A Bet After the Flop I Didn't Understand: Carlos Mortensen at the WPT

I picked up the entire second season of the World Poker Tour on DVD for $7 plus shipping from Daedulus Books. On the first disc is the Borgata Poker Open, featuring a number of outstanding players, including Carlos Mortensen. Early in the episode, Carlos made a play that puzzled me. It was a 6 seat table. Carlos is dealt 10 (clubs) and 8 (clubs), 2 players fold and 4 see the flop. The flop comes 2 (clubs), 3 (hearts), and 8 (hearts). There is $38,000 in the pot and Carlos opens the post-flop betting with with a $10,000 bet. This means of course, that the first caller needs to pay $10,000 for a chance at a $48,000 pot. That's 4.8 to 1 pot odds, which justify a call in many situations. With top pair (admittedly a middle pair), shouldn't Carlos have bet more to discourage callers and attempted to win the pot right there? As it happened, he was only called by David Opphenheim (holding A-4, offsuit), who eventually drew out on Carlos by hitting a 5 on the turn.

One More Thought on A-Q: Phil Gordon Making Me Say Huh?

In Phil's Little Green Book, he summarizes a hand he played online (Phil Gordon, Little Green Book, p. 115) and I think it's worth examining because the logic behind Phil's play is not immediately apparent to me. Phil was in middle position with A-Q suited diamonds. He was first in and raised to $150, three times the big blind. The button called.

Ok, so there's $375 in the pot before the flop ($50 big blind, $25 small blind, Phil's $150 raise, the button's $150 call). The flop comes Q (spades), 9 (clubs), 2 (clubs). Phil bets $150, which makes some sense. He's got an excellent chance of having the best hand and he's offering the button 3.5 to 1 odds to call ($150 call to win $525 pot). The button called. So far so good.

The turn is K (diamonds). Worried about the straight draw, Phil checks. So does his opponent. At this point, Phil put the button on a flush draw or A-9. Let's take a break here and ask if Phil's check makes a lot of sense. Granted, if he bets and his opponent has a straight or a straight draw, then Phil will likely be called or raised. One might think that it is worth it to bet something here to find out what the button has. The problem is that there is now $675 in the pot. Phil has got to bet enough to: 1) make calling and playing a draw a bad bet; or 2) show that his opponent's hand is good enough now to justify a call. Figure the button is holding any one of a number of hands which will likely win if they get the right draw (such as J-J, 10-10, 10-9, A-J, A-9, or A-Q), or he's holding J-10 or A-k in which case Phil's likely already beat. The chance of holding any of these hands is roughly 25% (each of these hands has about a 1/11 X 1/11 chance of popping up, call this 1% x 8 of these hands = 8%). We'll raise the 8% up a bit since the button has shown some strength and let's call it 20%. This is 4 to 1, so all Phil has to do from a mathematical expectation standpoint is make a bet which makes this a losing proposition. With $675 in the pot, a $300 bet will do it ($300 to possibly win a $975 pot = roughly 3.3 to 1 pot odds). If the button calls this bet, he's either made a bad play or he's got Phil beat. Instead, Phil checks, the button checks, and the guy gets a free card. I don't think this makes sense. With a so-so hand, don't you want to know where you stand, force your opponent to take the worst of it, or, preferably, win the pot right there.

But Phil checked and the river is the 9 (diamonds). Phil checks and his opponent bets $300. Phil calls and wins the showdown when the button turns J-8 (both clubs). This was the right play for Phil because he was facing pot odds of 3.3 to 1 (see preceding paragraph) and he had to figure that he had a better chance than that to win the pot based on probabilities. Phil says that by checking, he made more money because the button would have folded if he'd bet.

Something Bothering Me About Pot Odds

Sklansky's Fundamental Theorem of Poker is widely accepted and it makes sense: make fewer bad decisions than your opponents and you win. How do you judge decisions? Well, there are a number of ways but one of the most prominent is pot odds. Pot odds tell you whether you're getting sufficient return on your money given the risks you are taking. Pot odds of course are based on mathematical expectation, in other words: (the chance that you will win X the amount you will win) - (your chance of losing X the amount you lose). If the difference is positive, you are making a good play, according to the standard wisdom.

As you've gathered, however, one of the goals of this blog is to question the standard wisdom and I'm going to question it here. First of all, I've got no problem in general with judging your plays based on pot odds. However, let's dig a little deeper. I want to make two points. First, there are differing degrees of positive expectation: your expectation could be slightly positive or it could be highly positive. Second, the accuracy of probability calculations depends to some degree on the number of trials. What do I mean by this: I mean that when you have an Ace-Six and you're hoping to draw another Ace, the probabilities look like this on the flop (3/50 + 3/49 3/48). This adds up to roughly a little better than a 1 in 6 chance overall of getting the Ace on the flop. Now you might expect that if you look for this draw 6 times, you might reasonably hope to get one Ace but not so. Probabilities are most accurate over large numbers of trials (see law of large numbers). You might hit 3 Aces or you might well hit none at all. Flip a coin ten times and it's highly unlikely you come up with 5 heads and 5 tails.

So what does all this mean? To me, it means this: before applying pot odds robotically, ask yourself how many hands of NLH you're planning on playing a year. If its tens of thousands, then play by the pot odds book. If, however, you're going to play in 3-4 tournaments a year, which the Hold 'Em Scholar is probably looking at right now, then you've got to be careful about playing tournament hands where the odds against your winning are 2 to 1 and the pot odds are 3 to 1. You just don't have that much of an edge in this situation, given the risk. In other words, you probably want to choose situations where the pot odds are more like 4 to 1 when the odds against you are 2 to 1 and you know you aren't going to be playing an NLH tournament every weekend.

Let me give an example of a hand I wouldn't play, that Phil Gordon apparently would. This example comes from Phil's Little Green Book (Gordon, Little Green Book, p. 42). In discussing a sandwich play, Phil says that he'd push in all his chips where the pot odds are roughly 2.5 to 1 and the odds against him are about 1.5 to 1. Mathematically, this is the right move. Pot odds tell you to make it, Sklansky would presumably tell you to make, but I ain't making it in the early to middle rounds of a tournament. Why? Because I'm only playing a limited number of tournament hands a year and the odds are that I'm going home if I make this play. I don't know that I'm going to play enough hands over the course of the year to make this play pay off. You'll have to make your own decisions...