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?