PF Raise question

Okay. So I'm in middle position in a full ring NLH game at FTP, one limper and some folds to me with a premium hand, so I decide to raise. I hit the "pot bet" button, and the raise that looks back at me is 4.5 bb instead of the 3.5 bb that I've heard called "standard". After toying around a little bit, I find the "pot bet button" gives me a 3.5bb raise if I'm the opener and one extra bb for each limper.

I understand that preflop raises accomplish two major things: 1) protect your hand from junk draws (A6o to your KK, for example) and 2) get more money in the pot. I assume that the 3.5bb raise to 3 limpers will get more callers than a 6.5bb raise will, but a 6.5bb raise will get more folds. My question is, then:

What hands do I want to:
-protect assuming low general skill level?
-get callers assuming low general skill level?
-protect assuming solid play?
-get callers assuming solid play?

Is there a general rule for 3.5bb + x for every limper?

And do these change if I'm suddenly in a MTT?

Also, first post. Hi everyone!

Edit: clarifications and such. I'm not too good at this post writing thing yet.

MTT are a different beast since your number of big blinds is much smaller then the average ring game stack. So, we will not discuss that here.

If the opp(s) is unknown, do your standard raise. If they are known to be tight then standard. If you know they will call big pf raises with almost anything, make them pay.

You assume getting callers and protecting your hand are opposites. Protection is the idea that you get your money in while you are ahead. You make it so that drawing hands have to pay if they want to draw, but you still want them to draw. If you have AA and go allin then you have protected your hand but you still want callers.

So really the better your hand is, the more you want a call. If your hand is bad enough so that it is worth less than the blinds on average (from your particular position/situation) then you would rather everyone folded. Against very bad players a hand like J8s is almost certainly worth more than the blinds from good position so you don't want to steal the blinds with it. Against better players you might rather have the blinds than a caller.

The other important point is that you shouldn't assume that raising more preflop necessarily gives you better protection. Consider two hands where you are out of position to one caller. You have AA and he has 44. In the first case you raise 4x the big blind (the same amount you would raise with a wide range of hands). Sometimes the flop comes down xxx and you win a relatively small pot (just his preflop call). Sometimes the flop comes down x4x and you lose a fairly big pot before folding the worst hand. Assuming he takes a call cbet, checkraise pot on turn, bet half pot river line (fairly common with a set) you will lose about 90bbs when he flops a set. He flops a set about one time for every 8 times he misses so the EV is about -55bbs.

In the second case you raise 8x the big blind (something you will only do with AA/KK) to better protect your hand. The 8 times the flop comes down xxx you win an extra 4bb for an extra profit of 32bb. The one time you come up against a set you will find it very hard to get away from in a bloated pot and are likely to lose much more than 32bb more than in the first case. In fact if the hand plays out similarly with the same sized bets relative to the pot you will lose twice as much so the total EV will be around -110bbs.

Raising more preflop meant you lost more on average since you played a bigger pot those times he outflopped you. You protected your equity in a small pot, but with alot of money behind, that equity is only a small fraction of the total money that will be bet. The moral of the story delivered in Sklansky-esque style is this:

Betting more to protect small pots is generally a bad idea in deep stacked no limit holdem if there is alot of money left behind, and it will cause you to lose alot more when you are outflopped, but not usually cause you to win much more when you are ahead.

Conversely if there is only a small amount behind you don't mind betting larger amounts since it will make both you and your opponent feel committed in a situation where you almost always have the best hand postflop.