Does this OP have logic behind his responses and plays?

very interesting thanks for responding. I was wondering if we look at villains re-raise on the turn

1.40/4.19=.334. =33% is how often his bet needs to work as a pure bluff to break even

If we give hero a range of: QQ+, AK. he has Ace-high 51% of the time, meaning this re-raise as a bluff is not such a bad idea since he needs to defend 67% of his range but only has a premium hand like over-pair and set a total of 48% of the time.. Although with AK he has a gutshot. I thought that part was interesting what do you think about this ?

Another thing I was thinking about was calling villains min-raise on the turn , We have about 29% Equity versus villains Check-Raise range on the turn:

JJ-TT,AQs-ATs,KJs+,QJs,AQo

we need to call $0.70 to win a pot of $4.19, we need roughly 2:1 pot odds given our Equity and we are gettiing 5.9:1, I know part of the reason of our good odds is because we just put .70c in. On the River if an Ace comes we have 50% Equity, if a King comes we have 73% Equity and if a Jack comes we have the nuts. Does this mean even on a river an A,K,J comes if we check and villain goes all in.

pot on river=$4.89

Hero checks,Villain shoves $2.58

Pot odds will be 2.89 to 1 meaning we need to be good 1 out of about 3 times and we have that equity assuming he is capable of doing this with his whole range of JJ-TT,AQs-ATs,KJs+,QJs,AQo which would be turning some of his hands into bluffs but I thought it was interesting to look at. We could also shove river on 1 of these 3 cards ? I'm not sure was just speculating the hand.