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Question related to the first example of maximizing value - is there a simple math calculation you use to immediately allow you to determine the best possible bet size on early streets that ultimately sets you up to make a pot sized bet on a future street?



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its called the geometric growth of the pot. C&A in MoP go through this quite extensively.

Pot=1
Player A bets some fraction of 1 into Pot=1, which is s1
If Player B calls, then the pot grows from 1 to (1+2s1)
r1=(1+2s1)/1
r1 is the ratio the pot will grow if the bet is called.
r2=(1+2s1+2s2)/(1+2s1)
r3=(1+2s1+2s2+2s3)/(1+2s1+2s2)

r1r2r3 is a constant where r1=r2=r3
That constant is the geometric growth of the pot. the optimal bet size on the flop gets your stack in on the river.
Depending on the texture of the flop, mandates if you want to grow the pot in 2 or 3 streets. A two-street growth of the pot is best for extremely dynamic flops, because of the clairvoyance effect that takes place on the river when your opponent is playing a draw. he in efeect plays with better information, because he knows when his draw comes in; and only pays when it does.