Two Plus Two Older Archives The paradox of making money from opponents mistakes
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#21
12-14-2005, 05:10 PM
 TTChamp Senior Member Join Date: Jul 2005 Location: Job Hunting Posts: 517
Re: The paradox of making money from opponents mistakes

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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?

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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.

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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.
#22
12-14-2005, 05:32 PM
 Xhad Senior Member Join Date: Jul 2005 Posts: 205
Re: The paradox of making money from opponents mistakes

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'.
#23
12-14-2005, 05:57 PM
 AaronBrown Senior Member Join Date: May 2005 Location: New York Posts: 505
Re: The paradox of making money from opponents mistakes

Thanks for the kind words.

You're right that the first example is not like poker, there is no hidden information. The last sentence is correct in my accounting. You make \$0.50 when he takes the bet, then you have an even \$1.50 win or loss on the coin toss. If you win the toss, you get \$0.50 from his mistake, and \$1.50 from the luck of the flip, \$2.00 total payout. If you lose the toss, you get \$0.50 from his mistake but lose \$1.50 from the luck of the flip, -\$1.00 total.

In the second example, I assume the bet is a push if he draws the same card (although I worded it wrong). The reason you are ahead \$0.1267 when he makes this offer is you have the option to accept it (which you do with a 9 or higher) or decline it (which you do on a 7 or lower, with an 8 it's a fair bet).

This case is very much like poker. He makes a bet, you can call or fold. It's simpler because it depends only on one card, there is no ante or blind, and you cannot raise. The point is that you make money from his bad bet, regardless of what you hold or what he draws. Those are random events that will add ot or subtract from your initial expectation.
#24
12-14-2005, 06:33 PM
 Guest Posts: n/a
Re: The paradox of making money from opponents mistakes

hi, my first post so please be nice.

the "paradox" arises from your mixing of correct move for specific events with ev for the long run--the right move for the long run may not be the right move for a given event. you can play perfect long-term poker and still get beat, sometimes.
#25
12-15-2005, 01:04 PM
 ErrantNight Junior Member Join Date: Feb 2004 Location: Boston, MA Posts: 1
Re: The paradox of making money from opponents mistakes

Only one of the following two scenarios is true:

(1) He knows you have a 9, and is therefore incorrect to call a bet or to make a bet

(2) He doesn't know you have a 9 and must therefore play against your range of hands in which case both betting and calling are close but you must start factoring in things like: what he thinks of you, what he thinks you think of him and so on and so forth.

You can't have it both ways.
#26
12-15-2005, 01:16 PM
 Guest Posts: n/a
Re: The paradox of making money from opponents mistakes

Because it is a game of imperfect information, poker isn't really about a particular pair of holdings, but rather about things like reading your opponent, and whatnot. Slanksy's fundemental theorem of poker doesn't explicitly adress exploiting opponent weakness.

One way to look at it:
You have to play the player, as well as the cards. You bluff more against weak-tight players who fold too much, and value-bet mercilessly against calling stations. So, what your opponent's correct move is, depends on your tendencies, and vice versa.

Another way to look at it:
The stacks go up, and down, but if a player does to much of one thing or another in a particular situation against a mathematically ideal (maximally exploitative game theoretically perfect) player, then, in the long run, said mistake will be costly.

A third way to look at it:
Since human players are imperfect, your opponent's weaknesses can make actions that would normally be costly profitable.
#27
12-15-2005, 02:26 PM
 CORed Senior Member Join Date: Sep 2002 Posts: 273
Re: The paradox of making money from opponents mistakes

One thing I would point out is that villain isn't necessarily making a mistake to call. He doesn't have pot odds to call, but likely has implied odds if he catces an A or J on the turn, assuming hero will bet turn or call at least one bet. Villain could also raise hoping to get a free card on the turn if hero bets.

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