Game Theory

Brayruit

I'd be interested in boardies’ views / experience in relation to game theory and poker.

After performing less well than I would have liked in recent tournaments, I came to the conclusion that I am not naturally very strong on psychology but that good GT understanding would be a useful addition to my play and would to a certain extent compensate for the psychological side.

I am strong on the maths side of the game and my thinking was that GT would allow me to “compute” the correct play at any point from a GT point of view and that that would in some way take away some of the psychology edge from players who are better at that side of the game than me. At the least, I think that GT would give me some insight into how to play against strong players who get good reads on me.

I have started to scratch the surface on some of the articles that have been written on this topic, but everything I have come across is one of:
a) the bleedin’ obvious (e.g. you should bluff sometimes because ……)
b) the probably irrelevant (e.g. GT theories that are based on a over-simplified version of poker)

Any ideas on where to go?
Anyone have any insights that they got from GT?
Anyone studied this topic properly?

bohsman

Im about to read Harrington on Holdem1 and 2, highly reccomended by people who read books.

Brayruit

I've read them, then read them again, then did all the problems again then ordered part 3 from Amazon (hasn't arrived yet). And from where I was starting from they are brilliant - better than Sklansky. But from a GT explanation point of view it doesn't do much more than explain why bluffing is a requirement......

Hectorjelly

http://www.amazon.com/exec/obidos/tg/detail/-/0486296725?v=glance

This is an excellent introduction into Game theory, once you've read it its easy to see the implications for poker yourself

ollyk1

Brayruit wrote:

I've read them, then read them again, then did all the problems again then ordered part 3 from Amazon (hasn't arrived yet). And from where I was starting from they are brilliant - better than Sklansky. But from a GT explanation point of view it doesn't do much more than explain why bluffing is a requirement......

Hey Stephen,

I think game theory and "mixing up your game" is very dependent on the players you are playing with and their level. Certain moves work at different tables and randomising your play is important against better players but you have to be able to judge if such subtlety is required or is optimal against generally weak and non deeply poker thinking players in low buy in tournies around town.

If you are more concerned with doing well in higher standard games and much bigger buyins then I think it would be better to play regular small buy in games and work on that reading of the game aspect that you feel you lack.

I think everyone can agree that the maths of the game aren't that complex and apart from applying and working through questions of how often a push will get through with x amount of players left to act or how much of your stack is it acceptable to commit preflop with a sooted connected hand as a randomising hand then the rest comes down to playing experience I feel.

Only experience will help you get a feel for the percentage of times a reraise bluff will work, or a squeeze play in a certain situation.

Reading through strategy threads here on boards helps a lot but I think in poker you can't beat practise, practise and practise.

Olly

PiperT

bohsman wrote:

Im about to read Harrington on Holdem1 and 2, highly reccomended by people who read books.

Agreed, I & II are excellent and worth reading and re-reading. I just got my hands on Harrington III - The Workbook. This helps you to put the lessons of I & II into practice and takes some real world examples from the best at the game. I've only just started it but if the first two are anything to go by I'm hoping it will help round off my game.

LuckyLloyd

This post has been deleted.

HauleyBear

Is a good understanding of game theory, highly benifical to ones poker game??? i have a very limited understanding of GT... Just wondering is it something the more senior players here would recommend learning...

Sangre

game theory?

Hitman Actual

HauleyBear wrote:

Is a good understanding of game theory, highly benifical to ones poker game??? i have a very limited understanding of GT... Just wondering is it something the more senior players here would recommend learning...

I think it's only beneficial if you've got all the general aspects of the game covered. If you've got a lot of basic leaks in your game, game theory sure as hell wont turn it around. Might make things worse, tbh. HectorJelly seems to be the only player on here who applies it in his game, but I could be wrong.

I also think it has practically no relevance in the tightly structured tournaments that people here play. But for the experienced online pro's/semi-pro's playing thousands of hands, I'm sure it helps eke out extra dollars.

Hitman Actual

Sangre wrote:

game theory?

I think it involves adding structured randomisation to your game so that you make money (long-term) with certain plays against specific players no matter what they do.

Hectorjelly

lenny_leonard wrote:

I think it involves adding structured randomisation to your game so that you make money (long-term) with certain plays against specific players no matter what they do.

