Understanding Implied Odds

The term implied odds is generally used to mean something like “the money you expect to win if you make the hand you are drawing at.” When you’re thinking about the pot odds you are getting to call a bet, you should factor in not just the current size of the pot but also anything additional you believe you will win if you hit your hand. Because implied odds can serve as a justification to call with hands that are clearly behind, they are one of the favorite tools of “The Calling Demon,” that devil on your shoulder who is always trying to convince you to play hands that you really ought to fold.

Before the flop, many players reduce a calculation of implied odds to a simple rule. They’ll call with small pairs for up to ten percent of the effective stacks, and with suited connectors and similar hands for up to five percent of the effective stacks.
To be fair, these rules aren’t entirely without grounding in mathematics. Your odds of flopping a set with a pocket pair really are in the neighborhood of ten percent, and your odds of flopping two-pair or better with a suited connector really are in the neighborhood of five percent. In fact, your odds are slightly better in both cases, but these rules usually aim to be a bit conservative.

Still, when misapplied, as they often are, these rules lead to play that is anything but conservative. The underlying, not always fully understood assumption behind them is that you will always get stacks in if you get the flop you want.

The biggest problem with this thinking is that you can’t count on your opponent having a hand that will play for stacks every time you flop a set or two-pair. When it comes to set-mining with pocket pairs, meaning calling a preflop raise planning to fold unless you flop a set, I modify the rule to say that I have to anticipate winning an average of ten times whatever it will cost me to see the flop.

Note that that’s very different from simply looking at how much is in the stacks. It requires assessing how likely your opponent actually is to play a big pot with you should you flop a set. There are two major factors to consider here: how strong is your opponent’s preflop range, and how likely is he to put his stack into the pot with an overpair or a good top pair?

To the first point, it makes a lot more sense to set-mine against a tight player who raises in early position than against an aggressive player who rasies in late position. The former is only playing strong preflop cards, which means he will flop an overpair or top pair with a very good kicker quite often. Even a very strong preflop range, though, won’t flop well as often as you might think.

Suppose that a very tight player opens in early position. You know that he would raise only with ace-king or a big pair, tens or better. He has thirty combinations of pocket pairs and sixteen combinations of ace-king in his opening range, so if there is no ace or king on the flop, he’ll have a pair only about two-thirds of the time. Even then, is he really going to put his stack in with pocket tens if there is a queen or jack on the flop?

If there’s an ace on the flop, he’ll have ace-king a little over thirty percent of the time, as that ace reduces the number of combinations of ace-king he could hold to twelve. The other seventy percent of the time, he’ll either have a better set than you or be reluctant to play a big pot.

Flopping a set with a king on the board is a little better for you, since he could conceivably play a big pot with both ace-king and pocket aces, but it will also presumably hurt your action from tens, jacks, and queens. So there really is no flop where you can expect even a tight range to make a second-best hand to your set consistently enough to justify investing ten percent of your stack in hopes of flopping a set.

Of course a player with a wider opening range will connect strongly with the flop much less often than this. When he does connect with the flop, he’s far more likely to do it in a way that gives him substantial equity against your set.

Consider a match-up between your pocket fours and an opponent’s suited eight-seven. Even on an 8-4-2 flop, he may not put his whole stack in. If he’s aggressive, he might make a big semibluff with a flush draw or open-ended straight draw, but you are not nearly as big a favorite against these hands as you are against an overpair.

The other danger of calling a raise from a loose player is that someone behind you could easily reraise. People will generally raise more hands for value against an aggressive player, not to mention that a raise from an aggressive opener followed by one or more calls can start to look like a pretty good squeezing opportunity even without a good hand.

With suited connectors, your implied odds are even worse. For one thing, even when you are lucky enough to flop two-pair, you aren’t nearly as big a favorite against one big pair as you would be if you had a set. For example, 8 7 has only 70 percent equity against A K and 75 percent against a pair of aces on a K 8 7 flop. A set of sevens would have 94 and 91 percent, respectively.

Note also that flopping two-pair versus top pair with top kicker also requires a more specific flop than does flopping a set. You need two of the cards to match the two in your hand plus the third one to match one of the cards in your opponent’s hand.
If you flop a straight or flush, the board will probably look scary enough that you aren’t likely to get stacks in against one pair unless your opponent has a redraw, in which case you are again not a huge favorite. On a J 5 2 flop, 8 7 has less than 70 percent equity against A A.

This may not seem so bad — after all, getting your money in as a 70-to-30 favorite is nothing to sneeze at — but it’s rarely good enough for a best case scenario. Remember, we are talking about a situation that will occur only about five percent of the time, and if you lose most of the pots where you don’t flop quite so well, all those preflop calls you’re giving away will add up.

I wish I could conclude this article with a new and improved rule to replace the five or ten percent guideline, but it just isn’t that simple. You have to do your best to estimate the answers to a couple of questions and act accordingly. How likely are you to see the flop for just this bet? How likely is it that your opponent will play a big pot with you when you get the flop you want? Just how big will that pot be? How big of a favorite will you be? Practice asking and answering these questions, and you’ll be on your way to making better decisions about how implied odds should influence your preflop play. ♠

Andrew Brokos is a professional poker player, writer and coach. He blogs about poker strategy on ThinkingPoker.net and is co-host of the Thinking Poker Podcast. Andrew is also interested in education reform and founded an after-school debate program for urban youth.