EV Explanation

Will someone, with patience, a good explanatory method, and an ability to keep maths simple, run through EV with me, over MSN?

That way it can be done super quick and where I can ask questions as the explanation is going on. The implied odds thread was a good example of not having that luxury and I find myself with questions when I'm only half way through the reply and so it becomes hard to concentrate. And as I glaze over as soon as I see numbers, you can see why I'd rather not do this via email.

Let's toss a fair coin. If it's heads, I'll give you $2. If it's tails, you give me $1. What's the EV of a single toss? $0.50. Why? That's the expected value you'll get on average.

Hint: After two tosses, you'll average being up $1, so that means after one toss, $0.50.

The extension to poker is pretty straight-forward.

I don't have MSN but that's my best shot at simple EV explanation.

Let's extend this to poker. You're playing a cash game, blinds $1/$2, you're in the BB with 8 8 and a $100 stack and it's folded to SB who also has a $100 stack (both before posting blinds). SB flashes you A K then shoves all-in.

What is your expected value here? Firstly, you need to figure out how much you will win or lose. If you win, you will win all of opp's $100 but if you lose you lose your $100.

Secondly, you need to figure out your chance of winning. According to Pokerstove (if you don't have it, download it, it's free), you are 52.11% to win and 0.36% to tie against opp:

Code:

	equity 	win 	tie 	      
Hand 0: 	52.288%  	52.11% 	00.18% 	     { 8c8s }
Hand 1: 	47.712%  	47.54% 	00.18% 	     { AdKd }

So 52.11% of the time you win $100, 47.53% of the time you lose $100 and 0.36% of the time you break even.

So your expected value if you call is (0.5211 * $100) + (0.4753 * -$100) + (0.0036 * 0) = $4.58. Your expected value if you fold to the push is -$2 (your big blind). Therefore, calling is +$6.58 expected value compared to folding, or stated another way, regardless of what actually happens on this hand, over the long run, every time you call here rather than fold you will make $6.58.

Note that the long run is a very important part of expected value. In the above example it would be by no means impossible to lose five times in a row with your 88 but the more times you repeat this hand, your expected profit per hand will converge on $4.58.

Let's remove another constraint. In a poker game you will almost never get to see opp's cards before you have to make your decision, so SB does not show you what he or she has before shoving. However, from your observation of his/her previous play, you are confident that he/she would shove with any pocket pair, any ace and any two broadway cards.

What is your expected value of calling in this case? Again, plug it into Pokerstove:

Code:

	equity 	win 	tie 	   
Hand 0: 	57.673%  	57.28% 	00.39% 	   { 8c8s }
Hand 1: 	42.327%  	41.94% 	00.39%     { 22+, A2s+, KTs+, QTs+, JTs, A2o+, KTo+, QTo+, JTo }

So you win 57.28% of the time, lose 41.94% of the time and tie 0.78% of the time.

Expected value = (0.5728 * $100) + (0.4194 * -$100) + (0.0078 * 0) = $15.34.

Know any insurance execs? Let's say it costs $400 a month to pay the health bills for a family a four. They charge $500 in premiums to cover the "expected value" of their costs, plus some for profit.

This is precisely what we do as poker players. We estimate the "cost," and bet to charge a premium. When we have big draw, we're on the other side, willing to pay that premium we're being charged.

We win whenever we can charge the correct premiums when we're ahead; and whenever we only pay premiums to villains when we're a good chance to be ahead by the river.

If you're betting on the flop with 11 real outs, but you're pretty sure you're behind at the moment, then you have about 25% chance of being ahead on the next card. So the villain needs to bet at least 2/3 of the pot, or you'll have correct odds to "invest" in another card.

I understand how to calculate EV in general. However, what about post flop with a big draw? And what about on the fly? Is there any shortcut to these calculations that you guys can do in your head while in a hand? I can't even type a hand into pokerstove that fast. Or do you just practice and memorize these things for different situations?

Ok, seeing as the replies are here I'll continue.

