Getting the Most Out of the Turn and River

by Daniel Kimberg | Published: Aug 13, 2004

I like adding things up. Although more involved math is occasionally required to solve difficult strategic problems in poker, many problems can be addressed just by estimating various probabilities (based on your knowledge of your opponents) and taking weighted sums of different outcomes. Of course, this isn't something you can do at the table. But if you spend a bit of time playing with different scenarios away from the table, you'll have a better idea what to do when faced with a new situation. And more importantly, you'll develop a sense for what's important in different situations.

Here's one situation worth thinking about: Heads up in a limit hold'em game, holding a likely winner, your goal on the turn and river is to get as much out of your opponent as possible. When you're forced to act ahead of your opponent, you'll make a few more mistakes than when you have position; you'll drop an opponent on the turn who might have called the river, or you'll fail to extract the most from an opponent with a strong second-best hand. The best you can do is assign probabilities to different outcomes, and see which path offers the best payoff.

Although there are many possible scenarios that fit this description, we can divide them into three for convenience: Your opponent may have a weak hand, a reasonably strong hand, or a drawing hand. I'm assuming a fairly tight game, in which a single pair can be a fairly strong holding, and in which the "weak" hand is one that's unlikely to chase but might call a single bet on the river, perhaps even without improving.

Here's an example: Suppose you hold K-10 and the board is Q-J-2-9. Ignoring suits, you can be sure you're winning. If your opponent has A-Q, there's little risk he will drop to a single bet, and he may even raise you on both the turn and the river. If your opponent has A-10, he will also likely call a bet on the turn, but probably not if he misses on the river. And if your opponent holds a hand like 9-7, or even a complete miss like 6-5, he will likely fold on the turn, but might be enticed to call a bet on the river (in the latter case, only if he catches a pair).

Should you open-bet on the turn? Not knowing what your opponent has, the correct approach depends on your ability to put approximate probabilities on these different situations, and to work out your expectation for each from betting out versus checking. Let's assume you were the preflop raiser (meaning your opponent has some reason to be wary, but also could reasonably imagine that you missed with A-K), there was no action on the flop, and you will play the river as aggressively as possible. The six tables below cover the possibilities – checking versus betting the turn against weak, strong, and drawing hands.

The probabilities are guesstimates, but do take into account the likelihood of your opponent improving, and include some considerations like possible semibluffs on the turn and scare cards (for your opponent) on the river. Of course, we have to make a number of simplifications to keep things manageable. We assume you know for certain (or are willing to pretend) that your hand will be strong enough to win the pot. We assume that your drawing opponent will raise on the river when he hits, and fold otherwise. We assume an opponent with a "strong" hand will never miss a bet on the turn. When your opponent opens on the turn, you always check-raise. And when you open and your opponent raises on the turn, you always just call. I could have varied some of these factors, but space is limited, and you can always play with the numbers more on your own.

Each table below has five columns. The first two show the action on the turn and river (you act first). The third shows the estimated probability of each sequence. The fourth shows the number of bets you get out of your opponent in each case. The final column shows the contribution of each betting sequence to your expected value (EV). The total EV for each table is the sum of the EV column.

What's most striking about these numbers is that for both weak and strong opponents, it makes little difference whether you check or bet the turn. Weak-hand outcomes are dominated by the likelihood your opponent will give you no further action, while strong hands will pay you off, but not to the tune of more than about three bets. For drawing hands, however, there's a fairly large difference. Since we postulated a small pot, it seems reasonable that many drawing hands would fold on the turn. In this case, you're substantially better off giving them a chance to semibluff the turn and make something on the river. If there's some chance they'll outdraw you, this pattern can reverse itself quickly. It's for good reason that poker players are advised not to slow-play vulnerable hands.

Since you don't know what kind of hand your opponent holds, the right decision here is a weighted average of the outcomes for all three hand types. But since two of the three cases come out about equal, it's almost always better to check the turn. Unless you're highly certain that your opponent does not have a drawing hand, the advantage for checking in that case makes it the right decision overall. Of course, this makes sense given the setup. Against opponents who will call on the turn with any draw, who will never semibluff, or who may have outs to beat you, the balance would shift somewhat.

The percentages listed here may not be appropriate for the players you face. And this is a very specific situation. I encourage you to download the spreadsheet I used to generate the numbers for this column and actually play with it (seriouspoker.com/turnbet.xls). Try out different scenarios and different opponent tendencies to see how the balance shifts. Add in a few negative outcomes for opponents who outdraw you. Set up a situation you've wondered about in the past, and see how changing a few variables affects the balance.