soccerskills123

On River we have 3 Value Hands and 1 bluff. ( 3:1) Ratio.
Villian has only a bluff catcher.

I'm i correct in assuming we should bet 50% of the pot. Therefore Villian gets 3:1 odds on a call, therefore zero ev when he 75% of the time, as are value/bluff ratio is 3:1. His Maximum Ev=0
and If i bet Pot and he calls 67% of the time I lose money as i would need 2:1 Value to bluff combos for his Ev to be zero given he calls ??
And if i was to be 1/4 Pot i would and he called 83% of the time i would lose money as i would need a 5:1 bluff/value ratio?

So.....
1-(A) = The frequency we need to call to stop villian auto profiting from bluff.

I'm a bit confused with how the related to the pots odds we need to call.

Eg.
Villian bets Pot on river.
A=0.5
1-A = 0.5

So if we want to stop Villian auto profiting we need to call 50% of the time.
But using Pot odds we only need the call 1/3 of the time or have 33% equity vs his range.

So we get to a river and our hand that is at the bottom of are top 50% of hands has less than 33% equity vs his range.
Do we call to stop him auto profiting from his bluffs or fold because we dont get the correct odds??

And im confused.... Can anyone help explain.

8k/16k ( 800 ante ) 9 Handed. 40 left in 500ish runner tourney.
Average stack = 350k
3 big stacks next to each other.. rest of stacks <350k. New to table both big stacks been fairly active from limited time ive been at table.

UTG (550k) Raise to 40k
UTG+1 (700k) Raise to 100k
HERO UTG+2 (600k) I've got Jacks......
Rest of table (80k-300k)
tough spot... UTG+1 shouldnt be light here as he's committed against a lot of the players behind him.