As a result of a hand I played yesterday where I made 2-3 good bets with AKs with four to a flush and then one bad one when a brick hit on the turn I made a realization.

AcKc has ~54% equity against Ts9s on Th6c2c. But I was thinking, what is the difference between raising on the flop and raising on the turn?

On the flop any action besides folding is +EV because we have more than 50% equity and our opponent has to choose now.

On the turn, we can either hit one of our outs or a brick. The EV of turn action depends on whether we hit or not. And for example the 3 of diamonds will send us down to 35% equity.

But then I asked myself how do we calculate EV if hero shoves on the turn IN THE DARK before the turn card actually shows?

Because in that instance hero still has 54% equity; that cannot have changed as there are still two random cards to come.

But the EV calculation has changed immensely because (assuming perfect play) villain will fold when he's beat and call when he's not. As long as the size of our all-in is large relative to the amount already in the pot, this makes shoving blind a -EV play even though it was done with greater than 50% equity.

So my question is are there other situations where it is -EV to make a play even with more than 50% equity heads-up, more than 33% equity 3-way, more than 25% equity 4-way etc.?

Or does this only happen in the contrived example of us making a decision with only knowledge of the flop while villain knows what the turn is?

Hunh answered my own question, can't believe I paced around my apartment for 3-4 hours thinking all this through when it seems so obvious now.

For example, imagine a couple poker bots playing each other. One bot is programmed with the exact ranges of the other bots, so it knows its pre-flop equity perfectly. However, this bot is programmed to shove KK 100% of the time pre-flop.

The other bots are aware of this and will always fold to KK unless they have AA in which case they call.

This means that even though KK has greater than 50% equity against the ranges it's playing against, it's still -EV (if stack sizes are large relative to normal pre-flop bets).

Although this has helped me realize a meta-strategy: Some of my underlying assumptions for EV I used from blackjack card counting DO NOT APPLY, AT ALL. And that means that my original goal of getting money in with good equity is garbage, EV is the only thing that matters. Although it can't be accurately calculated without my ranges, my opponent's ranges, my opponent's percentage to call with each of their holdings, and their percentage to fold, raise, or any other option they have on any board runout.

You think you have >50% equity, which is a “valid think” because you haven’t seen the turn card but that doesn’t mean it’s applicable to the situation. This is so because villain will not react to your blind shove until he has seen the turn card and will then act accordingly. Therefore, your actual equity does include the turn card, and it may be less than 50%.

Therefore, the contrived example doesn’t support the theory that you can make a negative EV play with equity greater than 50%. However, mistakes you can make with such equity is taking an action that doesn’t maximize EV such as checking on the river to an opponent who is most likely to also check whereas a value bet would be much better or betting so big with a monster hand that villain will almost certainly fold.

The situation you described in the OP isn't one to begin with, so framing this as "are there others" is misleading. If you use the same logic you could say extend it to comparing shoving AA preflop to shoving AA blind on the river, obviously the latter is not a +EV play.

More holistically, EV correlates strongly with equity but not entirely. For example if you take a blind vs. blind SRP hand on a T43r flop, 56 might have about the same amount of equity as K8 vs. your opponent's range but has higher EV since your equity distribution is more polarized. I've seen this called visibility, valor, realizable equity, and some other terms but nothing really commonly used.

You can certainly make -EV plays even with more than 50% equity. Imagine you have a pretty good hand that can profitably value bet for half pot vs a range of nuts + bluffcatchers. If instead of betting half pot you bet 1000x pot, youre making a -EV play, since now no bluffcatcher will be needing to pay you off and youll get called only by the nuts and lose a ton of money when that happens. You would be better off just folding.

Regarding your example, a shove on the flop is profitable because it takes into account the fact your opponent is paying that bet to see turn and river. A shove on the turn (in the dark or not, its the same to him) is not profitable because now your opponent would be paying that price to just see the river (he got to see turn for free), and now you have 35% equity when called instead of 54%.

Came back to this, I think I can summarize better:

While contemplating a raise, even if hero knows villain's range exactly and has greater than 50% equity against it, the only way to know if the bet is +EV is if hero accurately knows the chance villain will fold and the equity % he will have Against The Combos That Call.