Ace/King vs all in short stack and loose deep pocket

Blinds are 1-2-2
Minimum to play a hand is $5
Loose deep pocket player always straddle with $10
Since he straddled, minimum to play a hand became $20

Tight player - Short Stack = $130 (button)
Loose player - Deep stack = $1800 (to the left of the button somewhere)
Tight player - Hero = $900 (to the immediate right seat of button)

Hero has Ace King offsuit and is the first to call $20
Short Stack shoved all in $130
Deep stack calls $130

1. Would you call $130 and why? You will have last position post flop
2. Would you fold to the tight short stack player?
3. Raise? How Much? What to do when no ace/king on the flop?
4. Would you all in $900? Loose deep stack might fold because I play very tight

If I knew short stack has pocket queen and deep stack will fold, is it profitable to go all in with Ace/King in the long run? Equity question here.

Which of the four options would you do and why?

Limping the $20 pre flop is a disaster. Only weak players open the action by limping in a cash game (there may be some exceptions to this, but this isn’t one of them). You have a premium holding, so increase the pot size to maximise value for the times you win. I would open raise to at least $70 in this game.

As played, no brainier re raise all in. You’re too short stacked to do anything else and we’re perfectly happy if we get folds. Also fine as well see all 5 cards and would be very unlucky to be dominated.

I don’t know how you found a game so juicy, which you could crush with a limited amount of technical knowledge. I would strongly recommend reading through the strategy articles on this site, as you’ll get enough knowledge to beat this game in no time. Just make sure you have enough money behind you to avoid going broke.

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If I knew short stack has pocket queen and deep stack will fold, is it profitable to go all in with Ace/King in the long run? Equity question here.

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Very much so. Let's make some assumptions... first of all, let's say AKo vs QQ is 50/50... even though QQ is in reality slightly ahead, but it's obviously easier to calculate when we assume a coin flip.
Also, let's also assume the deep stack always reraises the shove with KK or AA. By making this assumption, we know when he calls the short's shove that we are never dominated, we are always at least 50% against him too.
We'll also assume no rake.

So... let's forget the deep stack called for just a minute. If everyone folded to the shove except for us, and we call, well we're 50-50 vs QQ. If we play the hand twice, we win one and lose one, we'll notice that our profit is $35... the blinds and the straddle, which we call "dead money". Likewise, the guy with QQ has made $35, since he had exactly the same equity as us (based on our assumed 50%). That's an average profit of $17.50 per hand.

Now, when someone calls, and then folds, that is also dead money. So this guy puts in $130, then faces a $900 shove. He hates life and folds. Thanks, that's an extra $130 every two hands we just won.

So you can see that by getting this guy to fold, we are printing money.

If we knew that the short stack would shove, and the loose deep stack would call, then limping AK was absolutely the perfect play, so long as we now reraise all in. But I doubt that's the case, since you say the short stack is tight. Therefore, we should be raising pre flop.

Only limp if you have a really good reason for doing so. Trying to see a cheap flop with AK is not a good reason to limp.

We're assuming he never has KK/AA when he calls the first shove, but it doesn't matter if he does.

Even if he only ever calls KK+ vs our $900 shove, so long as he's calling the first shove loose enough, then that $130 every two hands he's giving to us is more than enough to pay for the times he shows us KK+. Let's also not forget that KK isn't a disaster for us, we're still winning 1/3 of the time, so our overall equity isn't hurt that much by KK. It's just AA that absolutely crushes us, and that's a 0.25% probability. In fact, we could argue it's less than that, since the short stack has a range that has lots of Ax in it.

Reraising all in over this shove and call is printing money.