The Expectation of Action

“I would have flopped a full house,” my friend Fred said. The flop had come 6 6 4 in the $30-$60 limit hold’em game we were playing. “I folded wired fours,” he added.

I analyzed the situation from his perspective and from the point of his decision. “I would have called,” I told him.

Apparently perplexed by my statement, he asked me how I could justify the math on a call.

Fred was on the button. An up-front tight player called $30, then a very loose-aggressive player raised from early position and was called by a loose-passive player. The pot offered Fred $200-$60 when the action was on him. Fred felt that since he was getting only $200-$60 (less than 3.5-1) on his small wired pair and it was almost 8-1 to flop a set, the call couldn’t be correct.

Conventional poker wisdom dictates that when calling a raise cold with a wired pair, you should have at least four opponents, and Fred had only three for sure. That said, I don’t think the four-caller statement analyzes the situation deeply enough. The tendencies of your opponents, particularly their likelihood of giving you action if you hit your hand, is a much more important variable. The four-opponent theory is a tool for those who play on autopilot. I tend not to have much respect for an autopilot game, preferring to analyze an independently unique poker situation that presents itself.

Situations often play out very differently depending on player styles, positions, and so on. Good players adjust their hand selection based on those circumstances, creating more opportunities for themselves in positive-edge situations and getting away from more negative-edge situations than their conventional-wisdom opponents.

Fred took his analysis only to the level of the current situation, and did not include the potential future value of his small pair if he flopped a set. With cards to come (and excepting all-in situations), the value of the hand is its implied total expectation from the point of decision forward, not the current price that the pot is laying Fred!

Given the up-front limper and the cold-caller, Fred was virtually assured of having at least three opponents. Also, the two players in the blinds were yet to act, and the blinds generally have a greater propensity to call a raise than opponents not in the blinds. As it turned out, both blinds folded, but the possibility of them calling favored a call by Fred at his point of decision. Also note that the possibility of a reraise by one of the blinds is a variable to be considered; it’s one that diminishes the value of a call.

But what was most important in considering the value of Fred’s holding was the type of opponents he was facing. The loose-aggressive raiser was the key to the hand. He overplayed most of his hands and caused other players to overplay theirs in chasing him. The better the action that Fred could acquire both in terms of volume and quality if he flopped a set, the greater the value of his wired pair. By quality, I mean his opponents’ holdings having little opportunity to win if they gave Fred action. The worse their potential calls — and even raises in the case of the loose-aggressive player who had hit it preflop — the greater the expected value of Fred’s small pair.

If Fred hit his hand, the loose-aggressive player was certain to lead on the flop. The player between them was a calling station who tended to peel the turn with overcards, hoping to make a pair.

Without contemplating the possibility of winning unimproved, which has some real value, the true equation of playing wired pairs is whether or not you will average winning 8-1 or more of your preflop investment if you flop a set. Given the “incomplete information” characteristic of poker, it is difficult to quantify this variable. You are rarely certain of what your preflop investment will be, how big the pot will grow, or your likelihood of winning. But, applying the correct concepts should help you to better judge the value of small-pair situations. The looser and more aggressive your opponents are, the greater your ability to trap them; and, the weaker the quality of your opponents, the greater the number of them, and the cheaper your initial entry price, the greater the value of your pair.

Fred’s a bright guy, and is successful in business and in life. He’s a World Series of Poker bracelet holder. But in this situation, he played too tightly. He passed on an opportunity to take the best of his opponents in a pot. Situations in which you have the best of it are too infrequent. You must take advantage of them when they present themselves. Passing on them has a significant lost-opportunity cost. When you play too tightly and fold in situations in which you are able to create positive edge, you give up too much to opponents who are playing those situations correctly.

Starting hands that can make big hands in situations in which you are likely to get action have much more value than the current mathematical price at the point of decision might indicate. Throwing them away is like throwing expectation — and therefore money — into the gutter.

Longtime poker pro and author Roy Cooke’s Card Player column has appeared since 1992. A successful Las Vegas real estate broker since 1990, his website is www.roycooke.com. Should you wish to inquire regarding real-estate matters — including purchase, sale, or mortgage — his phone number is (702) 396-6575. Roy’s longtime collaborator John Bond’s website is www.johnbondwriting.com. Find John and Roy on Facebook.