To keep the math clean and well rounded say you have a 20% flush draw on the turn heads up with a pot of $100. Villain bets $50 into it, you call hit your flush then donk bet $50 on the river and win. So our risk was $50 and our reward was $200 I.e we got 4:1 and we broke even

But say we replay the exact sequence but this time he calls river with a higher flush and he wins.

Do we now say the risk was 100 and the reward was potentially 200. So we essentially risked 2:1? What I’m trying to get at is: do we keep the reward the same but tag the river bet of $50 on to the initial risk of $50 to get a total risk of $100?

In other words what exactly was my risk reward ratio after the fact?

A complete implied odds model should include the following:

You may not hit your draw
If you do hit you may not win
If you hit villain may not call

The following blog is part 1 of a 7 part series covering this with applications

https://holdemmathology.tumblr.com/p...-part-1http://

Thanks I’ll have a read of that but I was hoping for a specific answer to that specific example. I’m guessing that I might be trying to mix apples and oranges in that there are two seperate events that took place and not one. The first was a 3:1 event (turn) and the second was me risking 50 to win 200. Two seperate risks of 50 each time. I can’t combine them and say my risk was $100

Or (as your post says) it is just the one single event but reverse implied odds is part n parcel with the turn decision and must be factored in at that decision point (in a long term sense). Ok gotcha.

Correct. The model I described includes both implied odds and reverse implied. It includes hit probability, win given hit,current pot, hero call amount and future bet size along with villain future call probability.

nice work there statmanhal

Seperate it out into every conceivable scenario.

1) We call and miss our flush and lose the hand. - $50

2) We call and hit our flush then donk bet 1/4 pot:
2a) and villain calls with a worse hand. +$200
2b) and villain calls with a better hand. -$100
2c) and villain folds: +$150

Weight each scenario according to their probability then sum together to find your expected value. So in this case let P(1) equal the probably of statement 1, and so fourth:

EV = (P(1)* -$50) + (P(2a) * $200) + (P(2b) * -$100) + (P(2c) * $150)

Note that it's impossible to calculate your return without assuming some probabilities for P1 and P2. You could add as many scenarios as you like. Maybe you hit your flush, donk bet, and villain RAISES with a better flush and we call. Or maybe they raise with a worse hand. Or maybe we don't hit our flush but somehow still win at showdown. You can make this equation as complex as you like using the above method.

This is the right idea and is nicely laid out; it is basically what I did. Two comments. 1) I think the donk bet is 1/3 Pot. 2)Your example did not include reverse implied odds –H hitting and betting, V calling and V winning, which was the main issue in the OP.

1) On the river we're betting $50 into $200 right? We called the $50 turn bet so the pot on the river is $100 + $50 + $50

2) Reverse implied odds were included in 2b "we hit our flush, donk bet, and villain calls with a better hand".

Wow that’s epic. I’m gonna do some experimenting with this blueprint.

Great aspect of poker that most opponents don't consider during game play ... and are quick to complain about after the hand ("You called with nothing but a ... ?!).

Implied Odds are similar to set mining IMO. Although I'm all in on the value of the EV calculations above I think you need to take the mind set that you need to anticipate getting paid a little 'extra' for the risk. I wont even bother chasing spots like this when I don't anticipate an opponent paying me off (and is one who can't be bluffed off a blank River).

You could take this a bit deeper and bring in two other EV factors as well ...
1) How often can I raise my opponent off the pot on the Turn and win now? Obviously all of the numbers above get inflated when the opponent calls.
2) How often (at what size) can I bet my opponent off the pot on a 'blank' River?

I think those aspects are very prevalent in (high stakes) tournament play when the stacks start to get shorter.

It's probably a huge flaw in my game. But I've never really considered making an implied odds call on the Turn and then 'only' bet out 1/4-1/3 pot on an improved River. Based on my normal table image I can bet out 2/3-3/4 and it wont change the call/fold ratio one bit. This is probably a huge difference between online and live ... I'm never Donking a River for less than 1/2 pot in any of my cash games whether I'm looking for folds or calls.

There are times, against the 'right' opponents, that I can make a Turn call knowing the only way to win the pot is to use a flush card as a bluff. These opponents give off bet sizing tells that let me know they are afraid of the flush.

As usual, I'm probably muddying up the waters on a great topic .. but .. GL

Answer I’ll reply to you separately later

Statmanhal what I think would be fascinating is if you took that list of variables that you’ve thought up and created a spreadsheet that allowed you to input the answer to each line and the spreadsheet gave a summarising ev avg for the decision. If I was good with spreadsheets I do it

But adding to this you could add weight to each line

I.e
We call and miss x number of times out of ten
Villain calls with a worse hand x time out of ten

Etc etc then find the avg of everything when the weight has been factored in

I already did and it is described in the following 2+2 post. You need not include all that I did but if you know basic Excel, you should be able to develop your own spreadsheet.

https://forumserver.twoplustwo.com/3...21/index2.html

That's what the probabilities are for. I'm just using percentages rather than x/10.

So for example, say you hit your flush 20% of the time, and when you donk villain will call with a worse hand 80% of the time. The probability is then just 80% x 20% = 16%.

All the probabilities should sum to 100%. I might make and share a Google sheets thing later today just for the fun of it.

I think reverse implied odds are a myth. If you think about equilibrium, and come to the important realization that equilibrium strategies never make a negative ev play vs opposing equilibrium strategies, then you will see that future street negative ev calls are caused by opponent deviation from equilibrium and that these future street negative ev calls are always more than compensated in the form of free cards, free showdowns, or an increase of draw ev.

In addition to this compensation of ev, if you have the nerve to fold negative ev bluffcatchers on future streets when your opponent bets a non equilibrium range that is value heavy, then you will gain exploitive profits.