Poker

[hrothgar]

Interesting article at http://www.salon.com/opinion/feature/2007/07/28/poker/ that touches on a few issues that are (vaguely) related to bridge.

 

I found the complaints about game theoretic betting methods rather interesting.

[pbleighton]

Yes, it seems that whining about other players' methods isn't confined to bridge.

 

Peter

[jtfanclub]

Texas Hold 'em is an unbelievably stupid and simple game, which has been solved (unlike, say, 7 card stud). I expect them to have televised Go Fish tournaments next.

 

My question is, if people start winning the Vanderbilt and similar tourneys who have previously played only online, will we hear the same complaints from the pros in bridge?

[hrothgar]

Texas Hold 'em is an unbelievably stupid and simple game, which has been solved (unlike, say, 7 card stud). I expect them to have televised Go Fish tournaments next.

 

My question is, if people start winning the Vanderbilt and similar tourneys who have previously played only online, will we hear the same complaints from the pros in bridge?

My impression is that the core of complaints in the article was about style of play.

 

Online poker is significant because it provides a good interface between analytic computer tools and an enormous number hand records. In turn, this has allowed players to develop some much more sophisticated strategies.

 

The author also believes that said strategies detract from his (idealized) version of the game.

[glen]

Lots of problems with the article, such as " this all-in strategy has been become one of the most successful methods" -> actually, no the Kill Phil strategy (the book that updated the Sklansky idea) is quite the net $ loser. Also there is no single "optimal game strategy", since the best strategy is a specific one that counteracts the strategy that other players are using. A short example, you bet, the other calls, flop comes down. He bets, and you look at your cards and you have nothing. If this is a conservative player he has something so you fold. If this is an aggressive player the flop likely didn't not hit him (he has nothing, but is just betting since you are likely to have nothing too), so you should raise with nothing. So "optimal game strategy" becomes betting and raising a lot with nothing, which is flawed of course. Advanced strategy becomes delayed raising with nothing (you check, they bet, you make big raise, all with nothing). Others consider probability pictures such as in the semi-bluff approach - you bet with nothing but have a 1/3 chance of making a flush.

 

Sponsors also consider risking $$$ for a 5% single hand chance stupid, and those players tend to find the sponsorship dry up.

 

Notes the article mentions "great players, Bobby Baldwin" - some here will remember when Bobby was playing online bridge.

[hrothgar]

Also there is no single "optimal game strategy", since the best strategy is a specific one that counteracts the strategy that other players are using.

Game theory is not the same as constrained maximization.

 

I agree completely that the "best" strategy is the one that counteracts the strategy that the other player is employing. However, this isn't necessarily a game theory problem.

 

Game theory specifically requires that the other player is behaving in an optimal manner.

[EricK]

Isn't the stuff about people playing with backer's money and not their own a little bit ridiculous?

 

It is not as if the players have nothing to lose - they risk losing being backed in future if they don't win.

[Winstonm]

I really do have to chuckle at the "so called" experts around today. These are tournament players, and the difference between tournament play and live play is as large as the habitability of the earth verses the sun.

 

When I was playing, the buy-in for the World Series was $10,000 - regardless of what happened when you bet or called $100,000, $10K was your maximmum risk of loss. Risk became even more irrelevant if you had a backer or if you had won a satellite to get in - then the total risk was even less. Tournament play is like paying $1 to win $100.

 

Playing live, the amount you put on the table is your risk. The psychology of real money loss is what propelled people like Doyle Brunson to adopt tactics that placed the opponent into choices for "all his marbles" - over the years, he had learned that many players simply don't have the courage to bet or call with all their money unless holding the stone nuts. And it isn't easy to make the stone nuts hand after hand.

 

A true story: Many years ago I was playing stud at Caesar's Palace and a tourist asked the dealer how he came to live in Las Vegas. The dealer, Charlie, said he had been a no-limit poker player and he added that "When you get raised $80,000 dollars, it make you reevauate your hand."

 

The tourist replied, "Hell, that makes you reevaluate your life."

 

Exactly. And if you reevaluate incorrectly, you end up a dealer at Caesar's. That is the difference between live and tournament. Night and day.