Thats just one small element too it. Its more that just an understanding of game theory (which I have to only a certain extent) really helps in an understanding of poker.

eggie

http://en.wikipedia.org/wiki/Game_theory

RoundTower

I have a book called Thinking Strategically by Dixit and Nalebuff, you will find it on Amazon. I recommend that, it is an interesting read with very little hard maths. I don't think you need to understand much game theory to be good at poker but it is worth being aware of, and it would add another perspective.

phantom_lord

bohsman wrote:

Im about to read Harrington on Holdem1 and 2, highly reccomended by people who read books.

Did you get these on amazon or a bookshop? Most shops I take a look in don't have much of a poker selection and I haven't seen these anywhere.

cooker3

phantom_lord wrote:

Did you get these on amazon or a bookshop? Most shops I take a look in don't have much of a poker selection and I haven't seen these anywhere.

Yep, I bought part 1 and 2 on Amazon for $50 including shipping

Drakar

Game theory is a discipline examining decision making. It normally involves setting up a "game" with players, risks and payoffs and then performing a sequence of "if player 1 does this what does player 2 do" type analysis to ascertain what the best move for each player in certain situations is. It's primary use is in economics, but as at it's core it's just about decision making, it can be used anywhere people are making decisions (woot! everywhere), eg wargames.

As it involves decisions, payoffs and risks, one can see that it maps quite nicely into Poker. Is it a requirement to understand how to play good poker? No. The analysis which it has produced you will now find in most poker books you will find. If you have read, and understand, good poker theory, then game theory will give you a better understanding of the methodology of how people worked out that this was good theory. The techniques which you can apply from game theory will be pretty much common knowledge in "poker speak".

That being said, I did my degree in Economics, and game theory is interesting, easy and fun!

Lafortezza

Player 1 and Player 2 are playing a game.
In this game there is $100 to be split between the two players.
Player 1 gets to decide how the split goes, e.g. $90 for him $10 for P2, or $60 for him and $40 for P2.

Once P1 decides on the $$ share, P2 now decides whether he accepts the split or not.
If P2 accepts, then each player gets $$ as decided by P1. If P2 rejects the split, then each player gets nothing.

What is the optimum approach for each player to this game?



Edit: if you know the answer or figure it out, please wait a while before posting,
or use spoiler tags, [.spoiler]text[./spoiler] without the .'s, will give

text

Drakar

A good example of how real players would completely ignore game theory

If you look at this from Player 2's perspective (game theory revolves around this alot), if he chooses to accept the deal he gets what's offered, otherwise if he chooses to reject, he'll get nothing. A game theory assumption (though not a realistic one) is that all players will act rationally on the information they are given. So if Player 1 offers a deal where player 1 gets 90, and player 2 gets 10, player 2 would accept (as he's chosing between getting 10 and getting 0). Similarly if player 1 offered a deal 99/1 player 2 would accept. So player 1 can offer player 2 the smallest amount available in the game (perhaps 99.99/0.01) and player 2 should accept as he's still chosing between 0.01 and nothing.

For more game theory fun see the dollar auction.

Hectorjelly

It only gets really interesting if they run it a number of times.

Poker & Pints

Drakar wrote:

A good example of how real players would completely ignore game theory

So player 1 can offer player 2 the smallest amount available in the game (perhaps 99.99/0.01) and player 2 should accept as he's still chosing between 0.01 and nothing.

For more game theory fun see the dollar auction.

My take:

NOT! Player 2 would sacrifice his .01 to f#$k player 1 out of the 99.99 and would do so for must amounts if he didn't feel equitably compensated. Player 1 should know that player 2 will reject the offer out of spite and therefore offer 50/50.

RoundTower

Hectorjelly wrote:

It only gets really interesting if they run it a number of times.

actually I think this game is more interesting if you only play it once.

opr

RoundTower wrote:

actually I think this game is more interesting if you only play it once.

Why ? Surely the more times you run it the more its becomes a head fuk game between the two people involved.

I would have thought once was more of a mechanical thought process based on what is your optium strategy considering your only gonna get one go at it.

Opr

Drakar

Poker & Pints wrote:

My take:

NOT! Player 2 would sacrifice his .01 to f#$k player 1 out of the 99.99 and would do so for must amounts if he didn't feel equitably compensated. Player 1 should know that player 2 will reject the offer out of spite and therefore offer 50/50.

Presume that was mostly in jest, but that all hinges on the assumtion people will act rationally. Rationally people will accept 0.01 over zero.

The potential exception being a repeated game (as mentioned by HJ).

Hectorjelly wrote:

It only gets really interesting if they run it a number of times.

Surprisingly standard game theory suggests that repeating a game a specific number of times does not influence its outcome.

