Poker Theory Question: Can a -ev bet be the best play?

[ThrillCory90]

I don't know if how many people in this forum are interested in poker theory, but this came up disucussing this hand http://www.badbeatspoker.net/forum/h...-decision.html

on a different forum.

Basically, I have always thought, read, and heard that for a bet on the river to be profitable, you have to get called by worse 50% of the time or more. It makes sense because if you bet and get called by better most of the time you are losing
money you coulda saved by checking. But I started thinking, and maybe this -EV bet can be the best play in certain situations. If somebody could look to see if I made a mistake in my reasoning I'd appreciate it. Here was my argument pertaining to the river decision of this hand:

Party Poker $100.00 No Limit Hold'em - 2 players - View hand 164631
The Official DeucesCracked.com Hand History Converter

BossenNadde (BTN/SB): $100.00
Hero (BB): $145.00

Pre Flop: ($1.50) Hero is BB with K A
BossenNadde raises to $3, Hero raises to $11, BossenNadde calls $8

Flop: ($22.00) 9 8 K (2 players)
Hero bets $17.00, BossenNadde calls $17

Turn: ($56.00) 4 (2 players)
Hero bets $23.00, BossenNadde calls $23

River: ($102.00) Q (2 players)
Hero checks

-----Added 26 Jun 2009 at 03:39:50-----

So what I'm wondering now though is, do we need to have over 50% equity against villains calling range for the shove to be best though.

We have 3 options, check-call, check-fold, shove ourselves

Let's assume we have at least over 25% equity over his shoving range. Then we can automatically eliminate check-folding as an option since we have the pot odds to call. So now the options are between check-calling and shoving ourselves.

But, as I already argued, I believe his calling range is wider than his shoving range. Since we are never folding, if he has a better hand we are getting all-in regardless of if we shove or if villain shoves. So we might as well shove and get called by a few more worse hands. The range of hands that is calling our shove but not shoving themselves we have 100% equity over so we should shove.

This is interesting because with the assumption that he is calling range is wider than his shoving range, we can possibly have as low as 25% equity over his calling range, and still have a shove to be the best play. I always thought that you needed 50% equity for a bet to ever be better than a check, but this is not the case if my argument is correct.

OOP, If our equity over villians calling range is less than 50%, we should still shove if the (equity over villians calling range)>(equity over villians shoving range) and check/calling is at least break even.

Of course if we don't have enough equity over villains shoving range for check-calling to be break-even, none of this applies and a check-fold is the best play. This I am still unsure of. It is really close.