Question 3 for Dummies
You don't need fancy math. A must call with the top one third of his hands to prevent B from profiting from bluffing with bad hands. (B is laying 2-1 on those bluffs)
B should bet the top one sixth (3/18) of his hands for value since those hands are favored to win even if called.
Since A is getting 3-1 when bet into, B should bluff 1/18 of his total hands so that his bet to bluff ratio is 3-1.
Since we know that B makes 25 cents in the non raising game, we need only see how much the existence of a possible raise helps. It doesn't help on his bluffs since they break even. It doesn't help when both players have the top sixth of their hands. It helps only when B is in the top sixth and A is in the SECOND sixth. That gains a bet for B 1/36 of the time. His EV moves from 9/36 to 10/36. .278
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