Betting the River

Review time! There are two, and only two, reasons to bet the river in holdem:

1. You think you can get all better hands to fold.
2. You think you can get a worse hand to call or raise.

That's it. There are no other reasons to bet the river. Think about it - all the cards are out, there are no more to come, now it's just time to see who came out on top. With this in mind, lets consider the pros and cons of various options for a situation I commonly see misplayed: you've been leading the betting the whole way, you hold top pair and you are first to act headsup in a game of limit holdem. (Note: the ability to make large river bets completely changes the calculus for no-limit holdem. Go read Double As for excellent advice on how to proceed in similar situations in no-limit holdem.)

If you only have top pair on the river (or really, any pair), and you are heads up and first to act, it is usually best to check-call. Why? Simple. You are very rarely going to get a better hand to fold. More often, if you bet, and you are behind -- say, your opponent makes a hand bigger than top pair on or before the river -- you are going to get raised. And for one bet on the river, with probably at least seven or eight bets in the pot, you cannot fold. So you call, and you probably lose, and the river costs you two bets. On the other hand, if you bet, and your opponent was drawing the whole way and missed, he is probably going to fold his worse hand. Thus, net gain on the river when you bet the best hand: 0.

There are those rare times when your opponent has the same pair with a smaller kicker than you, or thinks his middle pair is good, and would call that bet on the river, but we'll cover those cases in a second.

Now consider what happens if you check-call. The times your opponent has a better hand than you, he will bet it, and you will call and lose. Net loss to you: 1 bet. The times your opponent has same pair, smaller kicker, he will probably bet, since you have just shown weakness and he has top pair, and you will call and win. This is no different from betting at the river and getting called in such a scenario. The times he's on middle pair, he might bet, he might not, but then again if you bet first, he might call and he might not, so you're not really gaining or losing much here by playing it one way or the other.

The big one to consider is when he was drawing and missed. If you check, he will sometimes just check it down, and you will get nothing out of him. On the other hand, sometimes he will try to bluff you out of the pot (especially if a scare card hits the river). You call his bluff with your top pair, and pick up an extra bet that you wouldn't have if you had bet straight at it, because he is NEVER calling a bet on the river if his draw didn't get there, and he will rarely RAISE on a bluff, because he knows that for one bet, you can't fold. (He will do this once in a great while, though, which is why you have to always call that raise on the river unless it is glaringly obvious that you are beat -- but usually it's only glaringly obvious in multi-way pots.)

In summary, when you're first to act, heads up, with only a pair at the river:
* If you bet and you're behind, you'll lose one or two bets.
* If you bet and you're ahead, you'll win one or zero bets.
* If you check-call and you're behind, you'll lose one or zero bets.
* If you check-call and you're ahead, you'll win one or zero bets.

This is one of those instances that David Sklansky often talks about, where playing a hand one of two different ways will not cost you any extra bets when you win (and may even pick up an extra bet or two by inducing a bluff) and will save you bets when you lose.

What if you're second to act? If the first player bets, just call it down. Simple enough. On the other hand, if he checks, the best option is usually to check, and some simple math should prove it. The times you get called by an inferior hand, you will win one bet. The times you get raised by a better hand, you will lose two bets. Since it is very rare that you will get raised by a worse hand when you're only holding top pair, we can ignore those cases.

So, in order for betting the river to be correct in this situation, you have to get called by worse hands twice as often as you get raised by better hands (so that you win 2 bets for every 2 bets you lose when you get raised). How likely is that to happen when you're holding only top pair? While it depends on the opponent, against an average opponent I would say "not very". More likely is that the opponent with the worse hand will fold to your bet. The few times that you will be called by a worse hand can be lumped into the category of "same pair, smaller kicker" and "middle pair or 'in-between' pair" (like AJ on a Q-J-5-2-2 board, or KK on an A-T-3-7-4 board). Of course, it depends on the opponent, as some opponents will call you down with -any- pair, but as I said let's assume an average opponent.

This is just one of a multitude of scenarios that present themselves on the river in holdem. The important thing to always remember about river betting is to ask yourself, "Self, why are you making this bet?" Is it because you expect a worse hand to call? Is it because you expect a better hand to fold? If you can't answer one of those questions in the affirmative, then you're better off checking it down or check-calling.