[Guest Jlall]

lol

[luke warm]

Texas Hold 'em is an unbelievably stupid and simple game, which has been solved (unlike, say, 7 card stud). I expect them to have televised Go Fish tournaments next.

i couldn't disagree more... it's far more complicated than you're suggesting and it's far from being "solved" ... can you explain why you say that?

Lots of problems with the article, such as " this all-in strategy has been become one of the most successful methods" -> actually, no the Kill Phil strategy (the book that updated the Sklansky idea) is quite the net $ loser.

yep, except the kill phil strategy might have an advantage in small S & G tourneys where it's used early on to build a bankroll, and then switch strategies once that's accomplished.. the advantage is, you can just put up another 6 bucks and play another if you bust out

I really do have to chuckle at the "so called" experts around today. These are tournament players, and the difference between tournament play and live play is as large as the habitability of the earth verses the sun.

absolutely, a tourney and a ring game are totally different and require different strategies... that said, some players (chris ferguson is one) play the two in the same way - at least he says he does

[hrothgar]

Texas Hold 'em is an unbelievably stupid and simple game, which has been solved (unlike, say, 7 card stud). I expect them to have televised Go Fish tournaments next.

i couldn't disagree more... it's far more complicated than you're suggesting and it's far from being "solved" ... can you explain why you say that?

I don't know whether or not anyone has formally solved Texas Hold'Em. I do agree with the claim that Hold'Em is a fairly simplistic game. Its certainly much less complicated than most other forms of poker (or, for that matter, bridge).

 

Each player is sharing the same three community cards. The only thing that distinguishes their hands are the two unique hole cards that they hold. Furthermore, you only have four rounds of betting.

 

There's not too much to the game. In theory, it can all be modeled as a linear programing problem and crunched.

 

If there isn't a solution, I suspect that it boils down to the size of the matrix. While this is a simple game, you have a hell of a lot of different card combinations out there. Solving the resulting matrix might very well be computationally prohibitive.

 

For what its worth, the real complexity in games like Texas Hold'Em is trying to derive optimal strategies to exploit suboptimal play by your opponents. Once you start allowing sub-optimal play and allow yourself to get "greedy" by deviating away from the equilibrium strategy life gets hard.

[jtfanclub]

Texas Hold 'em is an unbelievably stupid and simple game, which has been solved (unlike, say, 7 card stud). I expect them to have televised Go Fish tournaments next.

i couldn't disagree more... it's far more complicated than you're suggesting and it's far from being "solved" ... can you explain why you say that?

For any given hand, you can give an exact % chance of winning against one random opponent, two, three, etc. There simply aren't that many combinations, and many are effectively the same. A computer can easily tell you the odds of succeeding for any given set against a given number of opponents.

 

That's what I mean by solved.

 

I believe that most human professionals have it pretty much solved as well. Give them a hand, with or without a flop, and the number of opponents and they can tell you what their odds are.

 

Now, obviously, that has nothing to do with the human or the gambling element. But once you have the card element down, then the actual mechanics of the game are superfluous. You could just as easily draw one card, bet, draw a second card, bet, and draw a third card, and then high card wins (second highest on ties), at which point you're basically betting on War.

 

Try to imagine playing bridge where you had a handy supercomputer to do your calculating. When the dummy came down, it would give you the play to make and the %, best play to make an overtick and the %, best for down 1, etc. Then you'd just select which one you'd like to play for and it'd play it for you, and the defenders (with their supercomputers) would play as well. That's what Texas Hold Em feels like to me. It's poker without all that messy thinking about the cards, at least at the highest levels (or on the computer where you can ask it the odds).

 

In contrast, think about Draw Poker. You have KKQJT, all in hearts except one of the kings. Do you throw the offsuit King, or the QJT? You may think you know the answer. You're wrong. It depends on how many opponents you have at the table, and whether they would settle for a pair or pitch to try to make a flush or straight.

 

Does that make more sense?

