those calculations for all of the hands I play ???
Thanks , but No Thanks!

Math was never a strong point for me , I can figure out problems - abeit slower then most , but I can and do figure out the right answer - but to do this while it is my play time , this would no longer be a fun game for me !

Great article, I changed my concepts regarding the expectation of value, as I am a beginner in poker I have much to learn

If two players are the same skill level, but one will have a database with all of the hands that you have played together and is able to see how often player x checks/bets/raises/folds on every street then what will be the result?

You can get that with or without the database, all you have to do is pay attention when you play against someone

You can remember what hundreds of opponents did during thousands of hand history? You're some kind of genius then...

It's called taking notes? There's nothing stopping you from adding notes to a player on a poker client. I really don't appreciate the attack given that I just said something different from what you did, I simply gave an opinion.

This is an essential reasoning for anyone who is involved in the betting world, as well as being an important process for making the right decisions. And doing a good banking management and playing within the limit is quite possible to achieve success in the long term.

Frankly I'm not very good at math of poker. I'm more of a practitioner and I've got a lot of bumps in this field. Maybe I'll seem stupid but I had to read the article more than once to finally get to the bottom of it. More mathematics in subsequent articles, a modest request.

+1
EV can change a lot of our decisions, on the tables and in life.

Always do. All in helps.

Excellent article, maybe the best I've read so far, congratulations to the person who wrote it.
In poker you have to make decisions that benefit us in the long term.

Very good item !!

I have studied with the Brazilian community and learned a lot. This material has the effect of opening the head of a lot of player and leave more excited the freerols.
But it is no use to work with deductions and not apply concepts, theories and calculations in practice.
Nothing will happen if you do not do what you expect.

using a tracker gives much guidance if you have a sufficient amount of hands, but paying more attention to your opponents will reap rewards more then doing a calculation and missing a player's habits
With online poker and the limited time we have to decide, i'm not a big fan of formulas but i do love math
In live games i would say it is a must Asset

I noticed in the article, the 30/70 coin flip should have been negative.
I have found that running different hand vs hand, and hand vs Range% for various situations on equity calculators gives a general idea of where a hand stands.
Remembering a few percentages, converting bets and pots into big blinds, and a couple conversions, one could get a general feeling what their hand is worth.

TY for a great article! I jutt it's very importaint to understand how cardsc work agains each other. Often seomthing like 44 < 78s can feel like a badbeat when in reality... so TY again!

Also loved what @chicopaw said about tracker. It does help if not exploit your ops but to understand and find your leaks definitely.

- maybe, but then there is GTO and players actually buy (for $$) hand hisotry of other players... CC had an article about Victor Blom, if you remeber how he was beat ...
"Does that mean it's also unfair to manually track hands" - yep, yes it is (IMHO) that is why some poke rooms are trying to leave tracking soft.

Excellentarticle. I admit that some of the maths formulas was morr oike an impossible puzzle to me.
But I always use EV at my game. After doing this, I learned to not enter in very dominated drwas at the turn or even post floppy. This helped my game a lot.

Good article.

I remember reading about "Expected Value" in my first book I read about poker (Harrington's book) years ago (in 2012 as I remember).

I think that when it comes to the nanostakes, the fundamental maths is the only thing you need. And apart from that, a lot of volume. I'm not into advanced math concepts yet.

If it's more than 2+2=5 then I get confused!

I found this very interesting article had never stopped to think about the expected value. I had no idea how to make this article helped me a lot about the values ​​in poker now are trying to put into practice

An excellent article. However the practical application of it sitting at a poker table is as much use as an ash-tray on a motorbike. It is based upon an average, while in mathematics there can be an average, a mean or a median, in real life there is no such thing. As an example, there are two boys, one is five feet tall and the other is six feet tall. Their average height is five feet six inches, which neither one is. EV has been hoisted upon the poker world by faux intelligensia boosting their egos

When I make a combination of my English and math.... I am so confuse



Obviously will help. But unfortunately not to me

I didn't understand anything. And moreover: I don't understand for what it is.
I remember I watched live stream where A2 tried to bluff KK on pre-flop by raising, re-raising. When KK went all in, one commentator (who's now a player) said that A2 could call, because he has pot odds. Of course, guide is not about pot odds but EV includes it.
I find EV useless since it doesn't help right card to come. Moreover: 40-60% successful players don't count it. They tell it in interviews. And logic: "I can loose, let's lose some more" doesn't impress me. But it helps to sell the books.

The only thing I expect in poker is to lose to a BS hand. I try time and again...…..get close - like last two tables close and some 23 off suit all in hand will beat my AK or A Ten or something. Its wild - can't help but think there's some kind of software being used to get ahead.

I do have a math degree, so most of the math involved in poker is rather straightforward to me. On the other hand, as stated in the article, making these calculations on the fly is nearly impossible, unless you're the rain-man...
Most of the times I consider +EV moves and try to stay positive.
An example for a particular -EV move we often see in our CC games, especially free rolls: Blinds are 30/60, just second round, one player shoves 1500 from early position. He risks 1500 to win 90. Even if he gets called 1 out of 10 times and loses, this move is -EV.

It is a maths subject and maths are one of the main factors in poker. As the game progresses the times for decision all-in or fold are more critical. EV is something we always have in mind while playing a poker game, so this analysis reveals the maths of it which is usefull to calculate and to decide our move each time.

