Thoughts on Expected Value

[Lexander]

One thing I have noticed is a detailed explanation for the importance and necessity of Positive EV when making bets. As both a beginner and a player struggling to really learn the game, I do find that one area that I see very little discussion of what this issue is and why it is so important. I figure I would see what better players had to say.

The mathematical definition of Expectation is simple enough. Since we are dealing with discrete probabilities, we simply multiply the likelihood of an event (scaled from .00 to 1.00) times the result of that action. We add up the sum of all the results and we have our Expectation. (As a sidenote, I have wondered why the word Average is not used instead. Perhaps there is a difference, but I have heard Expectation and Mean interchanged regularly, and Mean and Average are also interchanged, so it would seem acceptable).

What I don't hear talked about much is that most Poker hands seem to have Negative Expected Value. I hear a lot of discussion of Positive EV, but very little discussion of this. More importantly, I hear very little discussion of something I am noticing. Some potentially good hands turn out to have very dangerous Negative EV for beginners and perhaps better players.

For example, I am a discovering to my amused surprise that in Low Limit games AA is currently an Negative EV play for me. Before all the better players look at me and laugh at my ignorance, I figure I should explain.

The biggest problem I have with AA in my game right now is that I don't fold it fast enough because I don't know I am beat. The second biggest problem is that losing with those AA causes a very subtle form of tilt to creep into my beginner game.

My experience with AA in tourney's has been good. It wins most of the time and often wins a big pot. In Low Limit, this hand is one of my worst performers. My results with KK have been much better (easier to toss, and beginning players tend to let you know they have hit their Ace).

The biggest problem is my play. I am turning what should be a Positive EV into a Negative EV. First, I am always putting in as many bets as possible on this hand. Second, I am usually only being called at the river when I am beat. Third, when I am not beat I am not getting enough action.

So, the 60% of the time or so this hand is beaten by somebody at the table I am putting 4-5BB's in. The 40% of the time I win with this hand I am winning about 6-7BB's. I know the textbook says I should be winning more. I hear better players say they manage it. Unfortunately, I am not one of those better players.

So, .6 times I am losing 4.5BB's and .4 times I am winning 6.5BB's.

The Expectation (EV) ends up at -2.7 + or 2.6, or about -0.1.

Now, I accept that perhaps I am just unlucky. But I think I am just playing poorly and producing this problem. I lose most of the time with AA and don't win enough when I do win.

But this -0.1BB would not be such a major issue if it didn't lead to tilt, which it most certainly starts to do. Most interestingly, this hand I fear right now. I actually hate seeing it in Limit since my mistakes with it are causing a problem. But as soon as the tilt hits, then the real disaster happens. I play a few too many Negative EV hands.

My first question to better players is how would you handle this situation? I personally think that I don't do myself many favors tossing AA right now. I figure I will accept that I need to learn to play this hand and reduce those losses and improve those wins.

But, for those other beginners reading this, I will say this. The real issue with most hands is that they have a Negative EV. That is, if you where to chart out the probability of any particular result and multiply it by how much you won or lost, the total result would be negative. And that would mean that the simply act of playing the hand costs you money. That simple idea, if properly understood and considered can do a great deal to reduce the loss.

A classic example I see with this is hands like A6o. It took me awhile to awaken to the understanding that this hand is trouble. You can lose your shirt playing it and you won't win enough to compensate. A lot of hands like K9o and KTo end up in roughly the same shape. They seem workable on the surface, but most of the time when you get in a big pot with somebody with these hands, you are on the losing end. I can see how better players will know how to win with these hands.

Anyhow, these are just some random thoughts. I am curious how better players would suggest dealing with hands such as JJ and QQ for beginners. The textbooks says these are good hands but I notice that most beginners (including myself) simply can't play these hands correctly enough to compensate for the losses.

- Lex

[Carlos]

A few comments.

EV is a theoretical (hypothetical) concept average is not.
If you have had Aces 10 times and actually lost $10 your average is -$1. The EV may have been $40.

Premium pairs and Aces in particular are by far the strongest hands. While your average may be negative I can't imagine that the way you play Aces is so bad that you turn them into -EV. Post some examples in the small stakes forum.

Going on tilt just because your aces gets cracked is very bad and may turn you into a loosing player. You really have to work on that.

You are correct that most hands are loosers. That's why it is so easy to beat players who plays almost every hand.

