How Many Clubs Would You Like?

Every now and then, it's fun to play hands like the 6♣ 5♣ in a limit hold'em game – hands that have a few ways to hit and will be hard for anyone to see coming. Of course, fun can get expensive, and few poker strategists place hands composed of small cards high on the list of playable hands. Most recommend that they be played only in exceptionally favorable circumstances, if at all.

The main drawback of small-card hands is that they almost never win with a single pair, or unimproved. They need to make some less likely hands – two pair or better – to take down the pot. But even when they hit, bad things can happen. While that's true for any hand, small suited connectors are more vulnerable than most. When they make two pair, it's often the bottom two, and a third pair on the board is rarely welcome. When they make straights, they're often non-nut straights that could already be behind or are readily counterfeited. And when they make flushes, even if a bigger flush isn't already out, a fourth card of your suit is liable to make someone else a bigger flush. Add these to the normal worries of all poker hands – straights losing to flushes, flushes losing to full houses, and so on – and you have a hand that will contribute a bit more to your poker heartache than most.

All of these are good reasons to pick your spots carefully if you really want to play small suited connectors. When a hand is at best borderline, small drawbacks take on added importance in your decisions. But for right now, I'd like to focus on just one of those worrisome outcomes, just to see what the numbers tell us. How often will that fourth suited card come to ruin your flush?

When you start with suited cards, the probability of your making a flush by the river is about 6.4 percent. The probability of exactly three of your suit hitting the board is about 5.8 percent. Do the subtraction and you'll see there's about a 0.6 percent chance of either four or five of your suit hitting the board, neither of which is generally a favorable situation (ignoring straight flushes). Half a percent chance of disaster seems pretty manageable, so maybe we really don't need to worry about those onecard flushes. On the other hand, it's almost 10 percent of your flushes. Let's break it down a little more closely and see if there's really anything to worry about.

First, imagine that you've hit your flush on the flop, which will happen about 0.8 percent of the time. As your intuition would tell you, flopping your flush isn't common. When you do, you're basically on a no-flush draw, with five of your suit accounted for. You'll survive the turn and river without another club 68.6 percent of the time. So, even though your hand is in danger, and you may already be behind a larger flush, on those occasions that your hand is good, you would want to extract maximum value from your opponents.

Now, let's consider the times you flop a four-flush, which will happen about 10.9 percent of the time. What are the possibilities? There are nine clubs left, and 38 non-clubs. The probability of a club coming on the turn is 19.1 percent (9÷47). Once it hits, the probability of a blank coming on the river is 82.6 percent (38÷46). So, the probability of club-blank is about 15.8 percent. The probability of blank-club is the same (the club is as likely to turn up on the turn as on the river), for a total of 31.6 percent. Using similar calculations, we can see that the probability of two blanks coming is a healthy 65.0 percent, while the probability of two clubs coming is 3.3 percent. Hitting a single club is almost 10 times as likely as hitting running clubs. Whether your situation calls for betting your draw or just calling along, that 3.3 percent possibility is unlikely to affect how you play the hand. The probability of there being a bigger flush draw out is higher, although the exact percentage depends on how your opponents play.

What about on the turn? You need to worry about losing to a one-card flush only if the turn is a club, in which case eight of the unseen 46 cards are dangerous. That's about 17.4 percent, or 4.75-1 against getting caught that way, even if your opponent does have a club. So, it's unlikely that you'd want to slow down without good reason to think you might already be beat. This isn't surprising – as your opponent is on a draw, and you want to extract maximum value while you're ahead.

In general, although a fourth card of your suit on the board isn't something you'd like to see, it doesn't happen often enough to affect your play once you're in the hand. Once you make your flush, it's like being up against a probable flush draw, something that in other circumstances would make you happy. On top of that, your small flush isn't completely dead in the water just because a fourth suited card is on the board. Especially if the field is small, your small flush will hold up often enough to have positive value, and may sometimes be worth a bet against a single readable opponent. Your level of risk depends on various factors, including most importantly the number of players in the pot, and how they've been playing the hand. But it may be more important to consider the likelihood that one of your opponents has a bigger flush, which you'll be able to estimate best if you know your opponents well.

On the other hand, it should be a more important consideration when you're deciding whether or not to call preflop. If your decision is truly borderline (and with hands like the 6♣ 5♣, it's borderline at best), knowing that a substantial proportion of your flushes will lose even when no one else has two clubs may help you make the right decision. In effect, you'll be losing a large proportion of the value of your hand on those occasions that you make your hand before the river. While being on a no-flush draw is an enviable situation, it's far from the value you normally expect from a made flush. And this is only one of the possible painful loss scenarios for small suited connectors. ♠

Daniel Kimberg is the author of Serious Poker and maintains a web site for serious poker players at www.seriouspoker.com.