Putting a value on implied pot odds

Implied pot odds are the pot odds, factoring in how much you think you'll get paid off if you hit, right? I want to be able to put a value on how much you need to be paid off to make it worth the draw.

So a made up hand, assuming infinite stacks.

Heads up, the flop is 9h, 5h, 2c and the pot is $3.
You hold Ah, 8h - the nut flush draw.

Villain bets $2. You have to invest $2 to make it a $7 pot. Ignoring other draws you have about a 1/6 chance of hitting, so the pot should be 6 x $2 = $12 for you to have the odds, but you think you'll get paid off so you make the call.

If you hit on the turn you need to win a pot of at least $17 to effectively win on the draw (they need to invest $5 more to make it a $12 pot - the $5 you invest on the turn doesn't count towards that).

If you don't hit on the turn. The villain bets another $4 and you call again without odds. Pot is now $8 +$7 = $15, and you hit on the river.

How much do I need to win now to cover my draw? First thing that comes to mind is that it's the same as on the turn: $4 x 6 - $15 = $9. $9 x 2 + $15 = $33. This covers the turn bet, but not the flop bet. To cover the flop bet as well I think we just have to cover the difference between the cost of a good draw and our $2 (if that makes sense). That would be exactly $1 (5 + 1 = 6 x 1). So our final pot needs to be $35.

I guess that means that the implied odds are only useful if you're slightly priced out of a draw.

If anyone can do better than my calculations I'd be glad to hear.

Originally Posted by flyingPenguin

How much do I need to win now to cover my draw? First thing that comes to mind is that it's the same as on the turn: $4 x 6 - $15 = $9. $9 x 2 + $15 = $33. This covers the turn bet, but not the flop bet.

The flop bet is "covered" by your estimation that if you hit the turn you would get paid off. When you are trying to decide whether you have odds to call on a missed turn you only need to take into account the size of the pot, the bet you are faced with and how much you expect to extract if you hit. Whether your flop call was + or -EV does not influence the turn decision - your turn and river decisions cannot make a bad flop call into a good flop call or vice versa, you should just try to maximise the value of the situation you are in regardless of how you got there.

Here's the math:

Pot: $3. Villain bets $2. We call. Pot is $7. Villain bets $5. We call.

Now let's say that if my draw hits on the river (or the turn), Villain will not put in any more money.

EV= -$7 + (36/100)*$17 = -$0.88

So this is basically what we need to make up for should we hit. Thus (36/100)*x=0.88 or x= $2.44.

So we need to get atleast $2.5 on the river if we hit our draw to make this play +EV.