sklansky on game theory...

[NYIsles 0]

In Theory of Poker (and in his recent response to DN's recent comments), Sklansky briefly touches on the application of Game Theory in poker. I had a few questions about it, for anyone who's familiar with the topic...In using Game Theory to decide when to bluff, Sklansky maintains the optimal method is to determine your decision in a manner that leaves your opponent's pot odds identical to the odds against your bluffing during a particular hand. This might mean you'd pick an additional 1 or 2 river cards with which to bluff, in addition to the 9 cards that would give you the nut flush, for example. That seems like a reasonable ratio.In using Game Theory to decide when to call possible bluffs, Sklansky maintains the optimal method is to determine the odds your opponent is getting by making the bet, and then make your odds against folding the same. (So, if your opponent bets $20 into a $100 pot, you would randomly fold to the river bet one out of every six times - assuming, of course, that you could beat a bluff.)(1) Would the application of this theory be similar in no-limit play, where you're potentially faced with an all-in decision? For example, let's assume you have $6K in chips, and your opponent (who has you covered) makes an all-in bet into an $8K pot. You have a decent hand, but not the nuts. He's getting 4 to 3 odds. Does that mean you randomly fold 3 times and call 4 times?(2) How would you randomize during no-limit play, when you won't know what a potential bluff bet will be until after all of the cards have come off? In other words, if you put your opponent on a draw in a fixed limit game, you know what the river bet would be (if any) - so you can determine how many river card(s) you will use to randomize your bet in advance. (3) Are there any good texts that describe the application of game theory to poker in significant depth?Thanks in advance...

[Smasharoo 0]

Well, this is a fairly deep post, but I'll give it a quick shot.1) Yes and no. In a NL cash game it's essentially the same. In a NL tournament there are other signfigiant factors that come into play like how close to the money you are, how good your bluff catching hand realy is, etc.2) I use the second hand on my analog watch. When the bet's made, I look and see wher the second hand is to randomize based on the odds.3) Not holdem specificaly and not ussually as the subject but there are lots of examples and shortish paopers. Try Google Scholar.

[NYIsles 0]

Thanks Smash, as usual. Re: #1, I'm assuming that in a tourney, you'd be randomizing against players on whom you don't have a good read, and/or who can typically outplay you.Re: #2, well... that's just brilliant. As simple as that might sound, I never would have thought of it. Guess I have to buy a watch with a second hand, if I ever get to the point where I'm regularly using game theory...If you don't mind my asking one more question, how did you practice and become proficient at making these randomizing calculations on the fly?

[Randy Reed 0]

Oddly enough, I was reading about bluffina and game theory in TOP yesterday and was thinking this is on the surface a simple topic, but to put into use one of the most difficult.His examples are in heads up play with simple odds, $100 ante, I bet $100 ($300 pot) thus 3-1 odds. I randomize the extra cards i bluff with to give optimal odds. So in head up play, in limit, it can be a fairly simple concept. Against multiple opponents it gets more difficult. In no-limit, where your tourney life's on the line it's vastly more difficult. I'd hate to have my but handed to me because some random player didn't understand the concept and called with bottom pair. On the other hand, I'd hate to be so weak as to never bluff and not understand the concept, assuming I had no reads. Make no bones about it, putting a large amount of chips in the pot on no limit against a random player without reads is a huge gamble, especially on-line. In the other post about the dispute between Daniel and Sklansky, this is precisely the debate on who has the edge in play. Someone who properly uses game theory or someone who can make great reads on the table and opponents. I'm very interested to see Phil's hands during the heads up tourney since he uses great odds in his favor and rarely uses huges bluffs in tourneys, but in a heads up tourney he was much more likely to have used some game theory.Ok, so I didn't answer your question, but it is a huge part of poker and one I am vastly interested in as well. Calculating odds on the fly and randomizing your bluffing odds is a difficult concept. Geez, half of Sklansky's concepts are so mathematically challenging it's very difficult.For example he often says things like, suppose your opponent will call 75% of the time. How in the he ck do I know my opponent will call 75% of the time? What if its 60% or 80%? Or even 20%? It can drive a student of the game nuts.

[justblaze 0]

here are some very interesting introductory game theory articles that relate to poker:http://tinyurl.com/6ptuh by the way, notice how my link isnt 70 characters long? anyone can do this. go to www.tinyurl.com its very simple and so much easier to use.

