prove higher level thinking to me

[GiantBuddha]

I wanted to reply to this thread earlier because it initially struck me as so wrong. The truth is that thinking on this level probably rarely is a decision making factor for players online. You don't see the same players often enough, and even when you do, it's much harder to get a sense of what they're actually thinking. However, in a live game with players that you're familiar with, I think this level of thought is routine. I personally have a huge gap between my online and live play, and I think it's primarily because I rely so much on knowing the players. I can play a solid, straightforward game, but with players you have good control over, it's possible to dominate the table in a way which I haven't figured out how to do online. It's easy to make up for this by simply playing ten times as many hands online, but I find it much less entertaining than the more people oriented live games. Maybe those live games are also just softer.

[thylacine]

[ QUOTE ]
find any hand posted wherever or post a new hand in which it is demonstrated that one of the players used level 4 thinking or higher.

level 0: what do i have?
level 1: what does my opponent have?
level 2: what does my opponent think i have?
level 3: what does my opponent think i think he has?

level 2 is used fairy often, i see level 3 demonstrated pretty infrequently, but i've never seen an example of level 4. i honestly don't believe it exists, except maybe used in <0.1% of hands played.

[/ QUOTE ]

Rock, Paper, Scissors example:

Level 0: I was going to throw Rock.

Level 1: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 2: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 3: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 4: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 5: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 6: Realizing that he was going to throw Scissors,
I was going to throw Rock.

Level 7: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 8: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 9: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 10: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 11: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 12: Realizing that he was going to throw Scissors,
I was going to throw Rock.

Level 13: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 14: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 15: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 16: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 17: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 18: Realizing that he was going to throw Scissors,
I was going to throw Rock.

Level 19: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 20: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 21: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 22: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 23: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 24: Realizing that he was going to throw Scissors,
I was going to throw Rock.

Level 25: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 26: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 27: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 28: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 29: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 30: Realizing that he was going to throw Scissors,
I was going to throw Rock.

etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc. etc.

Cliff notes:

Level 0: I was going to throw Rock.

For every non-negative integer n:

Level 6n+1: Realizing that I was going to throw Rock,
he was going to throw Paper.

Level 6n+2: Realizing that he was going to throw Paper,
I was going to throw Scissors.

Level 6n+3: Realizing that I was going to throw Scissors,
he was going to throw Rock.

Level 6n+4: Realizing that he was going to throw Rock,
I was going to throw Paper.

Level 6n+5: Realizing that I was going to throw Paper,
he was going to throw Scissors.

Level 6n+6: Realizing that he was going to throw Scissors,
I was going to throw Rock.


Results posted below in white:
----------------------------------------------
<font color="white"> Villian thinks on level 66666666666666666666666666666666666665 while hero thinks on level 0.</font>
----------------------------------------------

[img]/images/graemlins/grin.gif[/img]

[_D&L_]

So just play 1/3 rock, 1/3 paper, 1/3 scissors...

tada..infinite level thinking....

[gershwin]

Quote:
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As soon as you know about these different levels of thinking and you know that your opponent knows them too, all you can do is a game-theoratical based decision, on which level you will stop at this actual hand.


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Can you elaborate on this? I didn't make any sense of it.

-------------------------------------------------

I think it is a too difficult task for non-genius poker players.

What does he think about my hand and what does he think that I think about his hand?

First question: Are the answers of these questions important at all for my decisions on the actual hand?

If yes: does the level at which he is stopping to think make any difference for my decisions on the actual hand?

If yes: it is very difficult for humans to produce random patterns without help. So if you have detect any patterns in his level thinking in the past (At which level does he usually stop? Or does he stop at at different levels in different situations?…), you can use this pattern in your decision-making. But I guess this would be a very seldom case.

As long as there is no opponent-pattern to use, it is best to stop randomly at a distinct level, so that opponents cannot detect a pattern from you (all still in cases where it has a significant influence on your decision making).

