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.