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Discussion Thread for Bayesian Inferences and Developing Information

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Understanding problem.

"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

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? :)

The idea is that you never

The idea is that you never really guess what your opponent is doing, you just think probabalistically about all possible outcomes. It's kind of like how you don't put people on one hand "I guess you have AK!" - you put them on a range of possible holdings, and constantly update that range given new information.

Thanks, i had understood that.What is bugging me is that you talk of an EV of the guess. That cant be right.The décision you make has an EV (fold check raise bet). The décision is based on your guess. But the guess cannot have an EV.Please tell me this is a typo.

"But how can you say that we
OK, I think I get what you're

OK, I think I get what you're saying. You can just think of guess as to what's best as the decision.

I hope i can make me

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Can someone explain to me how

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

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

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

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

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.

Ajer ner blogi yajez 547 handi

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I did mean 5 to be an

I did mean 5 to be an arbitrary number that satisfies the conditions of the problem. We could also say there are 20 worlds, 8 in the left pocket, 8 in the right pocket, 4 on the desk. It's just a way of illustrating the problem in a way that matches all of the conditions of the problem. It's not really a solution - it's just reframing the question in a way that makes solving it more understandable.

Ok,

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

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

Why is this particular point

Why is this particular point driving you crazy? Do I need to link you to article 2? :) I'll re-write the sentence for you: Optimal poker embraces the uncertainty, tries to guess which option will have the best expectation, and constantly updates that guess given new information.

thanks :)

thanks :)  Happy New Year

In fact this is driving me

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

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

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

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

Nice article from Galfond btw.