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  #31  
Old 10-13-2005, 04:13 PM
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Default Re: Zizzling\'s Poker Theory Game

[ QUOTE ]

Suppose P1 has a 1. I'm not convinced that he should bet here ever. If you're dealt a 72 in hold'em and you're playing heads up, you're going to fold it.

[/ QUOTE ]

I'm convinced that, for any strategy that you come up with where player 1 does not bet with 1, I can come up with a strategy that does better where he does bet with 1.

Consider the following:
The reason to (straight) bluff is to get action on your good hands. You already know that a bluff is a loosing bet when you make it, and that the value of bluffing comes from fold equity, and from calling equity on the opponent's hands.

Now, it's clear that bluffing is a part of good poker play, so the question is really, what hands you should bluff with. Now, you're already making bluffs with the expectation to loose if you're called so it doesn't make sense to worry about the showdown value of bluffing hands - so there's no penalty from that. Now, the more hands your opponent has that he can call bluffs with, the more action you'll be getting on the legitemate hands. At the ideal bluff rate, you don't care whether your opponent calls or folds with these 'calling hands' so you want as many of his hands as possible to be calling hands. That means that you're going to be bluffing with the lowest hands you can use.

If your opponent has a weakness -- calling too much or too little -- you should not be bluffing hardly at all, or very frequently and can reasonably consider 'bluffing' with other hands to exploit that weakness.
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  #32  
Old 10-13-2005, 04:15 PM
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Default Re: Zizzling\'s Poker Theory Game

I agree with a lot of what you said, but I still don't see the value of bluffing a 1. Yes the bluff gets its value from the fold equity, however, the opponant is less likely to fold if he knows you bluff a lot. You can't just bluff all the time.
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  #33  
Old 10-13-2005, 04:39 PM
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Default Re: Zizzling\'s Poker Theory Game

[ QUOTE ]
I agree with a lot of what you said, but I still don't see the value of bluffing a 1. Yes the bluff gets its value from the fold equity, however, the opponant is less likely to fold if he knows you bluff a lot. You can't just bluff all the time.

[/ QUOTE ]

There is an ideal bluff rate. You can check TOP and a whole lot of other resources to verify that the ideal bluff rate is related to the pot odds the opponent is getting. If the ideal bluff rate is equal to the pot odds your opponent is getting from a dead pot that's (raise)/(pot+2*raise).

Now, since we're commited to bluffing, the question is, why bluff with 1, instead of, say 3. The answer is that bluffing with 1 gives the opponent more 'calling hands' where you don't care whether he calls or folds. Now, it's better for you to limit the useful choices this optimal opponent can make, ergo you should deny him the chance to safely fold hands wherever possible.
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  #34  
Old 10-13-2005, 06:46 PM
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Default Re: Zizzling\'s Poker Theory Game

I have answered this a couple of times already.

Check-raise is allowed.
Each player gets 1 raise.
I don't know how to explain it any clearer than that.

Hint: The way that I would appoach this is to 1st solve without the check-raise.
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  #35  
Old 10-13-2005, 07:01 PM
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Default Re: Zizzling\'s Poker Theory Game

I think that your assumptions are basically correct.

Knowledge of the PRECISE strategy for this problem will provide an enormous edge in heads-up play.

IMO - the solution to this problem could be the most important achievement in Game Theory ever.

Martin should get a piece of this.
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  #36  
Old 10-13-2005, 07:16 PM
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Default Re: Zizzling\'s Poker Theory Game

I'm here.

This is starting to get interesting.

I prefer a TAG posting style. [img]/images/graemlins/cool.gif[/img]
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  #37  
Old 10-13-2005, 07:29 PM
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Default Re: Zizzling\'s Poker Theory Game

Sorry if I missed this, but is this like NL, or can the raiser only raise the amount of the previous bet?

Thanks!
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  #38  
Old 10-13-2005, 07:30 PM
marv marv is offline
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Default Re: Zizzling\'s Poker Theory Game

[ QUOTE ]
I have answered this a couple of times already.

Check-raise is allowed.
Each player gets 1 raise.
I don't know how to explain it any clearer than that.


[/ QUOTE ]

Is this essentially your problem (I'm adjusting the ante so all the numbers are integers)?

100 card deck, so 100 is a certain winner and 1 is a certain loser.

Each player antes $1.

Possible betting sequences (ignoring different raise amounts) are:
kk kbf kbc kbrf kbrc bf bc brf brc
where k=check, b=bet, c=call, f=fold, r=raise.

We want the solution to the no-limit problem (where the min legal raise is $1 or the previous raise, whichever is the larger) and where each player has $100 initially before the ante.

Is that it?

Marv
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  #39  
Old 10-13-2005, 07:56 PM
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Default Re: Zizzling\'s Poker Theory Game

[ QUOTE ]
Each player antes $1.


[/ QUOTE ]
Actually each player antes .50 so that the starting pot = $1. It actually should make no difference at all to the optimal solution either way. I just prefered to make the starting pot size (P$)=1.

[ QUOTE ]
Possible betting sequences (ignoring different raise amounts) are:
kk kbf kbc kbrf kbrc bf bc brf brc
where k=check, b=bet, c=call, f=fold, r=raise.

[/ QUOTE ]
Yes. These are all the possible betting sequences.
The problem children are kbrf, and kbrc (check-raises).

[ QUOTE ]
We want the solution to the no-limit problem (where the min legal raise is $1 or the previous raise, whichever is the larger) and where each player has $100 initially before the ante.


[/ QUOTE ]
I think it is necessary and easier to represent the bet as (%ofpot) rather than a discreet bet amount.

Good luck.
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  #40  
Old 10-13-2005, 08:45 PM
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Default Re: Zizzling\'s Poker Theory Game

[ QUOTE ]

Knowledge of the PRECISE strategy for this problem will provide an enormous edge in heads-up play.

[/ QUOTE ]

For Texas Hold-em, not likely, that's much more complicated than this is. For straight poker (whereever you might find that) probably.
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