[templar999]

[ QUOTE ]
[ QUOTE ]
The continuation bet itself isn't necessarily profitable. However, as part of your overall strategy, your mix of continuation bets and value bets should be, if you are a winning player. Your continuation bets should provide more value for your value bets, and your value bets should provide higher folding equity for you continuation bets.

[/ QUOTE ]

True, but how about situations when it's highly unlikely you'll never see the opponents again, say you are on a trip to Vegas and play for a few hours against strangers. Say you raise AK on the button and get one caller, who looks like a calling station. You miss the flop completely and it's checked to you. You think he'll call any pair or any draw. Is there a reason to bet here?

[/ QUOTE ]

If I'm understanding you correctly, future and past actions are irrelevant with regards to mixing your betting strategies on the flop? Sure, even in this scenario, a continuation bet may be profitable. First, there's a decent probability that your AK is still the best hand. Second, if your AK is not the best hand, there exists a decent probability that your AK will improve to the best hand by showdown. If you have a rough estimate for these two, you can pretty much figure out whether or not the continuation bet is profitable.

Let's use your example of AK against a calling station who will call with any pair or any draw on the flop. Say You raise 4x the BB, and there are 10 BB's in the pot. Let's estimate conservatively that he'll miss the flop with no pair and no draw 40% of the time and will fold immediately. The other 60% of the time, he will flop a decent draw or any pair and call. We can assume we're a decent underdog when we are called. Again conservatively, let's estimate our equity at 20% when called. If you assume no post flop betting, your EV for a continuation bet of 3/4 pot would look like this:


EV(cbet) = winning immediately + called/lose SD + called/win SD

EV(cbet7.5BB) = (40%)(10BBs) + (60%)(80%)(-7.5BB) + (60%)(20%)(17.5BB)

Way to simplistic and unrealistic, I know, but it's applicable if we were to look at a continuation bet in a vaccuum.

p.s. The equation may not be correct since I have no caffiene in my body, but you get the general idea.