Lets imagine we repeat the above game 10 times. The way to solve this is to look at the releases backwards. Lets look at the 10th game. Well here there will be no repeating, so player two will accept whatever he is offered. Player 1 will know this, so will offer 99.99/0.01 (remember rationally player two will accept this because he is chosing between 0.01 and nothing with no repitition). Ok, so we accept that in the last game player 1 is going to be naughty to player two. Lets move up the chain to game 9. Here, people know the outcome of game ten, so what happens in game 9? Regardless of what happens, game 10 will always be the same (provided people are rational). So, guess what, player 1 offers player 2 a 99.99/01 split. Player two will accept, because if they reject they get zero, and we already know that in the last game they get 0.01. So game 9 has the same outcome.

You can follow the same process for each of the 10 games, similarly for any finite number of games.

So if we think about this, imagine the game is to be repeated a billion times, game theory suggests that if the players act rationally the outcome will always be 99.99/0.01. This seems very counterintuitive as looking at the first round of the game someone unfamiliar with how to solve this type of game would say that player 2 would refuse the round 1 offer to teach player 1 a lesson. However, what we are saying here is that this player would be acting irrationally as player 1 should continue to offer 99.99/0.01 on all further rounds because the rational outcome (stable equilibrium) is for the 99.99/0.01 split.

Interestingly the outcome could be 50/50 for each game if the game is repeated indefinately (the difference between infinity -1 and infinity is alot bigger than it appears :P).
[edit: weenied out and changed should to could]

Brayruit

Thx to all for some very interesting posts.

I agree that GT is probably already applied to the advice given by (e.g.) Harrington in relation to what plays to make in certain circumstances (for example he does indeed say that relatively weak hands are efficient randomisers for opening).

Let me give the sort of situation where I can feel unsure of the optimum move and where if i lack reads or feel I *think* that GT may have some answers. The situation described is not particularly unusual, but it is the area where I frequently am unsure of how to move.

Round 3/4 of a tournament... I have been playing tight and getting relatively poor cards so I have played very few hands... perhaps raising a few times in late position with so-so hands and either taking a small pot down there and then or folding to a re-raise... I have not been involved in any showdowns.

My stack is down to 85% of its original size - say 25BBs, so I think that I am in reasonably comfortable territory.

Now in MP I get dealt AQ and open for a raise of 4BB. Everyone folds to the big blind who raises to 10BB (his stack is 60BB). The BB has been an active player... I think that he is probably strong and observant.

I'm thinking that he could reasonably have put in this bet with any pair, a big ace or in fact with f all. So I call (right?).

I miss the flop completely (say 389 rainbow). The BB puts me all in (15BBs). I fold like a little girl and am left with 15BBs. Next time this happens I will be crippled, and chances are unless I hit a very big hand, I will get all in on what I hope is a coin flip with a strong player.

Now, this might just be illustrating that I am playing too tight / passive, but what I have been looking for is a GT explanation of what is going wrong here…. Looked at from a GT point of view, I *think* that there would be justifications for:
1) Concluding that I am playing too tight… after a run of bad cards I should make sure that if I do play I should not show myself to be easily bullied off hands
2) Concluding that when I get re-raised by an aggressive player before the flop I have to re-reraise (push with AQ?!)… otherwise I either have to hit the flop or I will be setting myself up as a sacrificial victim in the near future.
3) Concluding that I should be far more focussed on other players than mu own play (perhaps this is the key to applying GT).

The point is that I do not know what to conclude… and the question is:is there a clear GT based explanation of optimal strategy in this and similar situations? Just thinking “loosen up sooner” is not going to help my game.

Hectorjelly

I dont really see how that has much to do with game theory. If you think that he is reraising light at all then push preflop, if not fold preflop. Calling is the worst option.

califano

Game Theory?
Wheres 'The real Anto' when you need him?

Gholimoli

as HJ said i dont think GT can help here much but better play can.
you are not deep enough to just call in that spot its the worse possible option for the resons u said.
if he is active and has shown down a wide range of hands then push and if he is tight then fold(or if ur me still push)

Brayruit

Gholimoli wrote:

as HJ said i dont think GT can help here much but better play can.
you are not deep enough to just call in that spot its the worse possible option for the resons u said.
if he is active and has shown down a wide range of hands then push and if he is tight then fold(or if ur me still push)

I *think* that GT is actually what we are talking about. "You are not deep enough to call" is to my mind a GT based analysis.... because it looks forward to what happens next.

