"optimal poker embraces the uncertainty, tries to make the guess that will have the best expectation on average, and constantly updates that guess"we try to guess what our opponent is doing (bluffing, semibluffing, valueing, opening wide). And then we make a choice(check bet fold raise) based on that guess. And that choice has an expectation. We try to make the choice that has the best expectation.But how can you say that we try to make a guess that has the best expectation ?? how  can a guess have any expectation ?? I'm not native english speaker, but to me it sounds like you are saying "we chose to guess he is bluffing because it is better for us" thanks

Until mers can come in here and correct me, the expectation comes from the information you have gathered thus far. For example, if your opponent 3bet shoves you 100% of the time (over, say, 10 hands) you know he's probably doing it with any two cards. If you have King-Jack, you calling the 3b jam has a positive expectation because you are able to infer that he is shoving with any two random cards. If you call with King-Jack and it turns out your opponent has Ace-King, your call still had a positive expectation.How close am I, mers? :)

Can someone explain to me how it works out to be 2/3 and what the five worlds are for the keys example. 

The way i found it easy to understand is to look at what is defined as worlds, as scenarios.each scenario represent 20/100s 1 scenario the key is still inside on your desk 4 scenarios the keys are not inside on your desk but in one of your pockets                  2 scenarios where its in your right pocket                  2 where its in your left The question asked is, if we check our right, and its not there, then whats the probability that its in our left? To figure that out we simply have to remove the scenarios (or worlds) that are no longer true(because we checked)so we remove the 2 scenarios where the key is in our right pocket (since we checked and its not there) How many total scenarios does that leave?    3and in 2 of those 3 scenarios. (The 2 where its in ur left pocket)  we have the key on us Hence the likeliness that we have the key with us AFTER checking our right pocket and concluding its not there is 2 / 3 or 66.666% (im not sure if this answers ur question, but i found the term worlds rather awkward as a non english speaker and looking at it in this way deffo helped me comprehend it much easier) 

Thanks JTS. I thought about it the same way but for some reason I can't figure out what the two scenarios are when you have the keys in your left pocket. Is it the following? :Check right pocket first, not there. Check left pocket, in left pocket.Check left pocket first, in left pocket I guess I just want to confirm that the five worlds are as follows:1) Check right pocket first, not present. Check left pocket, in left pocket.2) Check left pocket first, in left pocket.3) Check left pocket first, not present. Check right pocket, in right pocket.4) Check right pocket first, in right pocket.5) Not in either pockets. So if we checked right pocket first and the key is not there then numbers 3) and 4) are not possible which leaves us with 1) , 2) and 5). Is this correct? 

Yes that is exactly what i understood out of it at least. if we would then proceed to check the other pocket we could eliminate "world" 1 and 2 leaving us with only world 5 or 1/1= 100% the keys are still inside on the desk and its a cruel world :(  @Mers I especially enjoyed the wording in this example ; " Perversely enjoying the sweat while we slip our hand into our right pocket" well done :)

The order in which you check your pockets is not important.The number "5" scenarios is chosen arbitrarily, it's just a convenient number because it allows you to weight the different posibilities with full numbers (80% is 4/5 scenarios, and 50-50 distribution for right/left pockets is 2 and 2 out of those 4)You could choose the number 100 worlds for example. Out of every 100 worlds, in 40 worlds you have the key and it's in your left pocket, in 40 you have it and it's in your right pocket, and in 20 you don't have it. Once you check your right pocket and the key is not there, you can discard the 40 worlds in which it was there. So what you have left out of the initial possibilities is 60 worlds, 40 in which the key is in left pocket and 20 in which you don't have it. Thus you have the key 40/60= 66% of the time. You could do the same distribution choosing 7 worlds to start with, and you'd just get decimal numbers, but the same proportions.The point is to understand what all the possible scenarios are and how relatively likely each of them is, and then once you get new information, understand how that information changes the initial probabilities.

Hi nicoasp, I do understand the point but I guess it bothered me that I wasn't sure how to come up with the correct answer. Correct me if I am completely wrong but I don't think in this particular example that the 5 worlds is an arbitrary number. There are only 5 possibilities to which you can have the keys which I listed in an earlier post. I get what you are trying to say though. The thing that did get me triped up though is the order to which you check your pockets like you said. I wasn't really processing the fact that it does not matter.Anyways, thank you all for answering my quesiton.