[NicksDad1970 0]

This may already be on here , if so...sorry.This is David's response to whatever Daniel supposedly said:I have several points to make about a variety of things that have been recently written about me, much of it in regard to the recent heads up tournament.It is important to read what follows because I am not only defending myself, but in some cases I will be talking about some important concepts that poker players need to know.First in regards to Mason's Doyle, Ivey, Chan, post. It was misconstrued by some because Mason didn't use the suggested phraseology "need I say more?" which would have suggested a bit more tongue in cheek playfulness than his actual wording. Of COURSE short term results don't prove much. On the other hand I did win four out of ten soon to be televised sit n gos against top players, and got a bad beat or it would have been five. That IS getting to statistical signifigance. And while the three for three headup victories are not statistically significant, they WOULD be if you were testing the hypothesis that I was a 2-1 dog in these matches. See why?On a personal note I want to say that even if it was true that I was the world's best theorist, but only a prettygood player, I would still much prefer that to being the world's best practitioner but only a merely good theorist. That goes not only for poker but almost any thinking type of field. Dr. Debakey didn't save anywhere near as many lives as Dr Salk. But that is off the subject.First lets get to the comment I made that when the blinds get high I would be favored over Phil Ivey or Johnny Chan. Some on this forum took issue with that satement but I doubt that Chan, Ivey or even Daniel would. Laying even 15-1 odds on preflop raises is not wrong with awfully mediocre hands in headup situations, because of the two ways to win nature of that play. When to do it against a random hand is something only me, Chris Ferguson and a few others know well. So is knowing when to call getting 7-5 odds or so given a menu of hands that the opponent might push with. When the stacks are thirty times the big blind or less, it is impossible that a player who is not intimately familiar with this stuff could be favored over me regardless of how well he plays. And that situation was reached pretty quickly in the tournament.Qualitatively, Daniel's comments about me perhaps had some validity. Quantitavely he was way off. He does that a lot, confusing his degree of certainty of something with the odds he could lay. I'm almost a two to one underdog against Ivey and Chan? I'll play right now under the same rising blinds format a series of freezouts getting $16,500 to $10,000, agree not to quit until I'm 100K loser but they can quit whenever they want. Let me hasten to add that there is NO WAY that either Johnny or Phil would lay 3-2. They do not share Daniel's opinion. I doubt I could get 1.30 from them. In fact Phil specifically said he wouldn't lay me any price before the match started. That's not to say he didn't think he was favored.In actual fact I thought I was about 48% in those matches. If we had equal chips when the blinds rose I put myself at 52%, more if they would fold quite a bit too many hands when I moved in. But since I thought I would have on average 45% of the chips when the blinds rose, I was indeed probably a small underdog.Here's the irksome part: I am sure that with big stacks and small blinds I am a lot closer to these fellows than some give me credit for. But the right strategy for me was to play in a way that would give my detractors fodder for their criticisms. It was in my overall best interest to play a very meek game early on (that would likely leave me with a smaller stack barring a nice cold deck) even though I am a lot better at playing otherwise than most people think. In other words, if there was never to be a increase in the blinds I would have played a lot differently and still, in my opinion, held my own. I'll gladly take 1.80 under those conditions.The reason I chose not to mix it up early was not because I thought I was clearly overmatched but rather because being even a small underdog made it the wrong thing to do. The main reason was, as already stated because of the soon to be increase in blinds. The other reason was TV face time. And avoiding the business disaster of early elimination. So I played the first half hours exactly as my critics predicted, not letting ego get in the way of business.The concept that I was the favorite once the blinds got bigger was echoed by Barry Greenstein and Huck Seed. Perhaps they were being polite. But I doubt it. Daniel's comment that I would "gamble madly" hoping to get lucky is absurd. The fact is that Phil Ivey made a critical preflop mistake, (that I would have never made), failing to move in preflop with two eights, that probably cost him the match. (To his credit he quickly realized his error and is not likely to repeat it.)As to this quote:"Name a pro that hasn't read his book. Just one? Chau Giang, Eli Elezra, Ming Ly, Lee Salem, Johnny Chan... shall I continue? --Daniel Negreanu"I'm sure Daniel believes this. But two of those players have told me otherwise. And one of them paid me $800 for four hours of limit holdem lessons about ten years ago.I know for a fact that some high rollers flat out lie when they tell people they haven't read my stuff. Phil Ivey has been quoted as saying he never read anything but when interviewed by NBC (I'm told) said that Theory of Poker was the first poker book he ever read. Maybe he was just being nice.As to Daniels assertion that Phil would be favored over me in "any poker game known to man", that's ridiculous. I'm uncomfortable expounding on this too much because Phil himself didn't say it. And Daniel himself must know he is exagerating. For instance what about straight five card poker, no draw, one round of betting? What about hi-lo split where the low hand gets 60% of the pot? What about almost any game where the rules are such that neither one of us has never played it before? Less contrived examples are regular high draw and regular high low. Straight lowball and even eight or better stud are games that its hard to imagine that he could be any better than even with me.What's exasperating though is not that Daniel would disagree with the above. He would concede those things, perhaps claiming a tiny edge for Phil, but then go on to say his words were not to be taken so literally. He would probably admit that games with a strong "mathematical" component are not what he was talking about. What he would say though is that Phil would crush me in the other games. And he is wrong. He might be a small favorite but not a big one. There are two reasons. One is that he underestimates me. With very little to go on he thinks I don't have a good feel for where my opponent is at. He mistakes the fact that I play on automatic pilot in middle size games for an inability to get off it if I really need to. But that is not really here or there. I will admit that my skills at reading are not as high as most world class players. (They should thank their lucky stars for that.) The important error that Daniel makes is equating that flaw with big underdog status in head up games against world class players. He forgot about something: Game Theory.There is no doubt that being a great reader is valuable. But it is only valuable when the opponent is readable! That means that a great reader will win more from readable mediocre opponents than a mediocre reader who plays well otherwise. That's why, as Barry Greenstein has said, Daniel out does the best players in tournaments even though he doesn't beat them in side games. He is great at reading readable opponents. But great players are almost impossible to read. In fact a mediocre reader might do better against them if he resited any inclination to try.Let me put it another way. If Danielplayed a pretty good player a 100 hour session head up, and then I did, he would out perform me by a nice amount, especially if he is right about my reading abilities. But if we both played Phil Ivey the difference would be less. (Assuming I did some game theory studying and would careful not to exude physical tells). Because against great players reading is as apt to backfire as not. If instead you play like a computer, randomizing both your bets and your calls you can't make great reads but you can't be tricked either. Of course playing perfect game theory is not yet possible for complex games. If it was, a computer would be the best player. But you can come close enough that you can negate this "people" aspect of your oppnents skills to a large extent. If he doesn't know his fundamentals well you might even be the favorite. In games like single draw lowball, IBM could design a world champion computer in a year. Phil Ivey would lose to it. And he would lose to me if I knew the computer's algorithms. (Space does not permit me to expound on these concepts fully.)Here's a secret. Those who watch the TV show carefully may notice that I did not always fully look at my cards. It is the best way to implement a quasi game theory strategy because you have no tells. Math is more than just numbers and probability. Throw in game theory and it takes away opponents edge in many people skills as well. That's a scary thought to some but the fact remains it is true. But some people don't want to deal with it.

