Math is stupid
So I did the math on this one.
According to ICM, folding leaves you with approx. 25% of the prize pool.
If you push, you need a FE of 25% to make this play better than folding. Given that he's a slightly weak-passive typical 22 player, he probably won't fold this enough to make this play correct (somebody correct me if they think a player like this *will* fold more than 25% of the time). So pushing is probably worse than folding.
To analyze calling is slightly more difficult since you will occasionally hit and lose, miss and win, and hit and win more than the amount you've called. To simplify, I'll assume you win iff you hit an ace or a king. If you lose you're getting about .218 of the pool and if you win you're getting about .316. This averages out to about 25%, which is about the same as folding, unless you think your opponent will make horrendous errors in judgement post-flop (which is also quite likely at the 22s).
In conclusion, calling is probably best, folding second best, pushing worst unless you can get a higher FE.
In the actual hand, I pushed, he called with KT and won and I got 4th.
P.S. Thanks to Yugo who worked a lot of this out for me.
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