Game Theory

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).