I am looking for information on the EV of made hands and draws on the flop. I have looked but found very little.

If you flop a made hand, AA or 22 or 555. If you flop a flush draw with a pair, a gutshot or have AKo hole cards. There must be some EV associated with each. There is a huge difference between the hands in this simple example.

Obviously knowing the EV ( even approximate ) would be very useful in making flop decisions.

Has anyone done research on this?

Pseudo GTO solver software does this sort of thing. The solvers not only work out a near-unexploitable strategy, they can tell you the EV of each combo in your range on whatever board texture you input.

On a more basic level, you can calculate your equity (chance of winning at showdown) with free software like Equilab, by inputting a range for your opponent, and running your hand against that range. There's clearly a pretty strong correlation between winning chance ("equity") and EV, although it's not perfect, because some hands don't realize their equity as well as others.

What I was looking for is the EV of the draw on the flop, not the EV of the hole cards. The flop plus the 2 hole cards.

What is the relative value of a OESD vs OESD-pair vs. Flush draw, vs 2 pair, vs a set, with 2 random cards to follow.

EV may be the wrong term. Maybe Equity. Not looking for ranges, just the hand with the 5 cards available to me so far.

The draw is never worth less than the immediate odds of hitting the draw on the very next card. Implied odds can increase this value, and lines of play that increase the chance of the draw seeing a river also increase this value. Reverse implied odds can decrease the value (you are drawing dominated or even dead).

Absolutely correct! What I am seeking is a way to estimate and quantify the value. I think simulation would be a possible method. I am wondering if there is a better way.

The draw is never worth less than the price of the call else we should fold. The actual profitability of the draw depends on the overlay from the pot. In no limit holdem facing 1/2 pot to pot sized bets, the profitability of draw that's going to hit about 18-30% on the next card is not as high as the above statement implies.

I drew this primitive model as an aide to visualizing pot distribution:



Now when you call a 1/2 pot bet with an 18% out draw, you either need to justify this through implied odds, free river cards, pair outs, profitable turn calls, profitable turn bluffs, or profitable river bluffs. What does this tell you about the profitability of other draws, like a monster draw that's going to hit a monster on the turn 33% of the time when calling a pot sized flop bet with 3 pots behind?

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Value hands are different. With monsters, you're earning >pot if there's more money to be won or lost. When you bet something like top pair on the flop? You're not actually hoping for a call because picking up the pot gives an ev of (pot) of course; when you get action with top pair, you've actually reduced your opponent's share in the pot, which naturally increases your share in the pot. So you invested 30% of the pot on a 3 way flop, then you bet a good hand and get one call, which reduces the profitability of your opponent's range to a value between (price of call/pot)* and price of (price of call/pot + overlay expressed as a fraction of the pot).*

*which is exactly what happens in the (nuts + bluffs) vs (bluffcatchers) game.

**which is what happens when a range contains the proper mix of (hands that can call overbets) and (draws of every kind) and (slightly profitable bluffcatchers) and (junk)

If I had to guess at the actual profitability of calling a 1/2 pot flop bet with various hands, it would look like this:

(hands that can call overbets) = range from (>pot) to (75% pot share) on the flop.

(draws) = range from (25% pot share) to (50% pot share)

(profitable bluffcatchers) = (25% pot share) to (65% pot share)*

(junk) not applicable; fold = 0ev = 0% pot share facing a bet.

*I think this value is directly influenced by draw potential to improve to a hand that can raise the likely turn and or river bet.