[jcm4ccc]

If he folds 37.5% of the time, then your bet is a break-even bet. If he folds more than that, then your bet increases your expected chip count. Otherwise, it's a loser.

Here's the math:

chip counts
Chips if folding: 6800
Chips if pushing and villian folds: 7400
Expected Chip Count if Called: 6440

[53s wins about 36% of the time against a combination of pairs and overcards. So if you push, your expected chip count is 6440: (.36*9000) + (.64 * 5000)]

Fold Equity needed

Solving x for this equation:
6800 = 7400x + 6440*(1-x), where x = fold equity

x = 37.5%

expected chip counts

If villian folds 37.5% of the time:
7400 chips * 37.5% = 2775 chips
6440 chips * 62.5% = 4025 chips
Total: 6800 chips (exact value if you fold this hand instead)


If, instead, the villian folds 50% of his hands:
7400 * .50 = 3700
6440 * .50 = 3220
Total chips = 6920 chips

outcome
Let's say that he does fold 50% of the time. Then your outcome is:

50% of the time you will have 7400 chips
32% of the time you will have 5000 chips
18% of the time you will have 9000 chips

So overall you gain a bit.