[Double Down]

I would disagree with pushing the flop after he bets 400. There is 100% chance that he calls, and with him completeling small blind but not raising, he almost certainly has some piece of this flop. I would venture to guess that you are behind, and essentially you are less than 50% to improve (you have 11 outs, if you include the king). And if he turns over straight draw and a pair, then you need to hit the straight just to chop and your only clean win is to hit the king.
The sad fact is that the odds of you coming in 1st are very very small because of the stack sizes and you should try to go for second. The best way to do this is not to push in when there is no fold equity and he is probably beating you!
If you are looking for that slim opportunity to try to get 1st, then the best chance to try to double up is when you get all the money in first, before the flop. Don't push here. You got enough chips left, try to get 2nd.