On my way home today I started thinking about Omaha and speculating a bit about how to play decent hands against two common types of opponents. The hands, more specifically, are middle set and a big (but not huge). For this example the definition of a big draw is one that is favored over top pair but a dog to bottom set.

The two sorts of opponents are quite common at the lower stakes although I assume they become more scare once you advance higher up the food chain. I'm calling them type A and type B here.

Type A
This guy is a bit of an honest calling station. He will pretty much only bet made hands, won't bluff or bet draws, and with made hands we mean top two pair or sets (we are assuming no straight or flush are out). If he gets raised, he will call down most of the time. If an obvious draw completes on the turn, he will check/call a pot sized bet and fold on the river unless he boats up.

Type B
This is also an honest player and very simmilar to type A except for one thing, if he gets raised he will fold bottom set and top two, but call or push with top set.

What started me thinking about this is that a lot of players will never fold bottom set. I like playing my draws aggressively, but part of what makes that profitable is the prospect of making someone fold a better hand, like a two-pair or bottom set. If I know my opponent has a better hand (he bet) and I know he's not going to fold (he's type A) then it is not going to be immediatly +EV. Yeah you will buy a free card on the turn, disguise your hand etc, but you're still putting more money in the pot while behind AND risk getting raised off your hand. Since your opponent *will* put in a full size bet on the turn when you hit and he's only ~20% to win (and with no implied odds since you have an easy fold when the board pairs and he bets), it seems clear to me that it is more +EV to play the draw passively against type A even though it makes it easier for him to put you on a draw.

Well against B then? Assuming he will fold bottom set most or two-pair hands most of the time it should be +EV to raise, right? After all, he's more likely to have bottom set OR two-pair than specifically top set. So he should in total fold more than 50% of the time which would practically make any bluff profitable. However, when he does have top set he will raise you off your hand and you will lose the chance to get a full size bet off him if you hit on the turn. So although it is profitable to raise him off his hand, it's not by that much.

So what about when you have middle set then?

Against Type A, you want to be raising since he will call when he's crushed, right? I'm not so sure. If we assume he bets top two and bottom set as well as top set he will be crushed as often as he crushes us, and the middle set vs top two will make up the profit margin since the set vs set balances out. That of course assumes that we won't fold middle set if he pushes back on the flop.

But if he's going to bet all these hands anyway, can't we make just as much by just calling him down? We know he's not on a draw, so it's a wa/wb scenario meaning giving free cards is not a problem. It also gives us some interesting other options when the board changes. Say a flush card arrives on the river and he prudently checks, now you can bet for value AND as a bluff. He might fold a better hand (top set) OR call you with a worse hand. Also, he's less likely to bet the river with bottom set or top two than with top set, so you could possibly get away on the river, and you can definetely value bet him when he checks and be almost guaranteed a call unless a draw hit.

Now against Type B you definetely *don't* want to raise. Even though you are ahead of his betting range, you're way behind the range he will call your raise with. Basically you want to let him do the betting to get max value when you're ahead and lose the minimum when you're behind. The bluff opportunity from the previous opponent is worth even more here against someone who is more prone to folding. If the board looks scary for top set on the river, there's a good chance you can bluff him off it.

So against Type A, we definetely want to call with the draw, and although raising with middle set might be better than calling it is not much better.

Against type B it seems clear that calling is best in both cases.

So.. by this reasoning I seem to come to the conclusion that against two very typical sorts of opponents, playing aggressively (ie: raising without the nuts) is actually a bad idea and you will win more by just passively calling. Did I go wrong somewhere or could this hold true?