More pragmatic is to find out at which level the average opponents generally stop thinking in different situations and go with that as long as there is no better information.

[_D&L_]

First Player:

[ QUOTE ]

Level 1: Realizing that I was going to throw Rock,
he was going to throw Paper.


[/ QUOTE ]

Second Player:

[ QUOTE ]

Level 6: Realizing that he was going to throw Scissors,
I was going to throw Rock.


[/ QUOTE ]


Second Player says to First Player, "I could beat you if you were a level 2 thinker, but you are just too dumb for me to be able to beat."

[_D&L_]

Here’s a poker example to help you. Pretend this is limit poker, and the pot is $80, its showdown, and bets are $10. The point is to show you how game theory can be used to exploit an opponent in poker, regardless of that other player’s strategy. My examples are highly simplified, because they need to be in this type of forum…But I’m sure you’ll see the concepts.

Option 1…

If opponent 1’s strategy is to only bid strong hands for value on showdown,
Player 2 will fold even semi-strong hands.
Problem:
Player 1 is not being paid for his strong hands, and is not bluffing any weak hands. In short he’s not using his opportunity to raise to create any positive expected value. He’s only signaling to his opponent he has a strong hand

Option 2…

If opponent 1’s strategy is to bid just every hand on showdown,
Player 2 will call with any hand that has a 10% chance of beating player 1’s distribution (10% * (80+10+10) = 10). And will re-raise more often.
Problem:
Bluffs have negative value. There are getting called to frequently, and we’re getting re-raised more often. Especially if we call re-raises with some of our semi-strong hands.

Option 3…

Player 1’s strategy now is to raise with his strong hands, and bluff with his Very Worst Hands 10% of the time he raises for value.
Player 2 is trapped with respect to hands caught in the middle.

If Player 2 calls, 90% of the time she loses $10 and 10% of the time calls a bluff, so makes $10. NPV = Negative $8

If Player 2 folds, 10% of the time she folds and loses the pot to a hand she could have beat. NPV = Negative $8

Thus, it doesn’t matter what Player 2 chooses, I’ve trapped player 2 into either paying $8 to my strong hands, or $8 to my bluffs. No matter what strategy player 2 adopts between calling or folding, I’m going to extract value against her distribution when its my turn to bid.

Problem:
Raising with ALL my strong hands, leaves my residual distribution exposed to aggression. I have to balance the MV of raising for value vs. check raising, where I can recapture some of the value for showing weakness.

Option 4 to Infinity...

It gets a lot more complicated.... But already u can see some strategies emerging that work better than others. E.g. Option 3 assures itself $8 versus player 2's middle range of cards regardless of whether Player 2 calls or folds, or chooses some proportion between those 2 options. Option 1 could in theory make up to $10, but against a moderately observant opponent it makes nothing (at least no added value).

[pencho]

[ QUOTE ]
Once you get to level 4 thinking it essentially becomes level 2 thinking, therefore I don't think you really can achieve level 4 thinking.

[/ QUOTE ]
I think I know what you mean: The choice you make (call, fold, raise, etc.) is the same on level n and level n+2. I believe, it is a bit more complex: The rule only applies from level 3 on (i.e. n&gt;2). Example:
A late-position player comes in first and raises. I call on the button and the blinds fold. It is a heads-up pot and I have position. My hand: ??
Flop comes: AA6 (rainbow)
My opponent bets. Since I have observed him betting a lot into his only opponents and since I tought this player regarded me as a tight player, I thought it would be right to represent the Ace, therefore I raised and he folded, obviously believing me.
From this play I could tell that he was thinking only on level 1: He is a tight player, so he has the Ace and he is not afraid of my hand. So I will fold.
But had he beed thinking on level 2 and 3, he would have played differently: He has observed me and knows that I often raise in late-position with weak hands and bet into my opponents often on the flop holding nothing (Level 2). With his raise, it becomes possible that he wants me to think that he has the Ace (level 3). Therefore he could very well NOT have it and I should re-raise and so ask back the question. And besides that: He would probably rather slowplay an ace, since he need not be afraid of giving me a free card.
And now comes my point: In the example, it is right to raise the player on the first level if you do not have an Ace, but you should only call if he is on the third level. (Respectively, if you had the Ace, you should call when he is on the first level and raise when he is on the third.)
If he is on fourth level, again a raise is correct if you do not have the Ace. Now my opponent thinks: He wants to trick me into a bluff-re-raise; he wants me to believe that his raise means that he does not have an Ace.
On level 5, a call is correct, on level 6, a raise is correct and so on.