.

perhaps i misunderstood the word "expectation" in the sentence, and that, for you, it isnt supposed to mean "EV" (which is the meaning of this word everywhere else in the book) in this partiuclar sentence. Perhaps were you saying something more like "we try to make the guess that have the best chances of being correct" .. anyway Have a nice day 

I dont want to be too insitent, but could you answer my question when you have time please ? i have read your book with attention, there is a lot of very usefull info, but this particular point is driving me crazy....thanks

thanks :)  Happy New Year  

In fact this is driving me mad because this is questionning my entire thinking process in heads up matches.This is not learning masturbation, this is directly linked to the game.The main confusion i feel resides in the difference between estimation (guess) and calculation (EV of a decision). From what i had understood, Bayesian thinking is estimation, and this is why it flirts with uncertainty as you say (because you cannot know your opponents cards).Bayesian thinking is used to estimate, for example, how he is likely to bluff in a particular spot. What this particular check raise means given the game history between me and this particular player, how this could be an adjustement he could be doing in reaction to my own cbet frequencies.Those are estimations.Then, and only then, we can calculate the EV of folding or shoving or checking, the EV of a decision. The EV will suppose a given range and a particular profile for our opponent. And this range is an estimation we made by bayesian thinking. But the EV calculation is not an estimation in itself, it is a real calculation.I dont see how you can use Bayesian thinking to calculate the expectation of a decision. For me, you do not "guess" which option will have the best expectation, you calculate it. And this calculation is based on the guess you made with you bayesian thinking, which has to be constantly updated. i could use some Bayesian thinking to conclude that (given all info given in the book) ,  even if your words in this sentence are strangely arranged, it is likely that you mean the same thing as i do. i have not decided yet. 

