[Jerrod Ankenman]

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The answer to the second problem is:
(There are co-optimal solutions, but where possible I present undominated ones)

B:
folds on [0,19/36]
raise-bluffs on [19/36,7/12] *
limp-folds on [7/12,2/3]
limp-calls on [2/3,5/6]
value-raises on [5/6,1]

A:
calls a raise on [2/3,1]
folds to a raise on [0,2/3]
raises after B limps on [3/4,1]
checks after B limps on [1/12,3/4]
raises after B limps on [0,1/12]

The value of the game is 1/4. (later determined to be wrong/JA)

To answer David's question, B should just raise the same amount of hands when the A's blind is made live. B, however, doesn't limp with his thinnest value calls, because he'll face a raise sometimes. He just folds them.

Jerrod Ankenman

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Ok, everyone seems to agree that JA's EV for B is actually 17/72. I haven't checked this, but I'll just accept it.

But I think I can improve on A's strategy if B plays that way. Everything is the same except the following:

A bluff-raises on [0,2/9]
A value-raises on [2/3,1]

This dramatically reduces B's EV to 179/1296 if my arithmetic is right.

(17/72 = 306/1296)

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The difference between the strategies is simply the hands [2/3,3/4] and [1/12,2/9].

When A has [2/3,3/4]:

When B has:
limp-folds on [7/12,2/3] -- same result as checking
limp-calls on [2/3,3/4] -- same result as checking
limp-calls on [3/4,5/6] -- loses one extra bet

When A has [1/12,2/9]:

When B has:
limp-folds on [7/12,2/3] -- win 2 bets extra
limp-calls on [2/3,5/6] -- lose 1 bet extra

Since 5/6 - 2/3 = 2/12 and 2/3 - 7/12 = 1/12, this is a break-even.

So your strategy loses an extra bet when A in [2/3,3/4] and B in [3/4,5/6] and doesn't gain any offsetting bets when compared to the optimal strategy.

Jerrod