Looking back at SNG #2

In SNG #2, I was in a position where I thought I had 51% to win the hand with 4 players left. I had T2500 (before the blind) and the button had T2300. He raised T500 and I raised all-in. I had thought the chances he would call was high. I also thought if he called, I'd have about 51% chance to win the hand. Was this worth it?

After using the SNG EV analyser, the answer is clear: NO WAY JOSE

Assume for a sec, that he's definitely calling.

I am 51% to build my stack up to 5000. In which case I have as many chips as the other two players and have an equity of $200/3 = $66.67. So 51% x $66.67 = $34.00

But if I fold, I am left with T2300 and an equity of $39.78 (per the SNG EV analyser).
So assuming he calls my raise 100% of the time:
$39.78 (folding) > $34.00 (raising all-in)

That's a no-brainer - I should have folded.

But let's give me the benefit of the doubt and add in the possiblity he will fold to my raise. What happens to my EV if he folds?

I go up to T3000 and he goes down to T1800. My EV is then $45.96

Assume X = the probability he folds

My EV of raising becomes:
$34.00 x (100% - X%) + $45.96 x X%

What does X% need to be for it to be equal to $39.78 (the EV of folding)? It is about 48%

$34 x (100% - 48%) + $45.96 x 48%
$17.68 + $22.06 = $39.74 (close enough to $39.78)

So my opponent needs to fold greater than 50% of the time for my raise when I have 50% chance of having the best hand to be worth it.

Actually it is possible that is the case. After getting a few more hands of experience, it seems the button when down to 4-handed is often willing to fold when raised all-in. That's because they don't want to get eliminiated on the bubble, as well as the fact they are likely raising without a very strong hand.

So the all-in raise may not be wrong after all. More thinking to follow.