 i wanted to write something about this but phil galfond nailed it in the following article, he shows you how to  use bayesian thinking to calculate evphil galfong wrote a great article about this (http://www.bluffmagazine.com/magazine/Wait,-Weight-Phil-Galfond-932.htm):Wait, Weight January 2008 | Phil Galfond 0 digg “Range” is a pretty powerful word in the poker community these days. I probably use it almost every time someone asks me about a hand he played. It seems like everyone who’s anyone knows about ranges. Ooooh. I have a fun idea. Lets play some “choose your own adventure” Do you know what range is? (If you answered ‘no’, read the next paragraph. If you answered ‘yes’, skip the next paragraph) A range, in poker, is basically the set of all hands a player can have at a certain point in a hand, given the way he played it. So, if a tight player reraises pre-fl op and bets every street strongly on an A♠Q♣4♥5♣A♥ board, you might be able to put him on the range of hands including A-K, A-Q, A-A, Q-Q. Putting someone on a range of hands is a massive part of playing poker and an inexact science. It also gets much more complex than the above example. There has been plenty of discussion about it. I talked my head off about ranges in my article “G-bucks” which can be found here: http://www.bluffmagazine.com/onlinefeature/gbucks.asp. Great! I’m glad you know about ranges, because I want to talk about weighting them. When someone calls a raise pre-flop, check-raises the flop, and bets the turn into you, you should be analyzing and deducing his range the entire time. You think to yourself: What hands would he play like this? Let’s say you decide that he would play a flush draw, two pair, or a set like this. (Don’t worry about the exact hand or the board for now.) So that’s his range. You can figure out how likely he is to be dealt each of those hands, calculate your equity vs. each of them, and decide the best course of action. Cool. The problem with this analysis is that t assumes your opponent will always play those hands in this manner (or that he’s equally likely to take that line with each hand). In reality, that’s not true. He might decide to just check-call with his flush draws and sets some of the time, while always raising the two-pair hands. Now when he raises, he’s more likely to have two pair than he was when we first analyzed his range. You need to adjust accordingly. That’s weighting a range. Let’s jump into a hand example to show The idea of weighting: You raise UTG 6-handed (at $50/$100NL) to $350 with QsJs and a $19,000 stack. UTG+1 calls with $15,000, and everyone folds to the BB who calls with $15,000. UTG+1 is a smart, tight aggressive player - almost definitely the best at the table. He is capable of big bluffs and thin value when The time is right. He views you as good, smart, and a little loose. Flop is Q♣T♣4♠ ($1100 in pot). You bet $900, UTG+1 calls, BB folds. Turn is the 5d ($2900 in pot). You check, UTG+1 bets $2200, you call. River is the 4h ($7300 in pot). You check, UTG+1 bets $7300. What should you do? That’s easy: You should put him on a range of hands. So you first start with hands that would call pre-fl op and call the fl op, and then narrow it down from there. You think he can have: A-Q, K-Q, Q-J suited, A-10 suited, K-10 suited, J-10 suited, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited, A-J. You decide that he wouldn’t slow-play a set or two pair on a fl op this drawy. Now you check the turn and he bets. You decide that he would check behind with any 10 and with Q-J suited. That leaves: A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited, A-J. Now the river blanks and you’re faced with a bet. So you look at how many hand combos you beat and how many beat you: A-Q – 2 queens left and 4 aces = 8 combos K-Q – 8 combos So that’s sixteen combos that beat you. 9♣8♣, 8♣7♣, 7♣6♣ = 3 combos K-J suited = 3 combos (you have the J♠ in your hand) J-9 suited = 3 combos A-J = 12 combos That’s 21 combos you beat. With that in mind, you make a no-brainer call with your 2:1 pot odds (you only have to be right 1 out of 3 times to break even). You put in your $7300 and he shows KdKs and wins the pot. Oops, you missed that hand. Did you do something wrong? Well, yes. Just because you made the wrong decision doesn’t mean that you were actually wrong to call. However, you made your call based on some faulty range building. Let’s go through the process and see what we missed. Well, first of all, as you can see, we missed K-K and A-A. You assumed that UTG+1 would reraise those hands pre-fl op. And you’re right, sort of. He usually would. From what you know about him, our best guess is that he calls with those hands about of the time and raises the rest. So, how do we account for that? We weight those hands in his range. So let’s take a look at our turn range again with these hands added: A-A (25%), K-K (25%), A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited, J-9 suited, A-J. (In reality, he probably also can have A-K along with a few other hands, and he will reraise or fold some other hands that we assumed he always called with some % of the time. All of that just going to complicate things further, and it won’t help my point) There we go. Did we fix everything? Not yet. There are a couple other things you forgot. First, UTG+1 will raise the flop most of the time with AcJc, KcJc, and Jc9c. He’s less likely to raise the J-9 for fear of getting it in vs. a higher flush draw. So the chances that he just calls the flop with the hands are (our best guess): A♣J♣ (20%), K♣J♣ (20%), J♣9♣ (50%). So now we have: A-A (25%), K-K (25%), A-Q, K-Q, 9♣8♣, 8♣7♣, 7♣6♣, K-J suited (KcJc 20%), J-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%). You decided that he’d bet the turn with these hands, which is reasonable. The problem is, the range you made had the built-in assumption that he’d bet all of these hands with equal frequency on the turn. Some of the time, UTG+1 would check behind, take his free card, and hope to hit on the river. However he would almost never (let’s say never) check behind with the top pair + hands. For the sake of simplicity, we’ll just assume he checks behind with all the nonmade hands 25% of the time, and bets them 75%. In reality, he’s probably more likely to bet some of the hands than others. Now we get to the river with our new range of: A-A (25%), K-K (25%), A-Q, K-Q, [9♣8♣, 8♣7♣, 7♣6♣, K-J suited (K♣J♣ 20%), J-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%)] - 75% The river is where you made your biggest mistake. You check-called the turn, meaning you almost definitely have a made hand, likely mid-pair or so in your opponent’s eyes. You check to him on a board that is very drawy and completely blanked off. He reads you as a little bit loose. My point? This is not a good spot for your opponent to bluff! He’s smart so he knows that. Because of this, we can figure he will bluff this river when checked to only 25% of the time if he misses his draw. Most of the time he will give up and check behind, figuring that you’ll call his bet with any pair. So, we should give every bluff in his range a 25% chance of firing again on the river. That might sound low, but it’s very, very reasonable. Think about what you’d do in his spot, against a loose-ish player, with J♠9♠. I would hope you’d usually check. So we give those hands a 25% chance of firing again, yet we keep the value hands at 100%, since he will always value bet strong pair hands when you check the river. His final range then is: A-A (25%), K-K (25%), A-Q, K-Q, {[9♣8♣, 8♣7♣, 7♣6♣, K-J suited (K♣J♣ 20%), J-9 suited (J♣9♣ 50%), A-J (A♣J♣ 20%)] - 75%}-25% So let’s break it into combos again: A-A, K-K = 12 combos (25%) = 3 combos A-Q = 8 combos K-Q = 8 combos That’s 19 combos that beat you. 9♣8♣, 8♣7♣, 7♣6♣ = 3 combos K-J suited = K♥J♥, K♦,J♦ = 2 combos K♣J♣(20%) = .2 combos J-9 suited = J♥9♥, J♦9♦ = 2 combos J♣9♣ (50%) = .5 combos A-J = 11 combos + A♣J♣ (20%) - 11.2 combos That totals 18.9 hand combos. Then we decided that he only bets the turn 75% of the time with these hands, so we take our total and tweak it: 18.9(75%) = 14.175 hand combos Then we take our 14.175 hand combos, and weight it to account for the fact that he will only bluff about 25% of the time on the river. 14.175 (25%) = 3.544 hand combos So after weighting our range, we go from being ahead of his range (21 to 16) to being way behind (3.5 to 19) and we have a clear fold on the river. The example was extreme and simplified, but it should get some points across; and it hopefully taught you how to weight a range. The number one problem people run into when putting opponents on a range is that they forget to weight the bluffs. If your opponent is representing the nuts, when you check to him on the river, he may or may not bluff, but he ALWAYS will bet with the nuts. The fact that the value portion of his range is so strongly weighted makes a big difference when you’re deciding to make a hero call. Don’t underestimate the likelihood of your opponent to just give up on his bluffs. When you’re facing a player you know very little about, that doesn’t mean you can’t weight his range. In fact, it’s actually more important that you weight his range since you’re so unsure about a lot of his tendencies. You have to keep a lot of hands in his range and weight them as best you can, taking the estimated chances of him playing hands certain ways, from street to street, and using them together to find a good estimated range for him. This is basically the way that Bayes’ Theorem applies to poker. (If you’re interested, studying Bayesian probability is great for your poker game.) Good luck. ANY calculation in the real pokerworld is an estimation, you can maybe get close to be 100% sure about your opponents hand but you never will have perfect information, so you are always guessing and weighting the probabilities of your opponents hand. Most people are just too lazy to weight every outcome most of the time,