I understand the basic concept that you guys have illustrated but it's when it gets moving like this, taken from http://www.cardschat.com/poker-odds-expected-value.php:

There are 6 possible clubs that he will call with. So six times, you will win an extra $10. As there are 8 clubs available, the chance of him calling is 6/8 (six out of eight):
$10 * 6/8 = $7.5

If he raises, we know that you have a worse hand, and you will have lost $10.
-$10 * 2/8 = -$2.5

So your expected value of betting here is $7.5 + (-)2.5 = $5. Not bad

It's all to do with card reading and what you think your opponent is likely to do. Now I have a hard enough time guessing whether he will call/raise or fold at all - let alone break it down into percentages of likeliness (35% of the time he will call $10, 45% of the time he will call $5 etc). And that means there is zero chance of being able to break into percentages based on possible cards!

Originally Posted by Thunder

Ok, seeing as the replies are here I'll continue.

I understand the basic concept that you guys have illustrated but it's when it gets moving like this, taken from http://www.cardschat.com/poker-odds-expected-value.php:

There are 6 possible clubs that he will call with. So six times, you will win an extra $10. As there are 8 clubs available, the chance of him calling is 6/8 (six out of eight):
$10 * 6/8 = $7.5

If he raises, we know that you have a worse hand, and you will have lost $10.
-$10 * 2/8 = -$2.5

So your expected value of betting here is $7.5 + (-)2.5 = $5. Not bad

It's all to do with card reading and what you think your opponent is likely to do. Now I have a hard enough time guessing whether he will call/raise or fold at all - let alone break it down into percentages of likeliness (35% of the time he will call $10, 45% of the time he will call $5 etc). And that means there is zero chance of being able to break into percentages based on possible cards!

Now I see where you're headed with this thread. Here's what I do. At NL10 FR, I run the following "ranges" through my head when I'm playing: premium hands AQ+ and JJ+, all other pp's, Ax, Kx and "junk." This covers the vast majority of hands villains play against me (I'm agro preflop, and raise most pots I enter).

Now, I'm in MP with AJs, and come in for my standard raise of 3.5xBB + 1BB per limper. The button calls and everyone folds. The flop comes T 5 2 rainbow.

Here I think is where your question lies. What could villain have? Any pp, an Ace, a KTs+ and maybe some junk like sooted cards. I'm behind AK, AQ, AT, A5 and A2 and not enjoying A3 or A4 with straight draw. I'm ahead of any reasonable K except KT, and behind to all the pp's, especially to TT, 55 and 22. I'm ahead of most junk but will need to deny the pot odds for any flush/straight draws, which a cbet of 2/3's the pot will do.

So my choice comes down this: I'm ahead of this range enough to cbet? The answer I come up with is that I'm ahead about half the range (I haven't done the math - just quickly estimated like I do during a game). I have some fold equity with a cbet as some AK, AQ, A2 and small pp's will fold. So it's probably worth a cbet. I'm not really worried about AK, AA, KK because I would think I'd get rr'd with those hands. So they're possible, but not all that likely.

Now, the rest depends on my specific read on my villain. I think that EV calculations alone can get us this far, but before we make a flop cbet we need to have some idea if the villain is likely to call or push back. That's not what you asked, and it's a whole different thread.

So this is my quick-and-dirty range estimating and EV thinking in-game:

1. Premium
2. pp's
3. Ax
4. Good K's
5. Junk

Again, it's important to combine your typical range estimates with how you play. Since I play FR about 16/13, I'm usually in position and came in for a raise, so villains generally have one of those 4 types of hands with "junk" just meaning any crazy bs they pull on me.

I don't worry too much about what % of the time they'll have which range, or doing any more detailed calculations at the table. I certainly don't use poker stove while playing. That level analysis is for when we post on FTR and when we analyze how we're playing a certain type of hand by reviewing PT HH's, imo.

Hope this helps. I'm sure others will have great things to say on this.

