If you are playing in a loose passive game, you can loosen up a bit, but the most important thing to understand is what you can loosen up with, and when.
In very loose games, (especially loose but somewhat aggressive games) you want to tighten up on hands like KTo, QTo, etc. These hands do not play well against a large field. When they win, they tend to win small pots. When the lose, they cost you a lot of money. In any event, they are extremely hard hands to play well.
A typical result for a hand like KTo is that you’ll flop a pair of Kings or a pair of tens. If you flop top pair with tens, a lot of weak players will hang around with one or two overcards and run you down. If you flop a king, a passive player with KQ will check and call all the way to the river, and you’ll never know where you stand.
To play such hands well, you have to know exactly who you’re playing with, and watch who called from what position. A weak-tight player calling from early position, and two or three callers after him? KTo is death. You’re probably look at AQ, AK, KQ, TT, or something like that. Hands that have you dominated. On the other hand, if one weak player calls instead of raising from late position and you’re on the button, you can raise and try to get heads-up with him with position. But if the blinds call the raise, you’re in a tough spot again because you have no idea what they have.
On the other hand, with five or more players in in an unraised pot, you can play any pairs or small suited connectors. These are hands that generally either hit the flop big or miss completely. The biggest risk with these hands is that you get ‘pot-stuck’ by having the odds to call for marginal draws. But in general, they are easier to play - if you don’t hit a four-flush, a set, or two pair on the flop, you’re done. It cost you a small bet. But if you hit your set, you stand to rake in a nice big pot.
One thing to remember about Hold-Em: It’s a community card game, which means it’s harder to outrun other players than in a game like stud. Therefore, there’s a premium on good starting hands. The surest way to lose in a ring game is to play too loosely, or to play without due consideration to position or where you sit in respect to the aggressive players. Playing raised pots with weak hands will wipe out your bankroll.
Omaha: Omaha high is a game that you can indeed play looser, as there are many hands that stand to make big multi-way draws on the flop. It’s harder to play the game after the flop, however, so if you’re not skilled at the game, you need to play big hands that can make the nuts, and that’s it.
Omaha-Hi Low: A totally different game than Omaha high, and a game that rewards people who play very tightly before the flop. You never want to play a hand that stands to only win half the pot. You need hands that can sweep both high and low, or hands that are huge for high and which, if made, won’t share the pot with a low hand (because no low will be possible). The range of hands that meet these qualifications are very small.
All of this changes playing heads-up or very short-handed. In my experience, Omaha short-handed in one of the most difficult games to play. You’re no longer playing for the nuts, but it’s extremely hard to tell what you’re opponent has. It’s also possible for opponents to hit a big hand on the flop, then back into an even bigger hand on the turn or river (i.e. hitting a set on the flop, then making a runner-runner flush on the turn and river). In addition, there are hands that can flop big draws in Omaha that are actually more likely to win than the current best hand. This makes it hard to use an opponent’s betting patterns to figure out what they have.
As for professional poker players not knowing the math - a lot of them really do. Chris Ferguson has a Ph.D in math, as I recall. Most of the top players know the math of the game just fine. But these guys also play a lot of short-handed games, and in short-handed and heads-up games, playing the player becomes much more important than playing the cards. When you see these guys on TV, it’s usually in the late stages of a tournament, and often when the table is down to six players or left. The strategy at that point completely changes. If you take their playing style into a limit ring game with ten players, you’ll get killed.
In addition, the strategy for tournaments changes dramatically. The climbing antes and blinds forces players to play looser, and the relative chip stacks and the payout rates of the specific tournament also affect strategy. So don’t assume that what you see on TV is how you should play.
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