Re: Some Thoughts
The problem is too complex. First solve an easier problem.
Assume button goes all-in and solve BB's strategy.
Assume button goes all-in.
Case 1. SB folds.
BB has a EV of 0.0145 by folding.
BB plays and loses for EV of 0.
BB plays and wins for EV of 0.2091
145x=(1-x)2091
145x=2091-2091x
2236x=2091
x=2091/2236=0.936
BB should only fold if he has less than 7.4% of winning.
Every two card holding has better than 7.4% of winning against any range of hands which include a non pair.
Therefore BB must play any two.
Case 2. SB calls.
2a. BB folds.
BB's EV is 0.0125 if button wins.
BB's EV is 0.20 + 0.0037 if SB wins.
Here BB must guess whether SB is more rational than
button. BB's EV range should be 0.08 to 0.14
2b. BB calls also.
BB's EV is zero if he loses.
BB wins and button beats SB.
BB's EV is 0.2222
BB wins and SB beats button.
BB's EV is 0.20+.0694.
BB wins about 18.5% of the time with a random hand.
BB's EV will vary from 0.04 to 0.07.
So the best strategy for BB is to call if SB folds.
Would need an extremely strong hand to call if
SB calls.
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