Carlos

[Dynasty]

[ QUOTE ]
I can't imagine that the way you play Aces is so bad that you turn them into -EV

[/ QUOTE ]

The worst poker player in the world should be able to show a profit playing AA. The only way to lose money with AA is to make lots of bets and raises on the early streets and then fold on the river regularly.

[Lexander]

That is encouraging. For some reason, which baffles me currently, AA is one of the most problematic hands I have had at Limit. Fine in SnG's, just really ugly at Limit. I suspect it will take hundreds of AA hands to really know. I will say that beginners can make a real mess of hands that normally should be big winners.

As for your comment in average, I had never thought of it like that.

I do need to work on tilt issues. I am constantly working on this, and I am getting better. I am reading and studying a lot on the subject, and finding it helpful.

- Lex

[MaxPower]

I had AA cracked twice last night and it is still the most profitable hand for me. I'm sure if you added up all the money you've won and lost with aces in low limit, you would be way ahead (Given a large enough sample size).

Also, when people talk of a hand being +EV, then are not really referring to the hand as much as to how you will play the hand. For instance, people will say that limping with a pair of fives is +EV in a loose passive game. This is true, but not if you automatically take your hand to a showdown. It is only +EV if you fold the flop when you don't flop a set (or better).

[Lexander]

I have been thinking over the AA question, and the more I consider it the more I am convinced that AA should have constant Pos EV. That is why my problems with the hand continue to baffle me. This hand is only a problem in Low Limit tables against a lot of players. They tend to call the 1st raise but only those with hands likely or actually beating mine tend to stay in past the flop. The result is that 6-7BB average, which includes a lot of times when everybody folds and I win the blinds. In practice, I lose a lot with this hand but overall about 40% of the time it probably wins (but that includes a lot of small pots that skewer the average).

What truly baffles me is that it is my favorite hand in SnG's, particulary NL ones. Suddenly the hand has few problems, and tends to win my largest and most valuable pots.

I appreciate your comments on the fact that EV must be recalculated at each step. This is not something I usually have a problem with. If the flop is AT7, I usually figure my pair of 5's probably isn't going to be worth that much. Particularly at the tables I play at where people play Ax anything and you will commonly be facing a higher pair or possibly even two pair.

- Lex

[MaxPower]

If you play online you should get pokertracker or pokerstat. They will show you how much you are winning with each hand. AA far and away wins the most money for me in low-limit games.

I doubt this is the case, but If you are only winning small pots with AA, perhaps you are not raising with enough hands pre-flop.

[Zetack]

This was a very interesting post Lex, because I hear so many low limit players moaning about the aces and how they never hold up and how much they hate em.

Also I enjoyed your comment about the kings because coincidently enough, the last two sessions I've had I had statistically way more than my share of kings and they've really held up well. I think I had them either four or five times last session and I lost with them once. Tonight (I'm playing as I type---good strategy eh?) I've had KK twice and won with em both times. That's just a statistical anomaly though, hard to draw the conclusion from that that Kings are better than aces.

Ok to the aces. First of all I'm wondering if your stat with the aces (40 percent win, 60 percent loss) is accurate or just a guess-timate. In a nine handed table, if all nine players stay in to the river and nobody folds on the river, aces hold up about 35 percent of the time....I'm assuming SOME people fold in your game, so you would expect to win with them more often than forty percent.

Ok, assuming its not a guesstimate but your actual win percentage I'd ask what your sample size is. To start drawing conclusions that hold much chance of being correct you need a large sample. I'd like to see your results for a hundred pair of aces. Even that's pretty low, but the problem is that you get pocket aces once every 221 hands, so to get them a hundred times you need to play 22,100 hands....that's a lot.

Ok, I was guessing that in my micro limit games I was winning with my aces 60 to 70 percent of the time (just a guess.) So then I hit a bad streak with them where they held up just once out of six tries so I started keeping track. Including that one for six, I'm now 6 for 13 of them winning including my last four times in a row. So that's what, 5 of my last seven? Perhaps they are streaky.

Ok Aces, as good as they are are just one pair. There's a lot of things that beat a pair. And in low limit lots of people may be in the pot. Unlike high limit where two or three people seeing the flop may be common, you are likely to find a lot of people in with you. If six or seven people are drawing at you, somebody stands a good chance of outdrawing you. Of course once every 8.5 times that you have poket aces you will flop a set...and if that's not good enough, on the turn with your ace set you will have ten outs to make quads or a boat on the river...