[luke warm]

ok, this is just my opinion so take it or leave it... i think both you and richard are using the wrong goal... you both mention the odds of winning a hand given any two starting cards.. i'm more interested in winning a majority of the money, not a majority of the hands... that's the reason, in no limit for example, pot odds isn't the (only) determining factor in an action... also, do the odds of two cards winning change depending on whether or not there was a bet in front of you? or a bet and a raise? if so, by how much?

[jtfanclub]

ok, this is just my opinion so take it or leave it... i think both you and richard are using the wrong goal... you both mention the odds of winning a hand given any two starting cards.. i'm more interested in winning a majority of the money, not a majority of the hands... that's the reason, in no limit for example, pot odds isn't the (only) determining factor in an action...

 

I understand, and I'm sorry I wasn't clear. When I said it was solved, I'm talking only about winning a hand given the flop and the number of people in (and the size of the pot). The actual card game is a nothing.

 

also, do the odds of two cards winning change depending on whether or not there was a bet in front of you? or a bet and a raise? if so, by how much?

 

It's dependent on patterning- how often the person has previously bet, how much, and how often he's folded. That's actually not what I was talking about either when I said it was solved, but apparently that's been solved too.

[hrothgar]

ok, this is just my opinion so take it or leave it... i think both you and richard are using the wrong goal... you both mention the odds of winning a hand given any two starting cards.. i'm more interested in winning a majority of the money, not a majority of the hands... that's the reason, in no limit for example, pot odds isn't the (only) determining factor in an action... also, do the odds of two cards winning change depending on whether or not there was a bet in front of you? or a bet and a raise? if so, by how much?

Please reference my last post in which I discussed the number of betting rounds as an explicit component of the linear programming model.

 

Even with all the points that you mentioned taken into account, Hold'Em is still fairly simple. Off the popular poker variants that I know of, I'd say that

 

1. 5 card draw is the easiest to model

 

2. Some version of seven card stud is probably the nastiest. (You have lots of rounds and lots of information available each round)

 

Compare Hold'Em to 7 card stud.

 

1. You have fewer betting rounds

2. You don't have to factor in nearly as much unique information about each round

 

(For the record, when I am talking about "Solved" I'm talking about a Nash equilibirum)

[BebopKid]

I expect them to have televised Go Fish tournaments next.

That may actually be more interesting than televised Bingo, which is on a Major US Network.

[luke warm]

also, do the odds of two cards winning change depending on whether or not there was a bet in front of you? or a bet and a raise? if so, by how much?

It's dependent on patterning- how often the person has previously bet, how much, and how often he's folded. That's actually not what I was talking about either when I said it was solved, but apparently that's been solved too.

i understand what you're saying, i'm just having trouble understanding how patterning enters into it... for example, doyle will sit down and play extremely loosely for an hour or so, often losing his first buy in... then he'll buy more chips and switch strategies, knowing his earlier play has given him a certain table image... it seems to me that patterning your bets to his would fail to take into account his switching of strategies, something he does off and on all session... i know that's a simplistic example, that's why i said i believe it's more complicated than it appears

 

also, it's impossible to ignore the gambling aspect of it... for example, imagine a 6 handed game, you're under the gun with pocket queens... you raise 3x the BB, 4 people fold, and the BB raises you all in... what do you do, assuming the bet is large enough to trouble you? how about if you *knew* he had either pocket aces, pocket kings, or AK suited?

 

i'm interested in case we ever play :P

[jtfanclub]

also, it's impossible to ignore the gambling aspect of it...

That's the only aspect of it that's left, at the highest levels. :P

 

i understand what you're saying, i'm just having trouble understanding how patterning enters into it... for example, doyle will sit down and play extremely loosely for an hour or so, often losing his first buy in... then he'll buy more chips and switch strategies, knowing his earlier play has given him a certain table image... it seems to me that patterning your bets to his would fail to take into account his switching of strategies, something he does off and on all session...

 

I don't know much about pattern theory, but I believe that it works on last hand pattern. ie., if he's been conservative the last few hands, bet that he stays conservative. If he's been free, bet he stays free. If he's been alternating, bet he keeps alternating. Yes, he'll catch you when he switches patterns, but he remains constant far more often than he switches, so you'll win more often than you lose.

