Quote:
Originally Posted by just_grindin
Now keep in mind we ignored any equity your hand might have when it is called, ....... All of those can affect how successful your bluff needs to be on this street to be profitable. There is no mathematical formula that will get you that information .
I’m puzzled why you claim this.
For the case you specifically considered, a hero bluff, assume the bluff has equity EQbl. Then
EVhero-bluff = F*P+(1-F)*(EQbl*(P+B)-(1-EQbl)*B),
and you can solve for F in the same way you did when EQbl=0.
F= (EQbl*(P+B)-(1-EQbl)*B)/( EQbl*(P+B)-(1-EQbl)*B – P),
which reduces to B/(P+B) when EQbl=0.
Of course, the equation also provides much more information. For example, a bluff has to be successful at least 1/3 of the time if you make a pot size bet that is called.