BTW I agree with your argument... but surely folding is actually a better option with AQ regardsless of how agressive the player is.... and wait for a better spot.

Hectorjelly

Brayruit wrote:

BTW I agree with your argument... but surely folding is actually a better option with AQ regardsless of how agressive the player is.... and wait for a better spot.

lol

the other guy will have AJo and worse here a lot of the time

Brayruit

Chris "Jesus" Ferguson is a GT expert... as I understand it, this is where he has his advantage. His father lectures on game theory at MIT or somewhere and he has co-authored academic papers on the subject.

Am I naive to think that there are some "magic lessons" to be learnt in this area that can be applied to poker?

MrPillowTalk

Brayruit wrote:

I *think* that GT is actually what we are talking about. "You are not deep enough to call" is to my mind a GT based analysis.... because it looks forward to what happens next.

BTW I agree with your argument... but surely folding is actually a better option with AQ regardsless of how agressive the player is.... and wait for a better spot.

no folding and getting all in are about as good as each other in that spot.

Brayruit

Hectorjelly wrote:

lol

the other guy will have AJo and worse here a lot of the time

yeah but plenty of times he'll have 88.....

MrPillowTalk

Brayruit wrote:

yeah but plenty of times he'll have 88.....

whats wrong with that?

Hectorjelly

Brayruit wrote:

yeah but plenty of times he'll have 88.....

then pushing is much better than folding, he might fold and even if he doesnt you are getting odds to race because of the dead money

Brayruit

No, no that's not what I meant... I was just being pessimistic and saying that he'd flopped trips (remember flop was 389?).... ignore that post...

Drakar

I'd agree with the others in that this can be analysed using standard poker theory. There isn't anything "magical" about game theory. A nice way of describing it would be to define it as the science of decision making, but that's being far too kind. The decision types presented in poker are generally well discussed in the usual recommended books on the subject. Game theory just provides a different set of terminology.

If you wanted to look at the position you mentioned above directly in game theory you could do a payoff matrix. So if you fold here you have 15BB. If you call there are three options, it's a draw and you have 25BB, you lose and have 0bb or you win and have 50bb. It's then about deciding what the chances of those outcomes would be, and then trying to assign an expected $ value to the bb outcomes. Generally assessing the chance of one thing over another is outside the realms of game theory, but you could do some "put yourself in the other person's shoes" analysis and look at what the villan did. After the flop he had 50bb, there was 20 in the pot, so this would be a decent stealing opportunity considering the fold equity (no way to know if he was stealing of course). After presumably considering your table image and possibly his cards he risked another 15 to put hero all in. So he wins 20 if you fold, and 35 if you call and he wins, and loses 15 if you call and he loses. Again he should be performing some sort of expected value and risk analysis to forecast your actions and the actual value of the potential outcomes (depends on the level you play as to how in depth those may be). I think the only conclusion we can draw is that it would have been a good stealing opportunity for him if he didn't have the cards, but there's no way for us to tell if he was doing so or not at this point.

All this is generally probably not all that interesting nor informative to most people I'd guess. I personally think this type of analysis could be easilly done using traditional poker methodology, it's just different terms for some parts.

At lower poker limits, looking at other players and putting yourself in their position can often be quite useful as you can say would he really go all in with trip 8s for example, but as you graduate to higher level players, sometimes they might go all in with trips specifically because they know that people won't expect them to do that with trips. All poker and game theory provide us with are methodologies for making the decisions.

DeVore

regarding the repetition of the P1/P2 game... of course running it many times alters the strategy.

If I'm p2 I will reject an offer of $1 because while I lose $1 that game and instead get nothing, I've pushed the decision BACK onto P1 for the next round. He just lost $99 (or so it seems) by offering me too litle.

The next round he may well reconsider offering me $1 because that failed on the first game. I've now made it clear that I'm willing to sacrafice short term gain to deny him. Hence my short term loss has a good chance of gaining me long term improvement.
Accepting $1 for 10 games nets me $10 over 10 games.
Refusing 9 games may well net me 50/50 on the tenth game!
Either way, I'm likely to improve the offer on subsequent games by refusing a tiny offer on the first game.

DeV.

Drakar

The point is that by refusing $1 the first time the player is acting suboptimally. This game has a definate mathematical solution (1/99 split using the solving method described above). Regardless of whether the player accepts or refuses, the next round the player should always offer 1/99. When we look at this game, it's sometimes easy to say oh they should just try to teach the other guy a lesson the first time, but if you imagine instead it's say $1billion, think about whether you'd turn it down to deny the other guy (in which case you get zero). So if this game was played by computers, they would end up with that result. Humans aren't quite as logical however heh, but it is one of the main assumptions game theory revolves around.