Summary: This example showed that level 4 does not "essentially become" level 2 but it becomes level 1. Perhaps you could give an example of your assumption?
In my example, the levels 2 and 3 are closely interwined. Once my opponent would think on level 2 he would almost be "forced" to go up to level 3, because he has to play one level above me in order to outwit me (he puts me on level 2). Here, the "right" choices were different in level 1 and 3. But on higher levels (I guess) your "rule" is correct: The choice is the same wether your opponent played on 3rd or 5th level, on 4th or on 6th level, etc.
If that is true, you only have to think about wheter your opponent (if they are not thinking on level 1) is a 3rd or 4th "equivalent" in order to come to a decision.

What do you guys think of all this?

[Dov]

I didn't read the whole thread yet, I will later, but I wanted to throw my 2 cents in anyway.

I think this happens very often in all structures when, for example, you have just gotten a big hand cracked or several in a row, and then you are dealt very good starters.

The table will generally put you on tilt and then you can use that tendency against them at the level you are talking about.

I think the biggest reason that you haven't seen the examples that you are looking for is that they involve a history of more than one hand.

To find what you seek, go to the HU forum where they post entire sessions with reasoning and explanation.

Dov

[welzer777]

You did not mention the size of game that you are playing in, therefore, my answer may not be accurate. However, it seems to me that you have not had the need to use, what I will call, beyond level 2 thinking. It almost seems from your apparant frustration that you have the ability to think along these "higher" levels yet the opponents you are playing do not.... Simply put, if you and I are contesting a pot and I "comprehend" that you are a good player I will try and deceive you. You can call it "levels", making a move or whatever you would like. The point being psychology becomes the biggest part of the game. At its highest level, although all "level 4" thinkers would probably deny this, anything beyond this level is too complex and breaks down to its simplest form, that being the cards they are holding. Don't get caught up on levels get caught up on the ability of a given opponent!!

[GiantBuddha]

[ QUOTE ]
I think the biggest reason that you haven't seen the examples that you are looking for is that they involve a history of more than one hand.

[/ QUOTE ]

Spot on. If I sit down at a table with strangers and I get involved in the first hand, I can't start out with level 4 thinking. Knowing your opponents thought to this level requires knowing your opponents to this level.

Four things which reduce the level of thought involved in a hand:

1) Lack of knowledge of opponent
2) Opponent's lack of knowledge of your playing tendencies
3) Lower limits
4) Playing online

When players list their reads as a set of numbers, they don't have a read. They have a set of numbers. When you have an honest to goodness read, it's because you've played hundreds of hands with your opponent.

I have a friend who I started playing poker with in high school. We learned the game around the same time, and we used to play heads up no limit freezeouts back before everyone played no limit all the time. We got accused of collusion at a club one time because we could read each other's hands cold. On consecutive hands, we correctly put each other on specific unimproved pocket pairs. He had eights. The next hand I had nines. The other players at the table got a little freaked out.

Point being, after a certain amount of experience with a given player, if you're both perceptive and talk about the game a lot, you're not thinking on levels anymore. You just know exactly what the other person is capable of, and why. You might even be able to put them on a page, meaning that you know precisely where they got the concept that they're using at the time.