bluff catching

[Ray64]

http://www.twoplustwo.com/magazine/issu ... tching.php

[GoneBoy]

Not sure if anyone in the world cares about this kind of thing (other than me) - but there is a pretty significant error partway through this article. When the author starts talking about adding some big hands to the calling range (things that can beat a flush) he says that those hands can take the place of some bluff catching hands, and that the overall calling frequency does not change. This is way wrong.

When you add hands that can BEAT a value bet to the calling range, then "Phil Ivey" is no longer indifferent to a calling range of 30%, because that number was based on him always winning when he was called. As soon as he sometimes loses here that changes significantly.

[Ray64]

It looks like the premise is that Ivey knows our range is bluff catchers only and his range is flushes and junk only. The premise also seems to include that Ivey is for sure bluffing enough that we can't just fold 100% of the time and have that be the best option. So we choose a calling frequency such that his EV from bluffing is zero whether he is bluffing a lot or a little.

When you add flushes as 10% of our range, Ivey is still going to bet his value hands most/all of the time because 90% of the time we have a bluff catcher and some fraction of the other 10% of the time he has a better flush than we do. And with 90% of our range being bluff catchers, he's still going to bluff enough that we can't just call with our flushes only and have that be the best option. So again we choose a calling frequency such that his EV from bluffing is zero.

I'm guessing it's implied that bluffs outweigh flushes in Ivey's range such that he can't just shove with his flushes and check behind with his junk without missing a lot of value. Plus he needs to be bluffing enough that we are missing out on value if we just fold to his shove every time.

[GoneBoy]

The devil is in the details here. The author states that if 10% of our HANDS (not calls) can beat a flush, then we need to call with an additional 20% of our HANDS to add up to the magic number of calling 30% of the time. So, actually, 33% of our calls would beat "Ivey's" value bets - that's a lot. My complaint is that the author is appealing to a game theory approach, makes a gigantic change to the strategy of one player (that is "strategy" in the game theoretical sense of the word) and argues that that change would have no bearing on the optimal strategy of the other player. This is like saying that we can swap some sugar in for baking soda and the vinegar will act the same way.

By the way, I liked the article anyway - I think that a little game theory is good for the soul, and the section about blockers is good.