Hand 1:
$1300 effective.
Only capable player raises to $35 in the CO, I 3 bet to $120 OTB with AK. Blinds fold.

Pot: $255

Flop: 2h4d5c
CO checks. I?

I think checking and better are both fine? I think betting with AK might be better because it can get called by AQ or AJ. But I checked.

Turn: 3h
CO checks. I check

River: As
Villain bets $450. What's the math behind a call?

So let X = the chances that villain has a 6 high straight or better.

-$450*X + (1-X)(($450 + 450 + 255) / 2 )=0
577.5 - 577.5x = 450x
577.5 - 575x = 450x
577.5 = 1025x
x = 577.5/1025
x = 56.3%

So this seems high and I think I did something wrong? So I need to tie at least 100 -56.3 or 46% of the time right?