I really like Robb's explanation here. I have been confused on the difference between in game thinking and statistical analysis for awhile (thinking that all the good players were super math wizzes). I think now it will be easier to understand these things now that I don't feel as far from the math skills as I thought I was.

Sorry Thunder. I'm not trying to jack your thread. I'm just getting a lot out of it, and want to encourage it to grow a little. So I am going to stay tuned to it. Thanks!!

Robb,

Thx for your explanation and it covered the example I had provided though there are other areas that I still need help on. Eg: as mentioned in my earlier post, there is the EV of betting - which I have no idea how to gauge: Pot is $100. You believe there is a 10% chance opp will call $65, 20% chance they will call $50 and 50% chance they will call $30 - therefore the +EV move is to bet.

A lot of the time, I have no idea what I think my opp is liable to call so that makes this hard. And in that link I provided, it goes every crazier with % and probability by breaking it down into cards, eg: if villain has a club then the chance of him calling is..... If he has an ace then the chance of a call is..... So if I can't do the former, I certainly cannot do the latter.

Now in you reply Robb, you talk about gauging your opponent and making a decision based on that but two points arise. I keep reading how you can only calculate EV with a sepcial calculator, so how do you do it in game and on the fly? Also, in one of my first posts, I mentioned how I don't explicitly use EV but make plays and bets based on my reads at the time (like an innate form of EV) yet I was chastised for doing so and told to dig out the EV calculator etc. But all I talked about in that post is what you've described in this: gauging where you are to determine whether it's worth continuing and if you're ahead, how much to bet to get paid off. So I am confused by the conflicting advice.

Another aspect of EV that requires help on has been addressed with the "K on an A flop" posts and quite simply, how do you know what is EV or not? In these posts, many people advocate betting out so quite a lot believe it is EV+. However, it appears on that occasion that doing so is EV-. But without that thread, we wouldn't know so how do we learn? And what about other hand flop combinations.

Finally, there is the aspect of bluffing, be it late in a tourney to steal the blinds, representing a flopped ace or just an outright bluff played up to the river with absolute nothing. All of these are EV- are they not? Yet they can be vital and even necessary and this seems to brings up the conflict of learning what is EV, making EV+ plays and then going against it, such as the KK on Axx flop scenario, thus leaving things just as confusing.

Thx

[quote = "Thunder"]Also, in one of my first posts, I mentioned how I don't explicitly use EV but make plays and bets based on my reads at the time (like an innate form of EV) yet I was chastised for doing so and told to dig out the EV calculator etc. [/quote]

Thunder, you were chastised for relying on reads and instinct when you had neither played enough hands nor understood enough about the fundamentals of the game for them to be of any value.

As you gain experience and knowledge, this changes. You see situations over and over again, and now you are able to develop "instinct", which is in fact a subconscious utilisation of your acquired knowledge. But it's unlikely to be enough - where the theory and the maths come in is here, when talking about and studying the game - when you can go through hands, concepts and statistics without any time pressures.

No-one told you to try and do complicated, mathematical EV calculations in the 30 seconds you have to make a bet - it's clearly going to be impossible. But once your knowledge is developed, you CAN stop for a sec, work out outs, check notes, consider reads, position etc, and work out a likely best course of action which will determine your next move. And just because you're not doing it on paper, with equations, doesn't mean you're not calculating EV in the necessary and practical way we all do when we play decent poker.

Originally Posted by Thunder

without that thread, we wouldn't know so how do we learn?

Well, for a start, you DO have that thread, and many like it, and a large source of savvy people who will discuss these issues with you. But you don't need a thread on every aspect of poker - you've got to be able to apply your knowledge yourself, and often this will mean understanding the maths behind it.

So what I'm saying, as I've said before, is a) poker is a holistic game, and in every situation there will be a number of variables, some known, some not, which you have to consider to make the optimal move, and b) there are no short cuts - at best, you read wise advice and apply it to your game, but otherwise, it's down to you to follow the logic and sums and come to the right conclusion.

