I'm just returning to poker after a long hiatus and I am extremely rusty to the point that I've lost all basic math concepts. Please can someone help me out with the maths in this spot and the calculations?

This is a very specific situation, but I just want to make sure I'm understanding everything as I really have forgotten almost everything!

Hero: A A
Hero stack on turn 300

Board: 5 9 K Q

Pot: 253
Villain over shoves for 300
Hero to call 300 in a pot of 553

Villains exact range
AA, KK, QQ, AK

Q1: Given the board, and hero holding, the range above comprises
AA: 1 combo (2*(2-1))/2
KK: 3 combos (3*(3-1))/2
QQ: 3 combos
AK: 1 combo (1*1)

8 combos - correct?

Q2: 553:300 = 1.84:1 = 35.2% (1/(1.84+1) which means I need equity of at least 35.2% for a +EV call

Correct?

Q3: I only beat 1 combo = 1/8 = 12.5%

However when I put this into a calculator, my equity is 7.81% comprising win of 2.84% and tie of 4.97%

Can someone please explain the 7.81% against the 12.5%?

I think I partly know the answer, and I think I need to weight all the possible outs for each potential hand combo but I'm not 100% sure. Eg against AA I chop for every card that's not a heart, for KK/QQ heart combo I win for every A, for KK/QQ no heart combo I win for every A, but drawing dead against AK and so on and so forth

Q4: Given my true equity is 7.81% against 35.2%, I can't make the call.

Correct?

Thanks in advance. I know I won't be doing this at the table but I'm just trying to switch my brain back into poker mode after 10 years

300 to call to win pot of (253+300+300) = 853

equity required to profitably call = 300/853 = 35.17% (ignoring rake)

Q1: Correct, there are 8 combinations of hands that you've listed.

Q2: Also correct, (ignoring rake)

Q3:

Yes, if you wanted to do it out by hand you'd break it down for (% of range)*(equity) and go through it all.

Q4: Under the assumption the range you gave him is correct, then you would not be able to profitably call.

Great, thank you!

No problem, welcome back and good luck.