Q's about the continuation bet on flop

I have noticed many of the better players of this forum advocating a continuation bet on the flop when you didnt hit, assuming you are the raiser preflop.

Some questions..

1. Should you do the continuation bet be done even when you dont have position on the other guy? (so you're betting into him with nothing)

2. Are there certain types of flops you should avoid continuation betting?

3. Why is continuation betting on the flop good in the first place?

My answer to Q's 1 and 2 is: I generally dont like continuation betting without position. I also prefer to continuation bet on more drawless boards, since the only calls you get are from made hands and you know right away you're beat.

My answer to Q 3 is: If your continuation bet is 2/3 the pot then it has to work 2/5ths of the time (some math follows)

Assuming pot is 30$ and your continuation bet is 20$, you stand to have a net profit after the hand of 15$ (if sucessful) or net loss of 35$ (if you arent). If you dont do a continuation bet you will lose the pot and end up being down 15$.

Algebra says..

-15 = -35*x + 15*(1-x)
-15 = -35x+15-15x
-15 = -50x+15
-30= -50x
3/5 = x

so you can fail 3/5ths of the time and still break even.

Is this good logic? If so, can the continuation bet be expected to work 2/5ths of the time?

Edit: Just realized something. If you dont have position and you do a continuation bet and he calls on a draw (unbeknownst to you!), you are forced to check the turn. He can then kick you out of the pot on the turn by betting with just a draw. So it seems like continuation betting without position into a board with a lot of draws is a bad idea. Correct?

A lot depends on the stakes, the table, etc. General rule of thumb: I continuation bet the majority of the time if I pre-flop raise. I am more likely to fire a continuation bet when:

- there are fewer people in the pot (if only one opponent, I almost always use a continuation bet; if there are three opponents, I almost never do)

- I have position (although I still am going to use continuation bets out of position, just not as much)

- the board looks unhelpful to others (low mixed rags, not draw heavy, no paired cards higher than a 7 that someone might be holding)

- my opponents are not completely loose (if they call most every bet any way, there's no point bluffing, ever)

The 2/3 pot bet is good at $25 and $50 NL. I don't find it to be as successful at my current level of $100 NL; players just don't respect it, and you get called a lot more, which puts you in an awkward spot of having no idea what they're holding. At the $100 level I find that I continuation bet somewhat less, but make the bet stronger when I do so. I would guess that when I miss the flop completely, I fire a bet about 70% of the time and it's usually at least 4/5 of the pot, if not pot-sized. At my previous level ($50 NL) I always bet, and it was always about 2/3 of the pot. This adjustment is increasing my profitability at my current level. You just have to know how the players at the tables tend to play.

At $25NL, if there are three or more people in the game, you don't have an ace, and the ace comes on the flop, you really might as well quit. One or more of them are bound to have called with ace-and-anything.

(or you can rep the ace yourself if the size of pre-flop raise/reads on the players concerned implies this would be a good idea - I just wouldn't do it as a rule)