Fundamentally, we are all here to take each other's money, so while sources of info like FTR are brilliant, don't ever feel you are owed help and guidance.

Thx,

Of course there's no deserved right to help and guidance, I was just asking how to better your knowledge of EV.

Any help with the other points I mentioned as so far it's going well?

Thx

Is it not fair to say that all EV calculations are based on incomplete information? (Rhetorical question.) The equations for EV are made up of knowns and unknowns, and knowing the formulas is basically only useful from a philisophical perspective. As the range of one of the unknowns approaches infinity (in this case, all possible cards), the value of the answer that the formula spits out goes to kak. Basically, learning (or developing the instinct for) reads (that intangible "gut feeling") should probably be the first thing you do, and then supplement that with the complicated math that allows people to keep winning at the higher stakes (eg. making a 52/48 decision because it is on the + side of EV). As average skill at a given level goes up, then the need to make marginal +EV decisions to make $ goes up?

Someone posted something somewhere (god knows where) on this site about practicing reads, which is what i'm doing for at least a half hour or so every odd session - only play a couple of tables (if you play a bunch - me i'm not that proficient yet), and write down what you think people have based on whatever info you have (past hands, bet sizing, timing), and compare it to what they show down (if they do), even if im not in the hand. If the price is small when i'm in the hand 1 on 1 (and if often is because people don't know how to squeeze the most value out of a winning hand) then i will throw the 0.06 into the 0.75 pot (even if i think i will prob only win it 1 out of 20 times) and look them up. Wow am i ever wrong sometimes, but it sure helps me. Feels good to get it right

Tear this apart please, good or bad.

I f'in love this website, one day i'll be "24 carat ballin", and you'll all be sorry for telling me all your secrets! :P (That or I might be able to contribute something useful back...)

Originally Posted by Thunder

Thx,

Of course there's no deserved right to help and guidance, I was just asking how to better your knowledge of EV.

Any help with the other points I mentioned as so far it's going well?

Thx

I disagree a bit with Biondino's point about no one being "owed" advice. So many people at FTR have helped me that I feel like I owe it to others who may be a few steps behind me to help out when I can. So while you aren't owed, you are in a community where people are trying to give back. Which is positive. I'm glad if my limited experience and expertise can help someone.

Biodino's right about everything else, however. You have to develop the ability to make reads, estimate EV and exploit. If I understand his post, he's preaching self-reliance: a systematic way you should be studying your own game with your own tools making your own decisions. Right or wrong initially, learning that process will quickly improve your game.

The first step is trial and error. I'll tell the story of how I used trial and error and then some poker tools to find my preferred line for baby pp's.

I used to HATE playing any pp 77 or worse. I tried limp/call pre from EP as many suggest. I just watched too many hands get away. And I was -EV lifetime for 77's and worse. Given how pros and FTR posters talk about pp's, even small ones, I knew I had to be giving away value.

So I decided to try a new line: open every pp for a raise, as some folks here and elsewhere suggest. Now, "no set no bet" is fine postflop in multiway action. If you get 3+ callers to your 3.5BB open raise, you've won. You need about 7 to 1 odds to make playing the baby pp's profitable, and you've gotten halfway there already. The one time in seven you hit the flop, you need to get about two 1/3 pot bets called to make a profit. Often, you can get it all in.

So that part was fine. But I hung up on what to do heads up or in a 3-way pot postflop when I missed the set. A pair of 2's ain't great, but it has a decent chance of being ahead against a lot of villains' range. And at NL10, villains get scared off pretty easily when you rep the premium hand.

So I started fiddling around with pokerstove, calculating the EV for various scenarios both heads up and 3-way, and the small pp's have value - more than I expected them to. So I should betting that value, at least some of the time.

