Part 4. Game Theory Notes.

Chart and formulas are reposted for convenience.

S = the size of the pot.
b = the size of the bet.
p = probability attacker is dealt a higher card.
(1-p) = prob attacker misses.
x = part of time attacker plays row B/B.
y = part of time defender calls.

Now the 2 X 2 matrix looks like this.

______\_____defender
attacker	Call	Fold
Bet/Bet	p(S+b)-(1-p)b	S
Bet/Chk	p(S+b)-0	pS

x = pb/(1-p)(S+b)
y = S/(S+b)

Note 1. Optimal strategy is optimal like Pepsi Free is free.

Note 2. y=S/(S+b) suggests defender should call with high frequency. Look thru the algebra(in part 2)to calculate y. There was division by (1-p) on both sides of the equation.When p=1, (1-p)=0. Division by zero is undefined. If attacker never bluffs, defender should never call.
Note 3. x = pb/(1-p)(S+b) If this value of x>1, defender should never call.
p/(1-p) > (S+b)/b.
When attacker bluffs with too low a frequency, defender should never call. In fixed limit this would be close to rarely bluffing. In nl with pot size bets, defender should not call if attacker bluffs less than 1/3 of the time.
Note 4. In poker optimal strategy does not always dominate exploitive strategies. It's rarely right to call players who underbluff. It's usually right to call players who overbluff. Don't bluff calling stations.
You must know the math to play well. But the math is a guideline, not something to be followed blindly. That's the art part of the game; knowing which math applies.