Interesting thread, although I avoid filling my head with numbers and statistics, I only calculate the basics between gains and losses, although it would be interesting to practice it, I think it would help a lot in the handling of your banrroll, in that article there are very useful tips

I use the program StarsCaption (PartyCaption), it shows me how many outs and sweat odds I need to call. It saves my time

Expected Value is of much importance to poker decisions, just as it is in other walks of life. I find it incredible that many members here say that they do not have time to or do not see the importance of making important calculations when making decisions about how to play a hand. I would ask them to consider their decisions when they buy something! Do they just pay the asking price or do they consider whether it is too high and therefore do not make the purchase? Alternatively if its a good deal, they may well pay for it, to ensure they get the deal.

I guess there are players out there that are simply considering whether they have the best hand and betting on it....rather than considering the expected value and how that may make their decision different.

You just need to play with pleasure and do not wait.

I find mathematics extremely incredible in itself. Everything with abliction, that is, theories of Poker is not only for the game, but for all situations of life. EV is an extremely important concept, for someone who wants to build their poker career, you should study this concept in depth. Analyze and reanalyse your hands. Always wanting to see if in the long run the action is right soon profitable.

Excellent post, looking forward to more like this =)

EV as explained in this article seems like a more advanced conception of equity. This needs to be studied away from the table as too complex to do these calculations in game setting. Much easier to make decision based on equity (chance of winning based on number of outs) vs. pot odds. If pot odds are higher than equity you should continue. If not you should fold.

every day that passes, but I realize that I am a newbie and that there is much to study, the truth I did not understand much haha I think that to understand it I will need a teacher to explain everything in more detail.

I don’t apply EV to my game because I don’t have a full grasp on the concept. It would take a lot of studying to fully understand and be able to implement properly and I just don’t have enough time to put the work in.

I am very afraid that you are right. It is unlikely that a regular player can keep in his head so many statistics on all villains in order to determine their range so accurately, for further accurate calculation of EV. And also to do these calculations for a few seconds of time, playing at several tables at the same time. Obviously, special software copes with this task faster and more accurately than people. And the program has no memory limit, it does not get tired, does not forget anything and does not confuse similar nicknames. This is the main reason why even a poorly tuned "poker bot" will play better than the average player. Sooner or later, it will either kill poker as a game for money, or force all poker rooms to take uncomfortable measures to totally limit the use of any additional programs.

But in any case, this is useful information, and you should understand the logic of such a calculation. Sometimes it can be used against a villain. If the calculation of EV shows him that it will be beneficial to call against my stronger hand - I will only be glad.

Interesting, if we have the software is another tool that could help us make a better decision, whether it is worth or not to bet, especially in online poker

EV plays a huge roll in how I will play a certain hand based on the EV of a call or raise or fold ect. Taking player type into account, I will use ev calc to help me decide how I will play the hand.

In any poker literature there is this information. Mostly I only play freerolls, but I know basic poker math. In freerolls, I almost never calculate EV for sure. Because in the freerolls people have fun and I can avoid border decisions.

That is a lot to figure and take in. I'm sure it becomes easier over time, but it is a lot to get as a beginner but likely necessary in long run if ever want to be really good plus probably a whole lot more math and statistics beyond this to know.

This is coming from someone who thinks he considers this for every action, every hand, every day. I wanted the article to walk me through the math to further understand what I think I employ thousands of times a day. Great article, but it's a little difficult to follow.

I missed the title "Limit Hold 'Em" for the first example and kept thinking "who the hell bets 10 into a pot of 100 there?!?!". It may have been interesting to use the same scenario for a No Limit example (with a bigger bet).

Typo:

typo.JPG

I'd Love to Have rain Man With Me at The Tables lol...

Seriously "EV(bet) = P(X)amt(X) + P(Y)amt(Y) + P(Z)amt(Z)"

Having Read Through the EV Thread and Post I'll Seriously Have to Work Much Harder at Understanding it Well Enough to Gain Value From It...

As PsychoVas States Having a Math Degree would be an advantage but still doing those calculations on the fly would be strenuous...

Between Now And The April Challenge I'll DO Some Home Work and See How I Can Make this Article Benefit Me More...

the use of mathematics in poker is really amazing, but I can not do all this analysis during the dispute in the morning chance of winning, only calculate my chance of winning if I play 80%

I don't go that far before making decision on the felt. Maybe I should.
It can help a lot if expecting value became a reflex.

Very interesting article. This is the first time I have met the words "Expected Value" in connection with poker. It has started a lot of thoughts in my mind. I think i got the essence of the meaning of the words.

EV is a fascinating, mathematical formulation that has been something I have thought about and read about.

Although, factual, when I play, my poor mind can not do those calculations within a 45 sec trip that is divided into preflop, flop, turn and river segments, leaving me with less than 10 seconds a segment to perform magic.

Although a good study, outs, position, who's betting and their strategy, board reads and how much to bet; is there a few seconds left? Naw. Shucks.

If anyone out there has been able to include this in each and every hand along with evreything else to consider and in the short amount of time given, I would ove to know how they do it, really.

It is always good to read up on this. I appreciate the article and find it informative, statistical (which I love) and always for me a mind challenge.