In The Theory of Poker, David Sklansky introduced his now famous Fundamental Theorem of Poker:
"Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose."
Basically, the Fundamental Theorem of Poker states that the net flow of money in a poker game is the result of mistakes. It asserts that money flows from those who make mistakes to those who don't. For a zero-sum game like poker, this idea seems ridiculously intuitive. However, as with many other seemingly intuitive ideas in poker, all is not what it seems.
It turns out that counterexamples exist, showing that the Fundamental Theorem of Poker doesn't hold in multi-way pots. To his credit, David Sklansky openly addresses this idea in some of his writing. For example, p. 173 of Hold'em Poker for Advanced Players states that "...there are exceptions multi-way."
A brilliant fellow by the name of Andy Morton, suspecting the existence of more than just a few counterexamples, went one step further and coined something known as Morton's Theorem. Known best by those who frequent online poker forums, Morton's Theorem asserts that times exist in multi-way pots where one's expected value is maximized when his opponents play properly. In other words, there are situations in multi-way pots your expected value decreases when your opponents make mistakes.
Morton's Theorem doesn't state that you always benefit maximally when opponents play properly in multi-way pots. Instead, it states that cases exist in multi-way pots where mistakes made by opponents can end up costing you money. Maybe a bad call by an opponent in a hand of limit hold 'em lowers your expected value in a hand by making the pot just big enough for another opponent to call with a draw. Or maybe an opponent raises the flop in Omaha/8 with the same type of hand you have-a low hand having no scoop potential, driving mediocre high hands out of the pot and costing you extra bets when you and an opponent quarter the pot.
Thinking about this concept from a slightly different angle, a group of players who make mistakes as individuals can act as a team to defeat a particular individual at a table. This kind of teamwork can happen via explicit collusion, which is cheating. This kind of teamwork can also happen via implicit collusion, which is perfectly within the rules.
On one end of the implicit collusion spectrum are lines of play adopted by intelligent players who aren't working together explicitly. One the other end of the implicit collusion spectrum, teamwork can happen between players who have no idea whatsoever of what's going on!
When playing games that aren't heads-up, it's important to account properly for the different dynamics that can exist in multi-player pots. This is important for the play of individual hands and for table selection purposes.
Times have existed where I've been at what I now describe as "a tough table filled with easy competition." For example, if you're sitting in a $2-$3 blind no-limit hold 'em game with a bunch of players who are too tight and it's pretty much impossible to beat the
$4-$5 rake per hand.
When thinking about your competition, identify the edge you have over each person at the table. Additionally, identify what advantage you have over the collective combination of your opposition.
Tony Guerrera is the author of Killer Poker by the Numbers and Killer Poker Shorthanded (with John Vorhaus). Visit him online at www.killerev.com, and check out his weekly show, Killer Poker Analysis, on Rounder's Radio (www.roundersradio.com) Fridays from 5:00PM to 6:00PM Pacific Time.