In this article phil doesnt use bayes to calculate ev, he uses it to estimate ranges.Phil talks about uncertainty about opponents hand, not about ev.The only reason the EV of a given decision is "this high" or "this low", is because we have weighted (estimation) our opponents range towards bluffs or towards certain value hands. But EV in itself is not a guess.The weighting of the range uses bayesian thinking, and reevaluates (and narrows) from street to street (and from hand to hand). But the EV calc is a simple calc that does not use bayes.In its simplest form, ev is like this :EV= how much we win * %of the time we win - (how much we lose * %of the time we lose)this is a simple equation. a calculation. not a guess. What we guess is range of our opponent (%of the time we win/lose), no the EV.You have to keep a lot of hands in his range and weight them as best you can, taking the estimated chances of him playing hands certain ways, from street to street, and using them together to find a good estimated range for him. This is basically the way that Bayes’ Theorem applies to poker.Phil never says once in this article how you use Bayes theorel to calculate ev.  He says you use bayes to estimate RANGES.And THEN (and only THEN), you use those estimated ranges to CALCULATE your ev. You do not GUESS your ev.   

of course but you use the estimated range to calculate your ev, you never know for sure what your opponents range is so your ev is an estimation, so i guess we both are talking about the same thing: yes you are right in that in ev calcs you don't directly see or put in the estimations led by bayesian thinking, but indirectly they are there because your range guess already is made using bayesian thinking so in your simple EV formula: EV= how much we win * %of the time we win - (how much we lose * %of the time we lose)% of the time we win and % of the time we loose are both bayesian inferences or guesses so yes they appear in the formula, not directly, i guess what most people misunderstand is that any estimation of a range is a guess, we don't weight it using numbers, but we choose some hands / delete others  , so we "weight" the hands in our opponents range,so yes you don't "guess" your EV, you calculate it using guesses, but basically the whole EV formula is made up of guesses so the number you come up with is a guess as well, guessed EV= how much we win * % guess of the time we win - (how much we lose * % guess of the time we lose)

I agree . We are saying approximatively the same thing.I think i just wanted to underline the fact that the last sentence's construction can be weird for non english speakers (like me), and be subject to misinterpretation if taken at the letter.The EV equations contain our estimation of our opponents ranges. Therefore, EV can be considered as a temporary thing, which will be subject to reevaluation once we have figured our opponent in a better way and reevaluated their range.but its a calculation, not a guess. not directly. Bayes interferences are directly used to figure our opponents range. And indirectly to figure our EV.have a good night.   

Nice article from Galfond btw.