So I began experimenting with cbets against different villains on different boards. I started by targeting those who looked most aggressive. (Why?) And second the most passive (Why?) And then the in-betweens. And I developed a set of "rules" for green light / red light for my cbets. I color-coded my HUD flop stats to turn green when the villain was ripe to fold to cbets and red when he was likely to call or raise. I tried that for 5k hands, and then refined my color-coding and my "rules."

I cbet heads up about 80-90% of the time, depending upon individual villains, reads, table image and other factors. But I'm almost always willing to fire a cbet, especially from LP after a check. My typical cbet is 2/3's of the pot.

I cbet 3-way pots about 60-70% of the time, more often from the 2nd to act spot and VERY often from the last to act spot, usually about a pot-sized bet (after it's been checked to me). I generally fold to bets in front, and I cbet from first betting position about half the time, depending on reads, etc.

Why do I what I do? Trial and error. I tried a lot of differently sized bets on various board textures against tons of different villain profiles. And some things worked better than others. Now my lifetime win rate for pp's 77 and lower is 32 BB/100 (22's are 112 BB/100, but two of the six pp's are slightly negative).

Do I have it figured out? Nope. I'm still concerned that, even with my "rules," I'm being too aggressive from EP in loose-passive FR games. So now I'm experimenting with playing 22 - 66 for a limp/call from EP about half the time. When I get enough HH's to make the analysis meaningful, I'm going to track how profitable each different mode of play is by looking at a thousand hands of small pp's.

That's my story on pp's for the last three months. Let's see if I can summarize and target some of your questions.

1. How do we know EV?

We don't. Ever. We have to estimate it. That's why people disagreed with Gabe in the KK against Ace on flop thread. But there are reasonable estimates for what villains might have and what they might bet or call with. And most experienced players agree on that part. So, given those estimates, a clear picture of EV can emerge.

2. How do we estimate EV?

We can use theory in the form of PokerStove, guessing at villain ranges for different scenarios and seeing "who's ahead" and how much equity each player has. We can use historical data from HH's in PokerTracker, but it's time consuming since we can't always filter to the exact right group of hands for the comparisons we need. We can use experimental data by play ing a certain line for 5k hands, and see how it goes. And we can use experience to estimate the ranges and potential actions for each segment of the range.

In the end, we simply don't know for sure. That's why the experienced players here on FTR usually counsel noobies to play tight. When you do, you stay in more situations where a clearly +EV line exists. The estimates are accurate enough to almost always have a good idea of what to do. When FTR posters talk about betting "thin" value, they mean that the estimates of the EV involved are so close to break even that it's not always precisely clear whether hero is +EV in the long run.

3. EV decisions are heavily influenced by what level you play, what your style is (tight/loose), and who your opponents are.

While I agree with Gabe's points in general and have altered my play to include his ideas, at NL10 there are enough weak-tight villains to make betting the KK against an Ace on the flop +EV against SPECIFIC VILLAINS in some cases. And I said so in the thread. So even if someone like Biodino could tell you his EV estimates for a situation, your EV might be far different because you play at lower levels and against weaker villains.

4. How to think about EV.

You will find yourself getting better at EV calculations if you focus on some "trouble" hands, something in your playing range that everyone else says is +EV but which you have difficulties playing. Search FTR for various lines people discuss, and try something new. Play that way for a few thousand hands, and see how it went. Try to ignore the bad beats and focus on whether or not you made the right decisions. If you can figure out how to turn a group of trouble hands into consistent money makers, you will have learned the skills of estimating EV well enough to be getting on with.

EV is long run. One hand isn't EV, it's variance. So make some choices, write them down on paper, and then experiment, analyze with the stove, check hh's from PT, etc. And then make your best and most profitable decision about how to play them. That's using EV to improve your play, imo.

5. Answers to my two "why" questions above.

Why target agro villains for a cbet first? Well, aggressive means they bet or fold. If they check to me, they hate their hand. And if I cbet ahead of them, they tend to fold the garbage. So a cbet gives me a lot of information about where I am against an aggressive player. Aggressive players (AF > 3) who check/call my flop cbets are very strong typically. I'm shutting down and letting them take it away on the turn or river. If they're a good bit ahead but don't have a monster, they generally rr.

