The cards have all been dealt at this point, and we're in to our final round of betting. Since we've stayed this long, we should have a good chance to win the hand, and we'll be assessing our chances in terms of how much more it will cost us to show down our cards, how much money can be made by winning, and what we realistically feel our chances of winning the pot may be.
The first thing we need to ask ourselves is - do we need to be here in the first place? Often, players will push their hands too far, and then get to the river where it may make sense to show down, but it didn't really make sense to take this hand to the river in the first place. As a rule of thumb, you need to be winning more hands than you're losing here, or you're overplaying your cards. Remember, we want to either be the favorite, in terms of a combination of hand strength and fold equity, or be drawing to win with favorable odds to do so.
So not just take your cards through the hand without an advantage of doing so. Anyone can play the good cards. What seperates the winning players from the losing ones though is that winning players save bets by not playing on when they are at a disadvantage. As you become more experienced, you will learn to better determine in which situations your advantages lie, and which need to be avoided, but starting out, it's better to err on the side of caution here, because lesser profits but still profitable sure beats overplaying and thus unprofitable.
However, at the river, we've made it, and now we want to decide what to do. Calculating the money odds is much more straightforward here than at earlier streets, since there are few decisions left by opponents. We don't even need to worry about how much more will be contributed in fact, since most of the money that's going in there is probably there now, but it's still a good idea to try to calculate what the total pot should be, based upon our predictions on how players will see it through.
So, let's say there's 8 big bets in the pot, and it's come down to you to act. Let's say you missed your draw, and figure to be probably beaten here. You still have a chance, but let's say you feel that it's 4:1 against you that your opponent will win. What do you do? Well in this situation, it would actually be correct for you to call, and here's why. You win 1 out of 5, which nets you 8 bets. You lose 4 out of 5, which loses you 4 bets. So in calling, you're going to average almost a full bet to the good, even though your chances of winning aren't that great.
Be careful though to not overvalue your chances. This isn't a license to call with any kind of trash that has no realistic chance of winning. You can save bets here pretty easily by folding, which will add up. If you're in doubt about this move, better to fold. As you go along though, you'll become more experienced in determining what your chances are, and can add extra profit this way.
So now that we've touched on calling, let's look at betting. There are important differences here on the river as well. While we want to be aggressive generally, there a lot of situations where it's more correct to check and call rather than bet. For example, say you have a marginal hand, where you're not sure if you're ahead or not. You've decided that your opponent either has you beat, or has nothing. If he has nothing, and you bet, he'll fold, so you're no further ahead. If you bet, and he has something, the chances of him raising you are high, whereby you'll be folding.
So, what it comes down to is that the only real way you can get a call here is if you are beat in the hand. Whenever that is the case, it makes no real sense to bet, and you must check instead. While you should always think on what your opponent or opponents will do each time you act, it's particularly important here.
What about raising? Well, if you're down to 2 opponents, things are a lot more clear cut. Remember though to try to anticipate the opponent's actions prior to acting. If you feel that the only way he'll call your raise is if he has you beat, and may indeed re-raise, calling is correct. Otherwise, let him have it and make him pay to see your cards.
If there's more than one opponent though, things get more interesting. You have to be thinking about the actions of more than one player. And if you feel you have the best hand, it's often correct to call instead of raise, when that will put more money in the pot. Consider this: There's 3 opponents in the pot, and you've hit the nut flush. You've got this sucker won, and you want to raise. But if you do, the 2 to act after you will probably fold, since they now have to cold call 2 bets. So the most extra money you'll get this way is 1 bet, and that's only if the original better calls, which he may not.
On the other hand, by just calling, you will get 2 extra bets in there, from the 2 people acting after you, who will call the single bet. So, you actually get more money out of the hand by just calling than raising, even though you have the nuts.
The bottom line through all of this is that, while there's lots to think about as the play evolves through the hand, you've got to take a little extra time and think things through even more on the river, since there are often other things to consider.