Tired, so I couldn't figure out the proper play, good sign to stop playig. Which way are the odds pushing me here?

PokerStars No-Limit Hold'em Tourney, Big Blind is t400 (3 handed) from (Format: Bet The Pot)

saw flop|saw showdown

BB (t600)
Button (t5995)
Hero (t8405)

Preflop: Hero is SB with , .
1 fold, Hero raises to t800, BB calls t175 (All-In).

Flop: (t1025) , , (2 players, 1 all-in)

Turn: (t1025) (2 players, 1 all-in)

River: (t1025) (2 players, 1 all-in)

Final Pot: t425
Main Pot: t425 (t425), between BB and Hero. > Pot won by BB (t425).
Pot 2: t600 (t600), returned to Hero.

Results in white below:
Hero has 6h 2h (one pair, queens).
BB has 6d Jc (one pair, queens).
Outcome: Hero wins t600. BB wins t425.

Shove any two cards.

Seriously.

K cool.

My only dilema is, he's got the odds then to call with any two cards.

There's got to be a minimum equity vs a random hand to make this play +EV. (Apparently the converter screwed up the pot size. He should have won a pot of 1225. 200 + 400 + 75 in blinds and antes, then my 200 to complete + 175 to raise + his 175.)

(Ignoring the EV of possibly knocking him out, since thats difficult to quantify Real $ into TC) So knowing I'm going to be now risking 375 to win 1225, that's 30.6%, or about 2.3 -1. So I should fold any hand that is < 30% to win HU here. Which, on my trusty chart, the worst hand HU, vs a random hand, is 32o at 31.2%.

So yup, even without having to figure in fold equity (probably none anyways), putting him in with any two here is the correct move.

The problem with "getting him next round" is there's no reason to think you will definitely get a significantly better hand next time, and by folding, you are doubling his stack for free. Even if he wins the all-in now (probably as a 65% favorite, which is nothing that special), he still has to double up again to get back in there. But by folding, you guarantee he has already doubled his stack, and then only needs to win one all-in to get back in the game.

This is a very clear all-in with any two cards.

edit: Oh yea, and even though you have little fold equity, some people still will fold anyways.