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Exclusive Netbettor Texas Hold'em Article:

"When you check as the player who’s first to act, you're putting yourself in a spot where you are going to ‘pay off’ superior hands, but won’t have the chance to extract a bet from inferior hands".

Some River Considerations

The river may be the easiest of all the streets to play well; after all, all the cards are now out, and in most cases you either have a good hand or you don’t. Still, there are some situations where an expert player can extract an extra bet or two from a winning hand (or save a bet or two with a loser) that a novice player may overlook. Here we’ll look at a few of the unique considerations that go into quality river play.

1) Be more inclined to bet if you act first.
The reasoning for this is simple to understand. First, If your opponent has a hand that’s better than yours, you’re probably going to get raised. However, if you check he’s going to bet, so by betting out you only lose one additional bet. When you act second, though, you now have the option of checking down for free. If you bet, and get check-raised, you have now cost yourself two bets as opposed to zero. Thus, making a betting mistake when you're first to act can only cost you one bet, while making the same mistake when acting last can cost you two.

Secondly, a player who bets out when acting first will often collect a bet when he’s ahead, but will probably not collect a bet when he’s behind. When you check as the player who’s first to act, you're putting yourself in a spot where you are going to ‘pay off’ superior hands, but won’t have the chance to extract a bet from inferior hands (this is because the inferior hand will often check behind you). Here’s an example; say you have Jclub Jheart, and the board reads 9spade 9heart 6spade Theart. On the river the Kclub drops. If you are first to act you should probably bet here (especially if you’ve been betting all the way). You might get paid off by a ten, or something like 7spade 7Diamond, or perhaps even an ace-high hand. If you check, though, it’s likely that the only hands which will bet are hands that contain a nine or a king.

In sum: When you check here, you’re usually only going to end up putting money in the pot when you’re behind. If, however, you bet out, you’re probably going to be putting money in the pot when you’re ahead about 40-60% of the time. By betting, you give yourself a chance to collect from inferior hands. You won’t have this chance if you just check.

2) If someone bets, just call with a good-but-not-great hand if there are players left to act behind you.
Here’s an example. You have 6club 5club in the big blind. On the river, the board reads Kclub 6heart Qclub 9spade 5spade. Note that the river gave you two pair, but it’s the weakest two pair on board. If the small blind bets here, be inclined to just call along (so long as there are players left to act behind you). You have a good hand, but it’s far from the nuts. By just calling you give hands like KJ and AQ a chance to call—hands that you would like to have call, but that might fold if you raise. By raising you open yourself up to shutting out inferior hands behind you, while potentially getting three-bet by a bigger hand in the small blind. Even if the rest of the field folds it’s not a disaster, since there’s no guarantee that the small blind would have paid off a raise with a hand worse than yours. Similar considerations apply to those times when you spike top pair on the river (usually when you flop an ace high flush draw and catch an ace on the river) or finish a straight draw with a card that also completes a potential flush. In cases like this your almost always better off ‘going for the overcall’ as opposed to putting pressure on the original bettor.

"The river check-raise is a strong play, although it’s an even stronger play in online games where so many players go into ‘auto bet’ mode on the river if they’re checked to".

3) Look for spots to check-raise.
One of the most overlooked plays in hold ‘em is the river check-raise when the river didn’t improve your hand. Lots of players will check-raise the river when they finish a flush, for example, but very few will try it if they’ve been betting top pair all the way and a brick hits on the river. The river check-raise is a strong play, although it’s an even stronger play in online games where so many players go into ‘auto bet’ mode on the river if they’re checked to. Let’s look at a couple spots where a river check-raise is a play you should consider.

Example 1) Your in middle position and limp in with pocket 7’s. Two more callers and the button raises. You see a flop of 7heart 3Diamond 4Diamond. You bet, all fold to the pre-flop raiser who just calls. The turn is the 4spade. You bet again, and he calls. The river is the Aclub.

Strongly consider a check-raise here. The fact that he didn’t raise on the flop just screams two overcards, which means the ace probably hit him. Only the most aggressive players will raise the river here with AK, so you can’t be sure you’ll get three bets out of him by betting out. If you check, however, it’s a virtual guarantee that he’ll bet with any hand containing an ace. By check-raising here you collect two bets instead of one.

Example 2) You have KK, and raise in early position. There are four callers. The flop comes T 8 5 of mixed suits. You bet out and get two callers. The turn is another 5. Again you bet, and now you get one caller. The river is a 3.

Again, consider check-raising here. If your opponent was on a draw he’ll simply fold if you bet. But, he may bet a weak pair here, since your check on the river makes it look like you’ve been bluffing with AK. Also, it’s unlikely that you’re beaten since you probably would have heard from trip 5’s, or a full house, on the turn. Against very passive opponents you probably just want to bet out here. But if your opponent has a little ‘spunk’ to him a check raise in this spot can be quite a profitable play.

Another Poker Inforamtion Site:
Texas Holdem Rules
Texas Hold'em Poker Rules at MasteringHoldem.com