I am recently taking this MIT Open course, and trying to derive the Semi-Bluffing formula on my own. The formula can be found on Page 52 of the slide.
I am a bit confused about why there is a $2$ in front of the formula:
$$Fold\% = \frac{-2 \cdot BetAmt \cdot Win\% + BetAmt - Pot \cdot Win\%}{-2 \cdot BetAmt \cdot Win\% + BetAmt - Pot \cdot Win\% + Pot}$$
The $Fold\%$ required to have a positive Expected Value should be $$Fold\% = \frac{-EV_{call}}{-EV_{call}+ Pot}$$ Since $EV_{fold} = Pot \cdot Fold\% + EV_{call} \cdot (1-Fold\%)$
Where is the factor of $2$ came from?
The expected value conditional on them calling is $$ EV_{call}= Win\% \cdot(BetAmt + Pot) +(1-Win\%)\cdot(-BetAmt)$$ which rearranges to $$ 2 \cdot Win\% \cdot BetAmt + Win\%\cdot Pot -BetAmt $$