 

 

I don't play hold 'em, sorry. :D :)

[helene_t]

I never understood why it's sometimes said that writing a computer program that could play at expert level is more difficult than the same task with chess. Either there's something fundamentaly wrong with my ideas about poker, or with my ideas about game theory, or else poker is a rather trivial thing from a game-theoretical point of view.

 

As I learned poker, it can basically be reduced to:

- both players draw a number from the uniform [0;1] distribution.

- the dealer choses to lose the ante or to raise to twice the ante.

- if the dealer raises, the non-dealer choses to lose the ante or to raise to twice the ante. In the latter case, the one with the highest number wins.

 

It seems to me that the above described game can be easily solved. You can make all kinds of generalizations. For example, we usually played that you could trade any number of cards, sometimes for free, sometimes at the cost of an additional ante. Now your strategy should factor in the number of cards traded by the other player(s). You can allow the non-dealer to raise to more than twice the ante in which case the dealer can chose to lose twice the ante or to raise again etc. And you can play with more than two players. In any case, it doesn't seem particularely interesting to me.

[hrothgar]

i understand what you're saying, i'm just having trouble understanding how patterning enters into it... for example, doyle will sit down and play extremely loosely for an hour or so, often losing his first buy in... then he'll buy more chips and switch strategies, knowing his earlier play has given him a certain table image... it seems to me that patterning your bets to his would fail to take into account his switching of strategies, something he does off and on all session... i know that's a simplistic example, that's why i said i believe it's more complicated than it appears

 

also, it's impossible to ignore the gambling aspect of it... for example, imagine a 6 handed game, you're under the gun with pocket queens... you raise 3x the BB, 4 people fold, and the BB raises you all in... what do you do, assuming the bet is large enough to trouble you? how about if you *knew* he had either pocket aces, pocket kings, or AK suited?

 

i'm interested in case we ever play :P

Note my earlier comments about trying to exploit suboptimal play by your opponents (and the complexities involved).

 

It might be (easier) to illustrate this with an example using a very simple game like "Rock, Paper, Scissors" rather than a poker variant.

 

Rock, Paper, Scissors has a very simple, well known equilibirum. Players should randomize across the three choices with equal weights. Each time I play, I roll a "fair" D6. If a 1 or a 2 crops up, I chose Rock. If a 3 or a 4 crops up, I chose Paper. If a 5 or a 6 crops up, I chose Scissors. It can be demonstated that a situation in which both players adopt this strategy satisfies the criteria for a Nash Equilibirum. (This is a fancy way of stating that neither player has an incentive to change their strategy)

 

Now, lets assume that we know that we are playing against an opponent who has deviated from the "optimal" strategy. Hypothetically, he is playing

 

Rock if he rolls a 1

Paper if he rolls a 2 or a 3

Scissors if he rolls a 4, a 5, or a 6

 

In this case, we should adjust our strategy and always chose "Rock". However, as I have noted before, this isn't a game theory problem.

 

Life gets even more complicated if we're dealing with a finite repeated version of a game in which players could be attempting to establish a reputation for a certain style of (suboptimal) play that they can exploit later on in the game. In general, the solution to this type of problem (initially) requires solving the "one off" version. At this point in time, you need to study whether or not the equilbirum to the one off version is stable or unstable. In many cases, if you're dealing with a stable equilbirum, you can safely ignore a player's attempts to portray himself as "loose" or "tight" or whatever.

[luke warm]

I don't know much about pattern theory, but I believe that it works on last hand pattern. ie., if he's been conservative the last few hands, bet that he stays conservative. If he's been free, bet he stays free. If he's been alternating, bet he keeps alternating. Yes, he'll catch you when he switches patterns, but he remains constant far more often than he switches, so you'll win more often than you lose.

does it seem fairly evident to you that if it was that simple you (or me) might find it more profitable to play poker than do whatever it is we're doing... now some people do just that, but none of the ones who do so have ever commented on the simplicity of the game... even mathmatical poker players like c. fergerson or d. sklanskey have said it's a complicated game

I never understood why it's sometimes said that writing a computer program that could play at expert level is more difficult than the same task with chess. Either there's something fundamentaly wrong with my ideas about poker, or with my ideas about game theory, or else poker is a rather trivial thing from a game-theoretical point of view.

