43 players left in a Final Phase tournament, Top 40 get a $530 ticket to a PKO event. I've basically freerolled my way into this spot over the course of three consecutive satellites and I figured I was (pretty much) save 10 minutes ago. As it turns out, I get zero hands for two orbits plus I get jammed on in every blind by players who seemed super tight.

Now we're in the BB with a 2,3bb stack, 40bb stack open jams (I have no clue why big stacks who should be done with the tournament bother doing this, but whatever), everybody folds and we look at TT.

I feel like I have the basics right in satellites but I tend to get lost in this type of spot. Do I have to call this off? The big stack should do this super wide and we have a decent hand that should be way ahead of his range. Also, winning this hand basically guarantees our ticket while folding w 1,3bb left means we'll be all-in within the next 7 hands anyway and we have no clue what cards might come.

As for folding, 1.3bb would make us the shortest stack and it will be obvious to everyone that we will be bleeding off our last antes after this hand. The guy in 40th spot has 2.5bb and he only just went through the blinds. According to the "gorilla math" in "Poker Satellite Strategy", the player in the last place which earns a ticket should have a roughly 50% chance of making it so our 1.3bb stack - assuming we fold - would indicate our chances are about half that.

I feel like we have to call it off when we look at the math, but is this still a "fold now and hope for the best" type of spot?

Well, you said it yourself - folding good bed you about a 25% chance of getting a seat. If you call, even if big stack has AA-JJ you still have a 20% chance of doubling up. That gets you about a 50% chance of cashing. If villain has two overs you have a coin flip; about a 50% chance to double up to give a 50% chance to win the seat. That is close to neutral. If villain holds anything else you improve your chance to win the seat.

Since the two overcard hands are approximately neutral, we can ignore them in the analysis. Does villain have more combos that give >50% winning chance than he has JJ-AA combos? I am not sure; it might be dependent on villain, but if he shoves 66+ or something along those lines, the 77-99 combos almost balance out the JJ+ ones. Not sure if he is shoving any non-pair combos with a T or lower in them, but if he is then the call is clear. If he is not shoving that wide then a fold might be in order, although you likely won’t get a better hand before you are forced all in, so I am leaning toward a call.

Is the 40BB stack jamming into any other bigstacks? If not range is likely to be much wider & is a slam dunk call - If there is a player that covers them then its a bit more dicey but still a call imo - if we fold we have to post nearly half our hand on the small blind so we are going to have to gamble at some stage

Thank you for the responses so far.

Villain only had <6bb stacks to his left, so he wouldn't even need Ax or Kx to do this (assuming he's a bit of a prick and/or in a hurry lol)

Just one minor point on this one, and I may have ****ed this up in my OP, but calling and winning actually implies way more than "only" doubling my chances, I think. My stack would be almost 4.5x the stack (2*2,3bb+0,5bb+0,7bb in antes) I would have after folding. Having close enough to 6bb is actually MASSIVE in this spot. Even in the worst case, this would be more than two full orbits worth of blinds and antes and I could obviously stall every single hand so I may not even have to pay all of those before the bubble is over. What's more, I would cover the three players to my right. From my limited experience in satellites, money automatically tends to flow toward the bigger stacks given that noone will want to mess with you.

Calling and winning is pretty much 100% winning the seat.

I will admit I didn't think about it that way, but even calling it off bad vs JJ+ wouldn't make a massive EV difference compared to just folding but you obviously want to avoid doing that.