Breakeven Math Bluffing Question

[LivingTheDream]

200NL

Let's assume villain has been betting the whole way and on the river bets $20 into $83. I have position and effective stacks behind are $160.

I think I might be able to bluff him so I look at 2 options.

Bluff all-in betting $160 to win $103
Bluff $80 to win $103

What percentages of the time does he have to fold in each of my scenarios for this to be a profitable bluff?

[Ringmaster]

Suppose p = probability villain folds.

[ QUOTE ]
Bluff all-in betting $160 to win $103

[/ QUOTE ]

EV = p(103) - (1-p)(160)

set EV = 0 and solve for p to get:

p = 160/263 = 60.8%

[ QUOTE ]
Bluff $80 to win $103

[/ QUOTE ]

Using the same logic as above we get:

p = 80/183 = 43.7%