Strategies that make more against better players

[JaredL]

I feel pretty strongly about an answer, and am curious to get the thoughts from others. I suspect there will be some disagreement.

The question is:
Are there strategies (defined in the game theory sense) that do better against good players than bad players?

In other words, suppose I have a plan for what to do in every possible situation - with every possible hand, every possible action sequence by the other players, for every possible board. Is it possible that this plan does better in the long run (makes more money) against players who are solid, but not great, than it does against players that are bad (too loose say)? Is it possible for this plan to do better against world class players than bad players? Is it possible for this plan to do better against world class players than merely solid players?

Please backup your answer with some reasoning.

edit: revised question:
OK, so as to avoid this whole thing devolving into a semantic argument, let me revise the question.

Suppose you have two sets of players, A and B. In the long run, the A guys will make more money (or lose less) than the B guys. You may assume whatever you wish about them otherwise. Suppose you are playing any form of poker you wish. Is there a strategy (ie plan of action for every situation) that does better against table A than table B?

[alphatmw]

a "good" player molds his play to his opponents, so no. but then again, the way you define "strategy" is different than how everyone except the most mechanical of players actually play.

[JaredL]

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a "good" player molds his play to his opponents, so no. but then again, the way you define "strategy" is different than how everyone except the most mechanical of players actually play.

[/ QUOTE ]

Not really. It would allow you to play differently against different people. It also allows for randomness.

I should have added that it could change over time as you get reads on people, which would make it just like how people play (granted, they don't have it all planned out but will do something when whatever happens so overall there is some plan in place).

edit: I'll leave the above there, but actually, you're right. Thinking more about it, what I had in mind was specifically not adjusting to the play of others. However, mixing would be allowed.

[alphatmw]

look, the point is, if the answer is "yes" then the question becomes "why does the good player or world class player not shift his style closer to that of the bad player as you play?

if the bad player is too tight but wins more, then why is the world class player not tighening up? likewise if the bad player is too loose, why is the world class player not loosening up? if they can't realize a tighter/looser strategy would work better, then theyre not world class.

i'm standing by no.

[pzhon]

Yes, it is possible that there are complete strategies which do better against typical good players (with one style) than against typical bad players (of another playing style). The good players may be exploiting a weakness of the bad players, but they may leave themselves open to being exploited by a strategy which does not punish the bad players as much (or at all).

As a simple example, suppose bad Rock-Paper-Scissors players always choose rock. Good players choose paper 40%, rock 30%, and scissors 30%. The strategy scissors 100%, and any convex combination with optimal play, scissors 1/3+2x, rock 1/3-x, paper 1/3-x, would do better against the good players than against the bad players. If there are many more good players than bad players, and opponents are chosen randomly, then scissors will do better than the good players on average.

As Mike Caro has pointed out, there are collections of poker styles which dominate each other in an intransitive way, just like rock beats scissors beats paper beats rock. So, you can construct poker strategies which exhibit the same behavior as in this simple example.

[alphatmw]

unfortunately, you're rock-paper-scissors players can't be categorized as "good" and "bad", as you have labeled them.

[pzhon]

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unfortunately, [your] rock-paper-scissors players can't be categorized as "good" and "bad", as you have labeled them.

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You see no reasonable way to call the players "bad" who consistently lose, and who always play rock? You see no reasonable way to call the players "good" who consistently win against the population of players, and who can't be as severely exploited by any strategy? Perhaps if you take more than 3 minutes to look, you'll see some of the ones I see.

[Siegmund]

[ QUOTE ]

Are there strategies (defined in the game theory sense) that do better against good players than bad players?


[/ QUOTE ]

Sure there are.

Ever tried bluffing a calling station?

[alphatmw]

1. if the player were in fact "good", he would play 100% paper.
2. the "good" player would realize you keep playing scissors and would adjust his play.
3. the "good" player would not use the exact same strategy against the bad player as he would with you
4. this is only analogous to poker if poker were made 100x simpler
5. would you like me to go on?

[pzhon]

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1. if the player were in fact "good", he would play 100% paper.

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Even if we redefine good to mean what you want, that the player is adapting with full knowledge of the other players' strategies, this is wrong. Maybe you need to think about the example I gave more, as it seems you don't understand rock-paper-scissors! If you don't want to think about it, let's wager a large amount of money on it.

It is unreasonable to assume that you know all of your opponents' strategies and have adjusted or else you can't be considered good.

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4. this is only analogous to poker if poker were made 100x simpler

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No, as I mentioned that Mike Caro pointed out, and as the example of calling stations versus bluffers versus weak-tight play shows, there are parts of the space of poker strategies that are analogous.

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5. would you like me to go on?

[/ QUOTE ]
No, I think it is about time you stop.