Lets take a stab at the math.

Ok, pre-flop odds are (approximately):
A6 off = 36.7%
J10 = 28.6%
KQ = 34.7%

After the flop, nobody improves and there is $300 in the pot. The odds are now:

A6: 53.7
J10: 23.4
KQ: 22.9

Eliminating Ivey is worth 15K to each player as it secures second place.

If you bet out your A6, and KQ folds, you face the J10 heads up in which case you are 73% to win the hand. So the question is whether the marginal gain of getting heads up is worth the trade-off of lowering the chance to secure 2nd place. Vic's instincts are correct that going heads up improves his OWN chances, but it decreases the chances of eliminating Ivey.

Expected value (check through) = 53.7% (15,000+ 300) + 23.4% (-300) + 22.9% (15,000 - 300)= 11512.

EV (bet out) = .73(15000+300) + .27 (-300) = 11088.

This is a rough calculation as I am making a number of simplifying assumptions here, i.e. not counting the marginal increase in probability of getting the additional 20K at stake for first place. I am also not counting the marginal impact that the additional $300 might have in increasing your chances of later securing 1st or 2nd (which Vic mentions). But I think it suffices to show the value in the play.

For the record, I would not think, however, that it would be an egregious violation of this norm to bet out Ax in this situation with such an ugly flop. Of course, betting out with that 6 kicker is a problem since Hellmuth may have called (instead of raising) with AJ or AQ because he IS abiding by the norm. How is that for game theory?

Likewise, I do not think it would be a violation of this norm for Hellmuth to raise with a made hand. It may not be the right play, but I dont think it would work against the norm --- there is nothing that says a player cannot protect a made hand (which is consistent with the exception that allows one to protect a hand that improves on the flop or turn).

Re: tit for tat. It is my experience that a player who violates this norm in a tournament is likely to be punished. At the end of a tournament, of course, the incentive to deviate may be very strong since future punishment is not likely.

I'm strictly a limit player, so my comments may be off, but ...

Joshua's calculations seem to capture what is going on here, i.e. the idea that the expected value of checking through in terms of payout dollars exceeds the expected value of winning more chips (in either a side pot or the main pot).

But in those calculations, is it correct to combine payout dollars and chip values in the same calculation? I think it would be more accurate to express the chip values in terms of expected payout dollars. Again, I'm not a tourney player, but I seem to recall standard calculations for valuing chips in terms of payout dollars, based on the payout structure and the number of total chips in play.

Anyway, as you probably are already aware, if you want to get a more detailed answer to this question, you should post it at:
http://forumserver.twoplustwo.com/ubbthreads.php

Joe.

Joe. Good point. You are absolutely right. You would really want to replace the pot value of chips (300) with its analogous value in terms of expected payout dollars. It is probably more simple to think about it without making the conversion, and as you point out, the analysis would not change.

Vic: I'm puzzled. At the outset, you opine that "A poker table would be a strange place to find implicit agreements, as there is no honor among thieves." Yet, as you acknowledge at the end of the post, there are many social norms in poker, even (especially?) professional. There are obvious norms against cheating. Here's one that's purely social, however: Watching WSOP and WPT, I've noticed that if everybody else has gone out, you go all in, and I'm holding A-A, it's regarded as very poor sportmanship for me to slow-play my aces. There seem to be any number of other sportsmanship norms, especially relating to how one reacts to a bad beat and so on.

Now on a different puzzle. How on earth does PokerStars.net make money when the don't have ads and don't charge?

Steve, PokerStars.net, like most other on-line poker rooms, makes its money via the rake, i.e. a percentage of the pot taken out of every pot over a given size. Thus on-line poker is not, strictly, a zero-sum game, as you must not only win money from the other players, but win enough to beat the rake.

As for norms, I would think that they would be fairly strong at the final tables of large live tournaments, since these are likely professional poker players and therefore likely to encounter each other again in the future.

Even at the (very) low limits I play, I have always been surprised at how friendly people generally are, given the fact that we are all trying to take each other's money. In fact, I find folks more friendly at the poker tables than at the blackjack tables, where we are all ostensibly on the same side. (I assume this changes at the higher limits, but I doubt I'll ever get a chance to find out first-hand.)

Joe: I know how online casinos make money off the rake. But at PokerStars.net, you're using play money. It's a free non-gambling site. So I still don't see how they make money.

PokerStars offers both play money and real money games. I assume they use the play money games to draw folks to the site, hoping some of them will convert to real money players.

I think the intuitive way to think about it is that by checking, they won't force the other player to fold, and with two people there besides the all-in player, it's more likely that one of them will beat the all-in player and eliminate someone, which is in both their interests.

Pokerstars.net makes no money. You are correct they have no cash games to take a rake from nor do they provide ads to make revenue from. Their "sister site" Pokerstars.com is the money maker. This is where people go to play for cash and as with most "gambling" type aveunues I'm sure they make quite a bit.

There are rules against advertising gambling for profit so it is pokerstars.net which is "all free" and therefore publisized on television and the like. But the people who spend their cash go to pokerstars.com

There are lots of rules against the advertising gambling for profit which is all free and therefore publicized on television and the like. The people who spend their cash go.