Misplayed on all streets?

[-Skeme-]

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However, this move is much more profitable against someone who actually will call while holding nothing more than top pair.

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How? In the theoretical hand we're using, Villain calls your all in with as little as TPNK. When you get it all in against TPNK your odds are:

Hand 1: 50.5122 %
Hand 2: 49.4878 %

You're barely a 1% favorite. Assuming you could know 100% that he had only top pair, this would still be slightly +EV, but you can't know this. If he calls with as little as TPNK, he's also calling with two pair, overpairs and of course sets. When you factor these hands into his range, your odds are now:

Hand 1: 47.8578
Hand 2: 52.1422

With you being the dog. At the risk of sounding like a jackass if I'm wrong, this is indeed an -EV situation. Now that's just the situation where we know you have no folding equity as he has a minimum of TP.

I'm terrible in math so I can't figure this out, but it seems the only way this situation becomes +EV is by getting the right number of folds to your all in bets. I don't know how often this is or how to calculate it.

Edit: Alright, this is a hard topic to talk about for me. In an actual cash game there is ALWAYS fold equity. In my theoretical situation there wasn't, making this difficult to analyze.

Your pot odds, as well as fold equity, play an important role in determining whether or not this 52/48 situation becomes +EV. Your % of winning the hand needs to be compared to how much money you've invested into the pot with your all in bet only. You also need to factor in the pot size when called.

If there is $50 in the pot and you push on your flop for $100 and get called, the pot is now $250. This means you must have greater than a 40% of winning for this to become +EV. Since you have a 48% shot, this becomes a profitable situation. Even moreso when you understand that you will have some degree of folding equity as he can't ALWAYS have top pair.

The above example is for the situation when your all in is called by TP and above. Does this make sense?