Two Plus Two Newer Archives  

Go Back   Two Plus Two Newer Archives > General Poker Discussion > Poker Theory

Reply
 
Thread Tools Display Modes
  #21  
Old 11-23-2007, 01:50 AM
jukofyork jukofyork is offline
Senior Member
 
Join Date: Sep 2004
Location: Leeds, UK.
Posts: 2,551
Default Re: Fictitious play for multi-player games

[ QUOTE ]
[ QUOTE ]
I guess the challenge here is:
Can we model the "strategy-negotiation process" in a way, such that the Caller eventually "realizes" that its profitable for him to stay at a wider call range, given that the pusher is adopting his ranges?

Even when the pusher is pushing tighter now and switching to a tighter call range would be immediately profitably for the caller - the idea is to simply to "keep" the pusher from loosening up again, because tightening up will eventually end up in a worse state for the caller.

[/ QUOTE ]
Ah, I'd forgot that the wider calling, leading to winder pushing, would end up with the caller being able to exploit by calling thinner the the original NE (I was thinking that it would just be like NE+SpiteCall for some reason). So sadly this means that their will be no "spite-call" equilibrium possible.

[/ QUOTE ]
OK, I've thought about this some more and how about if we add the extra constraint that the caller is forced to state his exact strategy before the pusher pushes?

This should get round the possibility of the caller to pass up on his spite calls and allow for convergence to a "spite-call" equilibrium?

Juk [img]/images/graemlins/smile.gif[/img]
Reply With Quote
  #22  
Old 11-23-2007, 03:40 AM
Paxinor Paxinor is offline
Member
 
Join Date: Sep 2006
Posts: 87
Default Re: Fictitious play for multi-player games

there is definitly no "spite-call" equilibrium.

it doesn't help to fix the callers strategy. then you just use the maximaly exploiting counterstrategy as a pusher. but then its not even a equilibrium since there is only one strategy...

so bascily the other guy is just moving out of the NE trying to make you adjust to an exploiting strategy and go into a kind of "tit for tat" game.

but its really exciting to see that players have GREAT power over the game and it's outcome if they do not choose to max payout.

however strictly theoretic, there is no "spite-call" equilibrium whatsoever. even if you add constraints...

if someone moves away from NE and the other adjusts somehow, there will be no equilibrium. so you cannot just lay back, play your strategy and wait that the opponent makes a mistake. then your in the "he thinks that i thinks that he thinks" not that the state cannot be profitably played

in pracice i think he makes a good move... i mean you should adjust. you improve your EV by that and he improves his. because your strategy will not be public he cannot exploit you perfectly. therefore it is very likely that you will turn out with a better EV than in the NE but he will too!

so actually we have the kind of paradox situation that because he cannot exploit you perfectly because he doesn't know your exact strategy he can improve his EV!! this is pretty sick if you think about it because this goes so much agaisnt intuition.

well (while im writing it) acutally i think there is some kind of equilibrium:

take all possible strategies of the caller and let them be exploitet perfectly by the pusher. there is an EV for all of those situations. if some of those EVs are for the caller are above his NE EV then he should just choose that strategy and risk to get maximaly exploitet.

of course the pusher then as a 23% pushing range and could be exploitet again by thigten up. but the you get into that tit for tat game where when it starts to ge sophisticated in strategy changing, NE strategy would be best again

so you simply don't adjust! you giving up the edge of counterexploiting him to preserve the edge you gain by getting maximaly exploitet over the NE EV (this sounds pretty sick)

so if the calculations of plexiq are correct, the other guy starts calling all the time and is therefore transfering EV to the folders. if you are a thinking player you adjust.

you just push 23% of your hands. good for you, you improved your EV again. but the loose caller improved his too! (if the calculations are correct). so he should keep his strategy up. and there you have a kind of equilibrium where strategys will not be changed due to lack of strategys that are known and the problem that you might loose in a tit for tat game.

well this is really really interesting!
Reply With Quote
  #23  
Old 11-24-2007, 03:55 PM
trojanrabbit trojanrabbit is offline
Senior Member
 
Join Date: Aug 2004
Location: dominated and covered
Posts: 188
Default Re: Fictitious play for multi-player games

[ QUOTE ]
OK, I've thought about this some more and how about if we add the extra constraint that the caller is forced to state his exact strategy before the pusher pushes?

[/ QUOTE ]

This doesn't work either. If I'm Caller, I'll say "I'm calling 100% and you know I'm stuck with it." Now Pusher has to fold almost everything since it's just the same problem in reverse. It's the right of first bluff.

Tysen
Reply With Quote
  #24  
Old 11-25-2007, 12:54 AM
jukofyork jukofyork is offline
Senior Member
 
Join Date: Sep 2004
Location: Leeds, UK.
Posts: 2,551
Default Re: Fictitious play for multi-player games

[ QUOTE ]
[ QUOTE ]
OK, I've thought about this some more and how about if we add the extra constraint that the caller is forced to state his exact strategy before the pusher pushes?

[/ QUOTE ]

This doesn't work either. If I'm Caller, I'll say "I'm calling 100% and you know I'm stuck with it." Now Pusher has to fold almost everything since it's just the same problem in reverse. It's the right of first bluff.

