A Satellite Problem

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A Satellite Problem

Hi guys,

Last week at PokerStars I played a qualifier to a live event. There was an interesting situation and I would like to know your thoughts on it. The tournament was an $82 re-entry with 40+ competitors. The top two players advanced to the $1,700 live event and got $300. Third place got $320. This was the final hand of the tournament:

Table '965296476 5' 9-max Seat #2 is the button
Seat 2: Hero (63011 in chips)
Seat 6: Villain A (269219 in chips)
Seat 8: Villain B (47770 in chips)

Hero: posts the ante 300
Villain A: posts the ante 300
Villain B: posts the ante 300
Villain A: posts small blind 1200
Villain B: posts big blind 2400
*** HOLE CARDS ***
Dealt to Hero [Qc 6s]
Hero: folds
Villain A: raises 266519 to 268919 and is all-in
Villain B: calls 45070 and is all-in
Uncalled bet (221449) returned to Villain A
*** FLOP *** [6h 6d Ts]
*** TURN *** [6h 6d Ts] [4h]
*** RIVER *** [6h 6d Ts 4h] [3h]
*** SHOW DOWN ***
Villain A: shows [Ks Td] (two pair, Tens and Sixes)
Villain B: shows [Ad Kh] (a pair of Sixes)
Villain A collected 95840 from pot
*** SUMMARY ***
Total pot 95840 | Rake 0
Board [6h 6d Ts 4h 3h]
Seat 2: Hero (button) folded before Flop (didn't bet)
Seat 6: Villain A (small blind) showed [Ks Td] and won (95840) with two pair, Tens and Sixes
Seat 8: Villain B (big blind) showed [Ad Kh] and lost with a pair of Sixes

In summary, one of the players had a huge amount of chips while the other contestant and me were relatively short. The big stack, who had moved in frequently over the past ten hands or so, shoved against the smaller stack and got called by AK. This is my first question: Given the prize jump, is it correctly to call a shove in this spot with AK?

AKo is roughly a 65% favorite against a random hand, meaning that Villain A will be eliminated about 35% of the time. I think this play has a negative EV. For simplification purposes, I assumed the big stack was going to get the big prize 100% of the time since he has so many chips. Therefore, the other two players' chance of getting the entry to the live event depended on the sizes of their stacks relative to each other. In other words, I (Hero) had approximately 57% of the chips that do not belong to the big stack, while Villain A had 43%. In my simplified view, these percentages should equal to our chances of getting the entry.

Had Villain B won the race, he would have been a 3-to-2 favorite against me with approximately 59% of the chips. With this in mind I tried to calculate his EV value before the hand and after it in case he wins. Initially Villain B's EV was roughly $1,050 (= .43*1,700 + 320). If he calls and wins, his EV goes up to $1,320 (= .59*1,700 + 320). This represents an increase in EV of less than $300, which does not look satisfying considering his 35% chance of losing the race with AKo. If we consider that he gets only $320 if he loses the hand, he actually loses EV with the call.

I hope my explanation was clear enough and I wish there were no major flaws in my line of thinking. After pondering about this situation carefully, I came up with some additional questions and would like to know your opinion(s) on the subject. 

What are the hands Villain B can profitably call the shove with?

How short would Villain B have to be to make this a profitable call?

If I were in Villain A's seat and pushed all-in, could Villain B call my shove more liberally? 

Given the stack sizes at the table, what is my optimum strategy?

Thank you for your attention.

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