Why target passive players next? Cuz I think passive players in general suck at poker. When I see AF < 1, I think "fish." They call way too much. So I pick my spots and plan to 2-barrel. Of course, this is profitable long run but can lead to some painful showdowns where I've bet myself into losing half a stack when I never had a prayer of winning. As a general rule, I've found that villains with AF < 1 have a HUGE leak: calling one too many streets with their medium and weak hands. So I exploit it when possible.

What to do with the rest? I feel like villains with AF's between 2 and 2.5 are "honest" with their bets, betting good cards and folding crap. I believe them, give them a chance to bet their hands, and generally fold to pressure. But I still cbet them regularly, just not as often as the agros and the weak-tights.

How did I learn? By trial and error. And by not getting too uptight when I showed my pair of deuces against a set of Kings. It's part of the learning process, and I just try not to repeat the dumbass parts of the experiment too often before backing off the aggression.

Thunder and others who struggle with EV situations,
As biondino and others have put it calculating + or - ev situations to a specific number is something that should be done while reviewing HH's, NOT during play. So what can you do to get better at instictively knowing what is + or - ev while you are at the table?

One of the first and most important variables in determining expectation value is putting your opponent on a range of hands. Once you have a good feel for the range of hands an opponent may have based on certain situations THEN you can start estimating how your hand fits up to that range (whether you are ahead, behind, hopelessly behind, etc.) and therefore how you should proceed. I can hear all of you going "EXACTLY!!!! but how do I do that?".

How do you get better at ranges? Practice, practice practice. I would suggest the following excercise for anyone who is struggling to put opponents on ranges. Take one of your hand histories from a previous session and put a piece of paper across it to blank out any lines below what you are looking at. As you go through the hands assign players a "range" of hands based on what has happened so far. (It may even be worthwhile to come up with the pre-flop ranges for calling in EP, MP, LP and blinds, raising in those positions, calling raises in those positions, etc. before you start). For examply you may assign an EP raising range of 99+, AQs+ and AK+, a LP calling limps range of 22+, 89s+ (connectors only), KT+, QJs+ and AT+ and a BB calling limper range of ATC.

Now, once you have assigned all of the players a range pre-flop move on to the flop. Take the first action and analyze what they did and how that fits into the range that you have assigned them. Now see if you can eliminate any hands based on what has happened to this point.

Take the following hand as an example: DISCLAIMER - The SNG forums on Pokerstars were down last night so I toyed around in a few ring games. All you ring game experts just hold your damn comments on how I played the hand once you see what I had. :P


PokerStars No-Limit Hold'em, $0.25 BB (7 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($11.45)
MP1 ($24)
MP2 ($24.65)
CO ($13.50)
Button ($24.25)
SB ($17.35)
Hero ($25)

Preflop: Hero is BB with ? ?.
3 folds, CO calls $0.25, 1 fold, SB raises to $0.5, Hero calls $0.25, CO calls $0.25.

Flop: ($1.50) K, A, 5 (3 players)
SB bets $1.5, Hero calls $1.50, CO calls $1.50.

Turn: ($6) T (3 players)
SB bets $4, Hero raises to $10, CO folds, SB calls $6.

River: ($26) 9 (2 players)
SB bets $5.35 (All-In), Hero calls $5.35.

Final Pot: $36.70


Assign a range to CO, myself and SB based on pre-flop action. If any of the ranges is ATC then that is ok for now.

Once you have the ranges set move on to the flop. Based on the action on the flop can you remove any hands? For example if CO's pre-flop range included pocket pairs 7 and higher could you now exclude any of these from his range based on the fact that he cold called two bets here?

Now do the same thing for the turn and the river. Once you have done that let me know what "RANGE" of cards you think myself and SB could have based on the betting that has occured throughout the hand.

Do this for AT LEAST two-three decent sized hand histories and I guarantee that you will get much better at putting people on a range of hands.

