The paradox of making money from opponents mistakes

[TTChamp]

[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

When a given hand is viewed from the point of view of the fundamental TOP, there is one right play, and it is impossible for two players to both play a hand correctly. For example, in a HU NL game, the sb goes all-in with AA, the BB looks down and has KK. By the fundamental TOP the BB is making a "mistake" by calling.

But this is useless from a practical point of view (I know that is heresy, hopefully I don't get banned). From a practical point of view, the BB puts the SB on a range of hands (e.g. TT-AA, and AQ-AK, and a 5% chance of a bluff) and notes that KK is profitable against this range. Therefor the BB should call. Let's use the words "error free" to describe the BB's play with KK since there seems to be a lot of objection to the words mistake-free.

It is possible for both players to play a hand "error-free". In the context of the FTOP, it is not possible for both players to play "mistake free" poker (save split situations).

I would like to see replies from anyone who disagrees with the last paragraph (including you David!).


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



You are failing to consider the difference between strategic and mathematical mistakes that Xhad mentioned in his post. As a result, you are entirely wrong that it is impossible for both players to play a hand mistake free. If I have AA and I know that my opponent has KK, then I am going to bet. No FTOP mistake so far. If I have KK and my opponent just pushed all in preflop, ordinarily, I would call for the reasons you mentioned. My hand is better than the range I put him on. That would be a FTOP mistake if he had AA. However, if I knew he had AA, then I would fold. That would be the mathematically correct play unless I was BB and he (or I) had a very small stack. While it isn't likely for someone to lay down KK in this spot, it would be the correct play. If BB lays down the KK, then neither player has made a FTOP mistake. It wouldn't lead to a very interesting game, and it certainly wouldn't be a profitable game, but it is possible for two players to both make the correct play in a hand.

[/ QUOTE ]

Good point, I should have been more precise. I was speaking of hands that get to SD. There is no way for both players to get to SD playing "mistake-free" in the context of the FTOP (save split possibilities). There is the possibility for both to play "error-free" and get to SD.

Agreed?

[Nomad84]

[ QUOTE ]
Good point, I should have been more precise. I was speaking of hands that get to SD. There is no way for both players to get to SD playing "mistake-free" in the context of the FTOP (save split possibilities). There is the possibility for both to play "error-free" and get to SD.

Agreed?

[/ QUOTE ]

Again, refer to Xhad's distinction between strategic and mathematical mistakes. It is possible to get to showdown without making strategic mistakes, according to Xhad's definition (I think), but it is typically not possible to get to showdown in a non-split pot without someone making a mathematical mistake. Someone has to have a losing hand, and calling with a losing hand is a mathematical mistake.

Of course, it is possible to get to showdown without making any mathematical mistakes if one player is hopelessly shortstacked and the money goes in before the river. If player A has an equity edge, he can bet correctly. If the all-in bet is small enough, player B may still have sufficient pot equity to justify a call, even if he does not currently have the best hand. In this case, the hand could make it to showdown without either player making a mathematical mistake.

[TTChamp]

[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

Good point, I should have been more precise. I was speaking of hands that get to SD. There is no way for both players to get to SD playing "mistake-free" in the context of the FTOP (save split possibilities). There is the possibility for both to play "error-free" and get to SD.

Agreed?


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



Again, refer to Xhad's distinction between strategic and mathematical mistakes. It is possible to get to showdown without making strategic mistakes, according to Xhad's definition (I think), but it is typically not possible to get to showdown in a non-split pot without someone making a mathematical mistake. Someone has to have a losing hand, and calling with a losing hand is a mathematical mistake.

Of course, it is possible to get to showdown without making any mathematical mistakes if one player is hopelessly shortstacked and the money goes in before the river. If player A has an equity edge, he can bet correctly. If the all-in bet is small enough, player B may still have sufficient pot equity to justify a call, even if he does not currently have the best hand. In this case, the hand could make it to showdown without either player making a mathematical mistake.

[/ QUOTE ]


Good point about the non-mathematical mistake SD in all-in situations.

I still don't agree with your first paragraph. Or more precisely I think that saying that betting the AJ in my original scenario is a " mathematical mistake" is a purely academic statement that has no practical application to actually playing poker.

So I guess my question is: who cares if the guy betting his AJ is making a mathematical mistake? It is not any type of error, mistake, or fopa (spelling?) based on the information he has at the time.

The definition of a "mathematical mistake" that Xhad stated involves being able to see the other guys cards. In any real game this isn't true. So if you want to call betting that AJ a "mathematical mistake", I'm fine with that, but I don't see what application that has to actually playing the game.

To me the issue here isn't that the AJ guy is making a mathematical mistake, the issue is that we have an information advantage over the other guy.

We know that our hand is better than his over all of his possible range. We also know that he will think his hand is better than our range of hands when we check to him. Because of this we know he is likely to bet when we check to him. Therefore we are exploiting our information advantage over him to get two bets into the pot instead of one.

When he calls our bet, he knows that against the range of hands we would call a pf raise with and then c/r him with he has the right odds to call. So again he has not made an error of any type based on the information available to him.

The fact that he is actually beat in this particular hand is inconsequential. What is important is that we will profit over the long haul.

[Xhad]

You're missing the point. You are trying to minimize mathematical mistakes by playing correctly. However, since you can't see anyone's cards, you can't eliminate them altogether.

You're right that you can't know that betting the AJ is a mathematical mistake this time. But the reason you bet it is that it is less likely to be a mathematical mistake than checking based on the limited information that you have.

Again, strategically correct plays are the plays that reduce the likelihood and impact of your mathematical mistakes while increasing the likelihood and impact of your opponents'.