Re: math quiz
1. Villain folds hero wins 4K.
Villain calls hero hits str8 15% of the time and wins 10K and 85% of the time loses 4K. Net -2K.
villain folds 33% of the time to break even.
2a. Who knows. hero calls 6XBB to win 7XBB and has to be 46.5% in the hand. roughly a big hand like KQ. (tight range)
2b. Not so tight a range ~QT
3a. Hero calls 4K to win 7K and must be 36% in the hand or have an avg of 17 outs against entire range.
2/3 of the time we have 3 outs and 1/3 of the time we have 43 outs, don't call. ~15 outs. Don't call but its close.
3b. Hero needs 17 outs. 1 out ~2% (1/50) so add 4%. Villain must have middle pair 37% of the time and top pair 63%.
this is of course way too complicated for at the table calculations, you would have to have a great read on villain to even consider him having top pair more frequently than middle pair when you hold a king.
the table dynamics counts for much more than than a few percent, so I wouldn't waste my time on these details. It's close enough to be a call in the first case inspite of the unlikely circumstances.
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