Now naturally you are going to have a couple of things happen.

First you are going to have a LOT of hands where you don't get to see the results. That is ok as the point of the excercise is to get better and faster at ranges.

Secondly you will find instances where players have something that completely does not fit within the range of hands that you had assigned them (like if SB or I had pocket 2's here, which neither of us do btw). Discount these during this excercise, but as you get better at these you will be in a much better position during play to take notes on these players because their hands will now stick out from what you think they should be.

Finally, there is one ABSOLUTELY CRITICAL component to this excercise. If you truly want to get better at this you HAVE to have something that covers up the HH so you don't accidently look down to see what people had.

As a secondary excercise you can go back through the HH's and look specifically at the hands that you played. Would you have played them differently based on the range of hands that you are now assigning to them?

Originally Posted by REDBRG

As the range of one of the unknowns approaches infinity (in this case, all possible cards), the value of the answer that the formula spits out goes to kak. Basically, learning (or developing the instinct for) reads (that intangible "gut feeling") should probably be the first thing you do

You wanted this torn apart, so here goes!

Your second point first - how one earth can a noob learn reads? unless you're a follower of the whole luck odds/psychic poker theory (we get all sorts here on FTR) then this is utterly false. As I said above, you only develop reads and gut instinct through study and experience - they are a conscious or unconscious application of acquired knowledge. Indeed, there are many circumstances in poker where what appears logical or obvious on the surface turns out to be very wrong - an example, which I still do to this day, is turning medium strength hands into bluffs where you'll fold worse hands and get called/raised by better.

So the first thing you do is make efforts to learn the basics through a combination of microstakes play and reading/discussing about the fundamentals. After you've been doing both for several weeks, you'll begin to find yourself in positions where you can make reads, and where your experience tells you that certain moves and situations are likely to have meanings that you can exploit. Try doing this too early, and at best you'll be flipping; at worse you'll use mistaken logic and take yourself to the cleaners.

Your first point is just as wrong. The great majority of players play a small minority of cards - even maniacs play <50% the majority of the time. Hands that are raised probably average <10% in low limits. And each street reduces the number of playable hands further. So rather than tending to infinity, the ranges you put your opponents on actually heads towards being a very manageable number of possible hands, and with practice you will be able to put most players on a reasonably accurate range on each street. So not only is the EV formula the opposite of worthless, but it gets simpler as the hand progresses.

But to give you an example - let's say you are heads up against a guy who plays 100% of hands. By your reckoning, that means information is effectively infinite as you can't have any idea as to his hand strength. But in fact, you have perfect information - as long as you play a hand in the top 50% (let's say 45% to deal with blinds etc.), your play is +EV. Similarly, if you are up against someone who plays 10% of hands, you can assign a very accurate range and respond accordingly.

Obviously, most players fall somewhere between the two, and often it is genuinely hard to construct a realistic range, especially for a good lagg. But not only can you still do so, but each street you play will further narrow it, meaning you are able to make mostly +EV plays versus pretty much any opponent.

Originally Posted by biondino

But to give you an example - let's say you are heads up against a guy who plays 100% of hands. By your reckoning, that means information is effectively infinite as you can't have any idea as to his hand strength. But in fact, you have perfect information - as long as you play a hand in the top 50% (let's say 45% to deal with blinds etc.), your play is +EV. Similarly, if you are up against someone who plays 10% of hands, you can assign a very accurate range and respond accordingly.

I've never thought about this, so I'm just reacting off the top of my head, but wouldn't playing anything in the top 90% be +EV? Even leaving 9% in for the blinds.

If he's playing ATC, and we're just slightly more selective, then the majority of the time we'll be ahead. Of course, maybe your point was that playing top 50% would VERY +EV.

I see what you mean, but the simple truth is the top 50% is ahead of his range so you can play it knowing you're +EV. similarly, the bottom 50% are behind his range. So the key thing is you actually have perfect info and playing this villain is automatic.