If the game was repeated infinately, then they can play games about the amount of the split.

Rnger

tell p1 at the start your only accepting a deal of 50/50 or better. If you strictly stuck to this strategy, would he not be a fool to do it otherwise?

Oodges

Repeated games are much more interesting than one offs.
One of the most fascinating things, is that equilibria of the whole game is not necessarily sequentially repeated equilibria.
(where a nash equilibrium is a particular strategy set for each player chosen a priori such that player a will have no incentive to change his strategy from his nash eq strategy given player b's nash eq strategy and vice versa
This can be more easily seen if we
simplify the above problem to the game played twice, where player a has the choice of say taking 99, taking 50 or taking 1.
(note that he now has 3 times 2 times 3= 18 strategies, i.e. offer 99 in first game and offer 99 in second if first deal refused etc.)

Now imagine player two mosied on over to player 1 before the game was played and said, I'll accept whatever you offer me in the first game, but reject whatever you offer me in the second unless you offer me at least fifty first time out, -( a punishment strategy)
say player a then decides to take 99 both times out, he gets it first time but not the second so his utility from this strategy is 99+0=99
we can see it would be preferential if he decided to take 50 both times,
= gain of 100!!(note offering 50 in an indivdual game is not an eq point but in repeated game is superior to repeated individual game eq point- note this isn't a nash equilibrium as player a has incentive to deviate from his strategy given b's strategy
player a's gain/utility will be maximised if he decides to take 50 first time out and 99 second time out but player b has an incentive to deviate!

Now what if B says Give me 99 first time out or i'll refuse whatever happens second time out. By similar arguments to above we can see that
A will only take 1 first time out and 99 second time out.
-(this might take some thinking about but it's right)
This is a nash equilibrium of the repeated game as neither player has an incentive to deviate given the other's strategy.
and both players will have a utility of 100 from the repeated game.
as opposed to player a ****ing b over twice which is what most ppl assume would happen.
Sorry if, that was a little long winded and technical- I'm a maths student so it's hard not be
I hope that was illustrative.

Oodges

Someone is probably going to come along and say now that player a
will just **** player b over in the first game anyway and then b will come crawling and accept a's offer in second game.
Think of it as taking both games as a single game -(with 1 a priori strategy)
or player b can say to player, I've instructed my autonomous computer to
follow this strategy regardless of if you screw me over in game 1 and locked it in a room and thrown the key away.
-(note b doesn't actually have to talk to a, since we're assuming perfect infomation- everyone knows everything- and 2 rational players)
-Isn't it interesting that player b actually gains by deciding his 2nd decision beforehand, and removing his ability to change his mind.
So you can see the obvious advantages to this in the real world,
for self enforcing contracts and making sure you don't get shafted by someone you don't trust.
As for applications to poker... it's hard to see, this scenario could be applied perhaps in a tournament with 3 players 1 of whom is away from table and the others are stealing his blind. -(although this would be way more complex and I certainly can't think through it at this time of night)

Drakar

If you remove one player's ability to change their mind, the game becomes trivial. In finite or infinite repeated games one player can implement a system where some process is put in place which means for example player 1 will always only offer 99/1 and the system will always operate this way regardless of what player 2 does. In that case player 2 would always accept the 1 offered as there is no benifit in trying to punish.

Similarly, player two could put a system in place which once started they could not affect and this would only accept 99/1 split in favour of them. Once this is communicated to player 1, and player 1 knows that player 2 can't change the system, then player 1 will always just offer 1/99 because he knows he can't get away with any more.

The common game theory example people use here is if two people are having a game of chicken (driving their cars at each other at high speed to see who will swerve first). If one player throws his steering wheel out the window as they close in, the other player knows that his opponent won't be able to swerve, so he knows that instead he will have to.

More real world examples are for example where a company builds a large shop in a certain territory, competitors can see that the first company has made a significant investment and is tied to being in this territory (whereas otherwise other competitors entering the market may have forced them out).

The poker application of this I would think is players acting out of turn. Here the player is (for example) comitting themselves to going all in, and other players in the hand know that this is going to happen regardless of what decision they make. This removes their ability to bluff (in game theory terms - makes use of first mover advantage), by removing this option opponents have only one way to beat you; with good cards. Obviously this would only useful in certain situations (and is also naughty).