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River Play in Pot Limit Omaha
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The decision to fold, bet if checked to, call, or raise on the river is dependent on math. There are no more cards to come so your implied odds are non-existent. If you are in position, you have the option to end the hand with the action of your choice. Because of this, position is very powerful.
The best rivers to bluff are obviously the ones that complete a draw. Because Pot Limit Omaha allows so many draws to complete on the river, it is easier to move your opponent off a strong hand. For some reason, people cannot fold top pair in NLHE but in PLO, they give up on a hand when a draw hits the river and they had the nuts on the turn. This isn't saying giving up on the river is a bad or a good play. It is just interesting how people are so afraid of the nuts in PLO. Thus, you should take advantage of this.
A common situation for bluffing the river is when Villain is potting the turn to represent a straight and the river completes a flush card or the river pairs the board. In this situation, you should highly consider bluffing whatever hand you are holding that can't beat a good straight. Most players aren't tricky enough to semi-bluff the flop and the turn and then decide to check-raise the river with the nuts. The most common line of thinking is, "I semi-bluff on the flop and turn. Now I got the nuts on the river, I have to bet it. I am going to look like an idiot if I check and he checks behind with a hand that might have called a pot bet." Therefore, when an obvious draw hits on the river, you should bet if Villain defined his range on the previous street. You will get more credit than you believe.
A lot of players don't bluff the river enough. When you are in a situation and you don't know whether to bluff or give up, you should consider bluffing. First, your river bluffing frequency isn't that high, so adding another bluff to your river range isn't going to imbalance whatever your river range is. Second, if you have never been caught bluffing, then you aren't going to get paid off very often. If you play against very bad players who play too many hands and will always pay you off, it is suicidal to bluff for balance purposes. Just play tight with big draws and big hands and win. However, the game will get tougher so it is to your advantage to make yourself a tougher player, and having the ability to bluff the river makes you hard to play against.
To see whether the decision to bluff the river is profitable or not, let's go to an extreme scenario. You have a really bad hand on the river that cannot possibly win against any hand. It is checked to you. Should you check 100% or bet 100%? Obviously, either extreme is bad but betting 100% is better than checking 100%. Assuming you are going to bet two-thirds pot every time, your opponent needs to fold at least 40% ~ 67 / (67+100) for you to break even. Considering it is PLO and people like to fold to river bets, bluffing rivers is more profitable than not. You are going to win some money some of the time when your opponents fold. If you get caught, opponents might be discouraged from peeling your flop or turn bets too light, fearing that there is a big river bet waiting for them. If you check back 100%, you will never get your share of the pots.
