I have talked before about there being no transitive property in poker, referring to players, The same holds true for hands. For example, look at these win percentages heads-up, preflop

A As5s v 2c2h: 50.2% v 49.8%

B 2c2h v Ad6d: 50.11% v 49.9%

C Ad6dv As5s: 56.6% v 43.4%

Hand A beats hand B heads up, B beats C, and C beats A. (btw, in a 3-way pot, the pair winns 38% of the time)

On a similiar note

D AsAd v KhKc: 81% v 19%

E AsAd v 6h7h: 77% v 23%

F 6h7h v KhKc: 22% v 78%

So, even though KK kills 67suited, the 67suited plays better against AA. (btw, in a 3-way pot, the Aces win 61% of the time, 67suited 21% and KK 18%)

So how should each hand play? Lets just make a very simple assumption – each caller is in for $100 pre-flop with no more betting. Clearly, hand A prefers two callers to win 38% of $200 over only app 50% of $100 with one caller. This is no surprise, as we know that 22 is a drawing hand, so you want lots of callers and no raise pre-flop. Same holds true for hand F, which fares better with more callers.

What is intersting in this example is AA does better with 2 callers (EV=app $80 vs heads up EV = app $60). While typically high pairs want to drive others out of the pot and go heads up, the AA doesnt mind a few callers in certain situations.

Lou has a nice article.

Some of my favorite points:

There’s no use in trying to induce them to take a certain course of action when they are not even going to notice what you’re doing.

Amen. Yet, as much as I know this, it is the mistake that I most consistently make. Why? Because I have spent so much time in medium stakes games in Houston cardrooms and big stakes pot-limit games in the UK where the competition is tough, fancy play always paid off. Now, I find myself playing at tables that always have 2 or 3 newbies and I don’t switch my style of play.

“I put you on top pair all along,” he’ll probably say, while thinking to himself that you were damned lucky to back into that winning flush. Why did he consider top pair as the only possibility?

A lot of players will do this and the key is when they openly state that they only put you on the top pair. These guys are dead meat when you get the 2-pair or set. The flip side of this lesson is for you to not do this yourself….always consider the full range of hands your opponent may have.

If he’s really sharp he’ll even go one step further, and think about what you think his hand might be.

Yes, he will. Be cognizant of this and don’t fall for the experts traps. A decent rule of thumb when playing against an expert that respects you is to consider what he wants you to do and do the exact opposite. (you should only do this in marginal situations like having 3:1 shot at a pot paying say 2.9:1.) Again, don’t only be cognizant that he is doing this; you, too should go to this third level of thought. My closest circle of friends (those who read this site) have all moved to the second level, which involves moving away from your hand and considering the other guy’s hand. I think a lot of us should consider if we have moved to level three.

What is an easy way to do that?

Broadcast a tell you’re sure they’ll pick up. Then broadcast it again when your hand is that proverbial horse of a different color. Once your opponent realizes that you are thinking at his level, he’ll usually realize that he does not have quite the same control over you that he might have thought, and he’ll begin to respect your play a bit more.

Sure, it will only pay off at first, but once he respects you, he will stop trying to trick you and focus his efforts on the fish.

Let me know if you have any interest in Super Bowl Props.

A decent resource if you are looking for rules for your home game. However, I disagree with one aspect of his Pig rule. (I had forgotten about this wrinkle until Judge brought it up a couple weeks ago)

If person A declares Pig (going high and low), person B declares low and person C declares high, and it works out that A does have the lowest, but C beat A for high, of course A wins nothing. But according to the rules above (and what is the most common set of rules) is that B and C split the pot. While I know this is common and I expect it to be the rule by default when nobody says otherwise, I think that it is not the best rule. B didn’t actually win lo, so he should receive nothing and C should get the whole pot. It is somewhat analagous to playing O/8 and two people don’t qualify with “8 or better”, so the high wins it all.

However, if A and B tie, then A is disqualified* and B does legitimately win 1/2 the pot. (A very technical argument could be made that B only wins 3/8 of the pot, but I won’t go there). C takes the other half and gets the odd chip.

*Now that assumes that ties disqualify the Pig, which again is the common and expected rule. However, this variant makes little sense to me and is completely inconsistent with other poker rules. In poker, ties alway result in a split pot. I would say that the Pig quarters the low and takes the high.

Since I will probably never convince a table full of 8 to make these rules, I will simply never declare Pig. There is way too much downside under the common rules.

This calculator seems much more user friendly than the one at two dimes.

Can you imagine losing a $150,000 pot?