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  #1  
Old 11-21-2006, 02:30 PM
thylacine thylacine is offline
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Default Ro-Sham-Bo and thinking levels.

In Ro-Sham-Bo (=rockpaperscissors) level n+3 thinking is identical to level n thinking, for every n>0.

Discuss.

More generally, for each form of poker are there numbers k and N such that level n+k thinking is identical to level n thinking, for every n>N? If so, roughly how big are k and N?
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  #2  
Old 11-21-2006, 05:56 PM
trojanrabbit trojanrabbit is offline
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Default Re: Ro-Sham-Bo and thinking levels.

[ QUOTE ]
More generally, for each form of poker are there numbers k and N such that level n+k thinking is identical to level n thinking, for every n>N? If so, roughly how big are k and N?

[/ QUOTE ]

k>=4 and the fraction of players that think on the 5th level and beyond is ~0%.
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  #3  
Old 11-21-2006, 08:42 PM
bigbootch bigbootch is offline
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Default Re: Ro-Sham-Bo and thinking levels.

[ QUOTE ]
In Ro-Sham-Bo (=rockpaperscissors) level n+3 thinking is identical to level n thinking, for every n>0.


[/ QUOTE ]

The world RPS champion program Iocaine was precisely based on the idea you just stated. You may find the discussion of its algorithm interesting, found here
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  #4  
Old 11-21-2006, 08:59 PM
AaronBrown AaronBrown is offline
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Default Re: Ro-Sham-Bo and thinking levels.

I disagree.

Level 0 strategies are naive. In the case of RSB, that means to play some pattern independent of the results, say, always R or alternating R, S, B.

Level 1 strategies assume the other player is Level 0. They attempt to discern the pattern and beat it.

Level 2 strategies assume the other player is Level 1. They follow patterns but keep changing them just at the right time to win more than they lose.

Level 3 strategies assume the other player is Level 2. These are quite different from Level 0.

Also, you don't have to walk up the levels one at a time. You can make other assumptions, such as the other player is the same level as you, or the other player learns. These lead to even more sophisticated strategies that have no level number attached.

Most poker strategies are two-valued: bet because you want to be called or bet because you want the other players to fold. It sometimes gets more complicated than that, as with semi-bluffs or when you want some players to fold but not others. But most of the time you're either playing straightforwardly for your cards, or deliberately deceptively.

Level 0 poker, raise with strong hands and fold with weak, is easy to beat. Level 1 poker, assume the other player is level 0 and play accordingly is much better, but still easy for an expert to beat. In some ways, an expert has an easier time with a Level 1 player, who can be manipulated, than a Level 0, who cannot. Level 2 is the lowest at which anything resembling poker emerges. Beyond that, you have to take account of things like other players being at or above your level, learning and strategy.
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  #5  
Old 11-22-2006, 12:31 AM
alphatmw alphatmw is offline
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Default Re: Ro-Sham-Bo and thinking levels.

i've always thought that at certain levels of poker thinking, everything completely breaks down. you can only repeat "he thinks that i think that he thinks" so many times before its all guesswork. but i could be wrong.
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  #6  
Old 11-22-2006, 12:36 AM
thylacine thylacine is offline
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Default Re: Ro-Sham-Bo and thinking levels.

[ QUOTE ]
i've always thought that at certain levels of poker thinking, everything completely breaks down. you can only repeat "he thinks that i think that he thinks" so many times before its all guesswork. but i could be wrong.

[/ QUOTE ]

Yeah, I think I know what you're saying here.
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  #7  
Old 11-22-2006, 12:45 AM
thylacine thylacine is offline
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Default Re: Ro-Sham-Bo and thinking levels.

[ QUOTE ]
I disagree.

Level 0 strategies are naive. In the case of RSB, that means to play some pattern independent of the results, say, always R or alternating R, S, B.

Level 1 strategies assume the other player is Level 0. They attempt to discern the pattern and beat it.

Level 2 strategies assume the other player is Level 1. They follow patterns but keep changing them just at the right time to win more than they lose.

Level 3 strategies assume the other player is Level 2. These are quite different from Level 0.

Also, you don't have to walk up the levels one at a time. You can make other assumptions, such as the other player is the same level as you, or the other player learns. These lead to even more sophisticated strategies that have no level number attached.

Most poker strategies are two-valued: bet because you want to be called or bet because you want the other players to fold. It sometimes gets more complicated than that, as with semi-bluffs or when you want some players to fold but not others. But most of the time you're either playing straightforwardly for your cards, or deliberately deceptively.

Level 0 poker, raise with strong hands and fold with weak, is easy to beat. Level 1 poker, assume the other player is level 0 and play accordingly is much better, but still easy for an expert to beat. In some ways, an expert has an easier time with a Level 1 player, who can be manipulated, than a Level 0, who cannot. Level 2 is the lowest at which anything resembling poker emerges. Beyond that, you have to take account of things like other players being at or above your level, learning and strategy.

[/ QUOTE ]

You could be right, but it depends on how you define your levels. I am curious at what you are saying and I would be curious to see references, especially abstract ones.

In my OP I was thinking of my level n+1 strategy as maximally exploiting my opponent's level n strategy (and my opponent's level n+1 strategy as maximally exploiting my level n strategy). In this case, I think my original statement was true, even if somewhat silly.

But I am curious to see serious work on the `level' concept.
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  #8  
Old 11-22-2006, 02:35 AM
Gonso Gonso is offline
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Default Re: Ro-Sham-Bo and thinking levels.

[ QUOTE ]
i've always thought that at certain levels of poker thinking, everything completely breaks down.

[/ QUOTE ]

I know I break down past certain points.

I've been trying to work out a rough 'Jekyll/Hyde' strategy. Each 'personality' has a few generic tendencies opposite of the other... for example, Jekyll will check a flopped set while Hyde will not (under normal circumstances) - and every betting round I check the second hand to determine which personality I am. Kind of a poor man's approach randomization.

This is obviously not a good idea as a long term approach, just something to fall back to if I start getting a little disoriented or tilt-y or something. I've been up against a better level of HU players lately and I'm trying to adjust.

[ QUOTE ]
In my OP I was thinking of my level n+1 strategy as maximally exploiting my opponent's level n strategy (and my opponent's level n+1 strategy as maximally exploiting my level n strategy).

[/ QUOTE ]

That sounds correct to me. But you already knew that I'd think that that would sound correct. I'm on to you now. But you would have known that I'd have figured you out...
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