[JackB03 0]

*I think the best thing for you to do is read "Harrington of Holdem".*-Its a great book that tells you alot about those questions you asked. -Its all about NL and in a tourn. ****TRY IT OUT****-Jack

[justblaze 0]

*I think the best thing for you to do is read "Harrington of Holdem".*-Its a great book that tells you alot about those questions you asked. -Its all about NL and in a tourn. ****TRY IT OUT****-Jack

actually this book contains very little on game theory. game theory is not equivalent to poker strategy. it is a mathematical theorem for making optimal decisions. The application to poker is an afterthought, rather than a primary goal. Its primary use is in economics.

[Mark1808 0]

I have been pondering the randomization of bluffs and calls as they apply to hold em. In Slansky's book he used a 5 card draw example where your cards are not exposed. In hold em it is easier to put people on flush draws and you can tell when they missed by looking at the board, so the Slansky draw example where unseen cards provide a random number generator would not apply to hold em. I am sure there is a way to apply the overall concept to hold em but I have not seen it yet.

[Randy Reed 0]

In reading smash's posts, he uses game theory on occasion, e.g. he'll raise with AKo and the flop will come random low cards. Sometimes he'll raise, sometimes he'll call, occasionaly he'll fold. I can imagine seeing him looking at his watch to decide sometimes.

[NYIsles 0]

In hold em it is easier to put people on flush draws and you can tell when they missed by looking at the board, so the Slansky draw example where unseen cards provide a random number generator would not apply to hold em.True, something as simple as the missed flush draw example wouldn't be as applicable - but that's not to downplay the importance of bluffing/calling bluffs in certain hold'em contexts.For instance, Sklansky alludes to sometimes not looking at his cards when implementing a "quasi game theory strategy" during heads up no limit play. Perhaps it goes something like this: Blinds are 10K/20K; Sklansky's opponent (first to act) fires 80K into the pot. He's laying 8 to 3, so Sklansky figures he should raise this bet blind 3 out of 11 times. Sklansky, like all of the poker greats, studies Smash's posts on a regular basis - so he's picked up on the use of the analog watch to help him randomize his decisions. Since the second hand is still in the first quadrant, he figures, "OK, I'm going to represent a great hand here" - without looking at what he has - so he puts in a significant raise.If the second hand was in the last quadrant, Sklansky would then look at his cards and decide whether or not to play the hand based on it's merits.Maybe that's a ridiculous example, or maybe that's somewhat along the lines of what Sklansky has in mind; I have no idea. But I certainly think there are ways to effectively apply game theory to hold'em...