 

As I learned poker, it can basically be reduced to:

- both players draw a number from the uniform [0;1] distribution.

- the dealer choses to lose the ante or to raise to twice the ante.

- if the dealer raises, the non-dealer choses to lose the ante or to raise to twice the ante. In the latter case, the one with the highest number wins.

because in chess, making certain moves at certain times leads to loss *every* time... the same isn't necessarily true about poker... it's possible to 'bluff' in chess, but nowhere near the same degree... if you get called in chess, you'll lose... in poker, you might win

Note my earlier comments about trying to exploit suboptimal play by your opponents (and the complexities involved).

yes, but my point is that suboptimal play at poker is not as easily quantified as subotimal play at chess (for example)... last night on 'high stakes poker' the UTG player opened for $10,000 (the blinds were, i think, $2,000 and $4,000)... he had a suck hand, i think it was a 9/4 offsuit, and was just fooling around... everybody folded to the button, who made it $30,000... the blinds folded and the UTG player raised all-in... the button had AK... what would you have done? what's the "optimal" thing to do? how do you know that?

 

as far as tight vs. loose, all the big money players are tight and loose depending on several factors, changing tempo based on their own criteria

[hrothgar]

yes, but my point is that suboptimal play at poker is not as easily quantified as subotimal play at chess (for example)... last night on 'high stakes poker' the UTG player opened for $10,000 (the blinds were, i think, $2,000 and $4,000)... he had a suck hand, i think it was a 9/4 offsuit, and was just fooling around... everybody folded to the button, who made it $30,000... the blinds folded and the UTG player raised all-in... the button had AK... what would you have done? what's the "optimal" thing to do? how do you know that?

I have no idea what "optimal" play is in this situation. I don't play Hold'Em. I don't watch Hold'Em. I haven' done an exhaustive search to look for game theoretic solutions to Hold'Em. As I noted earlier, its not even clear whether traditional concepts from game theory can necessarily be applied to a real world example like this one.

 

My comments have been directed towards a fairly specific set of propositions:

 

1. Texas Hold'Em is not a particularly complicated game to analyze. This proposition is based on the rules set to the game.

 

2. If Texas Hold'Em has not been solved, the problems are (probably) related to the size of the linear programming problem involved.

 

Since making my original posts, I found a couple interesting academic articles which back up my intuition. In particular, you might want to look at

 

http://www.cs.cmu.edu/~sandholm/texas.aaai06.pdf

 

This paper preserves the same distinction between game theory type approaches and opponent modelling. It also addresses issues related to the size of the linear programming problem. (From the sounds of it, they still haven't managed to munge the large matrixes)

 

I think that this discussion is boiling down to a difference in nomenclature between folks with an academic interest in the problem and those whose primary concern is winning at the table.

[jtfanclub]

does it seem fairly evident to you that if it was that simple you (or me) might find it more profitable to play poker than do whatever it is we're doing... now some people do just that, but none of the ones who do so have ever commented on the simplicity of the game... even mathmatical poker players like c. fergerson or d. sklanskey have said it's a complicated game

does it seem fairly evident to you that if it was that simple you (or me) might find it more profitable to play poker than do whatever it is we're doing...

 

Well, running the 100 meter dash is pretty simple too....

 

If I had the brains and the endurance for it, yes, I believe that if I spent a couple of years reading books and playing Hold 'em on the Internet as a full time job, and it didn't drive me insane, I could be as good as the 100 or so people who have done it and have the aptitude for it. Which I guess would give me the same 1% chance of winning that they have. People have certainly done this, and I don't think they're savants, so I guess I don't think I'm going out on a limb by saying that. Of course, I probably don't have the endurance or the brains, so I'd be wasting my time and money.

[luke warm]

I think that this discussion is boiling down to a difference in nomenclature between folks with an academic interest in the problem and those whose primary concern is winning at the table.

i think that sums it up nicely... the link you provided is well over my head, but i did try to read it