Ok, so it seems like you lose large pots with AA and win only a small amount? Well that's natural. Think about it, if a lot of people are in building a big pot, there's a good chance somebody will hit something, a set, a straight, a flush, that they will be willing to put even more money into. If its a small field well you showed agression pre-flop by raising and reraising (you did show aggression didn't you?) and then you led out or raised or check raised on the flop....anybody who is willing to get into a raising war with you (and make the pot large in a small field) after you've shown that strength, probably can beat a pair. It's important to either get out or limit your damage when you are likely beaten. And if you've showed that aggression and nobody has a good hand or draw, its likely that they are gonna go away with out building the pot too much. Again, its important to limit you damage when you have the worst of it, but don't try to be sneaky in low limit to build a pot....get the money in there fast...a smaller win is better than a bigger loss when you let them outdraw you for free, or on the cheap.

Soooo....pay attention to the action and the situation. If a ton of people come in, you are much more likely to get your aces cracked. In a big field be prepared for the possibility of the aces going bad...study the board and the action (and the tendencies of the players as well--a maniac or somebody who'll go to the mat with top pair big kicker is less scary than a better player in a raising war).

Yeah, aces sometimes cost you a lot, because they are hard to lay down, and sometimes you just get unlucky. I had one hand recently where my judgement of the board and the one player who stayed in with me was that I was ahead, we ran that pot way up, then he rivered a gutshot straight to beat me... Well that happens. But I tell you what, give me aces on every hand...(well scratch that, if I always had aces my competitors would figure it out)...give me aces on average once every ten hands and I'm a rich rich man...So don't fret the aces, just remember its still just one pair, and in low limit, one pair is very vulnerable.

Oh, and I would expect your results in NL tourneys to be better with the Aces, because you can shut down people drawing at you by makeing a big bet...you can limit the field and heads up your aces have a big advantage, and you can usually drive out people drawing to a hand that would beat yours, which is harder to do in limit, particularly low limit.

Ok, I was gonna comment on QQ and JJ but I find I've run out of steam, so perhaps another time.

--Zetack

[Louie Landale]

You seem to have two posts [1] what's EV about, and [2] darn it, I'm losing with AA.

[1] At any point in the hand you can check and fold which has EV of zero (0). That means that all other possible plays (betting, calling) should have a positive EV before you do it. But I would also like to point out that your job is to find the BEST play, not just one with possitive EV: calling may be plus EV when you have the nuts, but raising is better.

[2] Looking for reasons to fold AA in big pots is generally a mistake. By the time you figure you are probably beat, "probably" isn't good enough so you should call. I suspect, however, that [a] you are putting in one or two raises too many when its obvious that you are "probably" beat, and [b] you've had some bad luck with AA. Consider recalculating your results, turning one AA loss into a win and seeing how well you are doing then.

- Louie

[Lexander]

To answer a couple of questions.

I don't have a specific figure for my results with AA at the current time, only my more recent records. In some senses, the more important issue of AA is the fact that I find myself struggling with tilt with the hand.

All I have is a general fragmentary record of the hand.

I began recording it when I went 0 for 12 with the hand. I won 2 times, then went another 0 for 6. Since that time, my win rate with the hand seems to be right about 25%, since my best calculation is that I am 7 for 29 with the hand since that opening streak.

It is a small number of samples, and my comments probably aren't completely correct, but in Limit this hand has been a regular underperformer. I have not won a big hand with it, and have lost a couple of big hands with it (AA over KK when Q7s stayed in to the river and hit two pair comes to mind). I have folded it twice, both times I was correct in that I was beat. The 40% I quoted was based upon what others have said is the generally appropriate win rate in Limit in general.

In NL SnG's, my records are not as established. I have only lost with it 3 times but I don't have a detailed count of how many times I played it.

But, lets exclude the fact that my win record is probably below average (it happens with such a small number of samples). My basic problem remains. I am simply not generating large pots with this hands, particulary when I play the hand with a lot of raises, which I try to do. Most of the time the only time when the pot gets big is when somebody really hits the flop with it and re-raises. I am willing to fold in that situation, fortunately. I might even be generating a small amount of PosEV in general, but not a lot. I will go ahead and record the results in the future as suggested to verify this more completely.

But combined the overall result of winning small pots and losing large pots, I am not doing that well. Once you add the 'tilt' effect you run into my real problem. Suddenly I start to wonder if playing Q8s isn't such a bad idea and I have to remind myself not to play it.