[/ QUOTE ]
It does mean that the strategies will converge to something stable (not necessarily sensible though) and as you put it "right of first bluff" here is just the caller stating his spite-calling intentions before the hands starts. The really interesting thing I'd love to know is the answer too is this:

If we try all possible calling ranges (where the caller has to state his calling range first) and the pusher then computes his maximally exploitative strategy against each of these calling ranges, then the caller settles on the calling range which is most +EV for him. Will this strategy be more +EV for the caller than the strategy found by each attempting to maximally exploit each other's play (ie: the Nash Equilibrium found by fictitious play)?

If it does turn out so that the "spite-calling equilibrium" is more +EV for the caller and we assume that any attempt to pass on the spite calls will be seen instantly by the pusher and adapted for (hence the extra constraint of stating the caller's strategy before the hands starts to allow for convergence), then it would seem that the "spite-calling equilibrium" is the better strategy for the caller to follow and deviating from it towards the NE would be a bad idea.

If nobody answers this before xmas, then most likely I'll spend a few days getting the code together to try and answer this for SB vs BB situations.

Juk [img]/images/graemlins/smile.gif[/img]
Reply With Quote
  #25  
Old 11-25-2007, 03:26 AM
plexiq plexiq is offline
Senior Member
 
Join Date: Apr 2007
Location: Vienna
Posts: 138
Default Re: Fictitious play for multi-player games

@juk:
The problem with your approach is imo, that pusher & caller are treated differently. The caller is basically playing some non-zero-sum version of minimax, while the pusher sticks to maximally exploiting the callers strategy. I guess we would want to use the same assumptions for both players?

But i ll run the numbers on this later, definitely before xmas [img]/images/graemlins/smile.gif[/img]
Reply With Quote
  #26  
Old 11-25-2007, 03:37 AM
jukofyork jukofyork is offline
Senior Member
 
Join Date: Sep 2004
Location: Leeds, UK.
Posts: 2,551
Default Re: Fictitious play for multi-player games

[ QUOTE ]
@juk:
The problem with your approach is imo, that pusher & caller are treated differently. The caller is basically playing some non-zero-sum version of minimax, while the pusher sticks to maximally exploiting the callers strategy. I guess we would want to use the same assumptions for both players?

[/ QUOTE ]
Yep, I suppose it might be just as valid to consider "spite-pushing". Whether it's really possible in real SNGs, I don't know, but I guess another toy game could be made where the pusher could also spite.

[ QUOTE ]
But i ll run the numbers on this later, definitely before xmas [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]
Cool! [img]/images/graemlins/smile.gif[/img]

Juk [img]/images/graemlins/smile.gif[/img]
Reply With Quote
  #27  
Old 11-26-2007, 01:14 PM
trojanrabbit trojanrabbit is offline
Senior Member
 
Join Date: Aug 2004
Location: dominated and covered
Posts: 188
Default Re: Fictitious play for multi-player games

Depending on how you set up the game, whomever can "lock in" their action first will push 100%. That lock can come in the form of pushing your chips into the middle of the table or some artificially binding strategy declaration. There's nothing that the other player can do about this and it is the only stable equilibrium you can find. I firmly believe that the only way you'll be able to solve for spite calling is if you consider the EV of future hands beyond this one. That's what I'm going to be looking into.

Tysen
Reply With Quote
  #28  
Old 11-29-2007, 06:26 AM
jukofyork jukofyork is offline
Senior Member
 
Join Date: Sep 2004
Location: Leeds, UK.
Posts: 2,551
Default Re: Fictitious play for multi-player games

[ QUOTE ]
Depending on how you set up the game, whomever can "lock in" their action first will push 100%. That lock can come in the form of pushing your chips into the middle of the table or some artificially binding strategy declaration. There's nothing that the other player can do about this and it is the only stable equilibrium you can find. I firmly believe that the only way you'll be able to solve for spite calling is if you consider the EV of future hands beyond this one. That's what I'm going to be looking into.

[/ QUOTE ]
A bit OT, but I managed to get a copy of your new book and from initial impressions it looks awesome! It's basically what I had hoped both Chen's "Mathematics of Poker" and Moshmans's "Sit 'n Go Strategy" would be about: applicable theory, as opposed to toy-game theory and/or endless HOH-style hand examples.

Great work! Juk [img]/images/graemlins/smile.gif[/img]
Reply With Quote
  #29  
Old 11-30-2007, 01:11 PM
trojanrabbit trojanrabbit is offline
Senior Member
 
Join Date: Aug 2004
Location: dominated and covered
Posts: 188
Default Re: Fictitious play for multi-player games

[ QUOTE ]
A bit OT, but I managed to get a copy of your new book and from initial impressions it looks awesome! It's basically what I had hoped both Chen's "Mathematics of Poker" and Moshmans's "Sit 'n Go Strategy" would be about: applicable theory, as opposed to toy-game theory and/or endless HOH-style hand examples.

Great work! Juk [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

Thanks, Juk! I've heard that before that KE is the book people were hoping to get when they bought those two. Perhaps some of this effort here can make its way into another volume... [img]/images/graemlins/tongue.gif[/img]

Tysen
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 05:42 AM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.