[mvdgaag]

These calculations are mostly made when you want to optimise your EV, but you'll have to know more about the current odds you lay.

If you always bluff he will always call and if you never bluff he will never call. So in both cases you are far from optimal. Now what you want to do is make the EV the same for when he calls or folds, so it doesn't matter what he does.

Let's take another example first (very hypothetical)
-magic 72o which always loses
-magic AA which always wins

Now if you bet $4 in a $2 pot only with AA and fold 72o he's going to fold all the time and you win nothing

If you bet all of them you are going to have 72o 12 times and AA 6 times and he's always going to call, which makes your EV 12*-$4 + 6*$6 = -$12.

How often will you have to bet 72o to optimise your play? This is where the odds against your bluffing are the same as the odds you lay, which is 2-3 ($4 to win $6). So for the 6 aces you'll need four bluffing 72o's.

So EV if he calls = 4*-$4 + 6*$6 = $20.
And if he fols = 10*$2 = $20.

Whatever he does, with this distribution you'll have an EV of the current potsize ($20 / (4+6)) for ten out of 18 deals.

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In your example there is no pot yet, so if he folds your EV = 0. To balance AK and AA so you'll have an EV of 0 when he calls had no point. But..

AA has an equity of 80% against a possible pocker pair caller and AK 45% (this is a pocket pair, but you could check your equity against his range and do the same). If you were raising all your AA's or none of your AK's you'd be giving information and he'll call if you didn't raise giving you an equity of only 45%. The solution here is to sometimes not raise AA (If you sometimes raise AK, the times you don't raise still signal your hand being AK). Suppose if you do not raise you want an equity equal to when you do raise. Here's the trick:

You want your (optimal playing) opponent to have the same expectation when you raise or when you don't so he cannot adjust his play to your strategy. To do this you need the same equity when you raise as when you don't. So you raise half your aces and half your AK's for an equity of 54% and you check half your aces and half your AK's for an equity of 54%. This will be the same equity as always raise or always call and is the optimum. If you want to play al your AA and AK hands than the only point is not to give information so he can adjust his strategy to yours.

In practise players will not play an optimal game against you and either fold too often or call too often. If they call too often you should bluff less and if they fold too often you should bluff more. Same goes for optimal strategies, if they fold too often to a raise add more of the possible low equity hands to the raising group and vice versa.

GL