It doesn't mean you're making -ev plays, you're right. But it does mean it is possible to lose more than the 1 sb you put it on the flop. Even if you're making +ev plays on later streets, you can and do still run into reverse implied situations all the time. This is a concept that just isn't understood very well by very many players because they've never done the math and so don't see exactly the mechanism by which it works.

Take the calc for this hand and instead of giving hero 3.295 outs, give him 0.00. The result with this play and any other situation where we have net negative implieds will be a loss greater than the average bets you put in on the flop (or turn, as the case may be). The reason being, in this particular case, is that the odds we're being lain to make our b/d hand are not quite as they seem. We aren't being asked to pay 1 sb to make them, we're being asked to pay more. In this particular hand, I seemed that number to be 1.92 sb (1 sb + average turn sb * avg vpip turn cards) / 47).

Let's say I were running a lottery that cost $5 to enter and one winning ticket was drawn. The winning prize was a chance at a +ev proposition, getting $1,100 : $200 on a fair coinflip, and I were offering you, the stinkypete, a chance to buy a ticket or three. If you know the chances of you winning the lottery drawing are 99:1, is this a good bet? You could look at it and say "oh, chance to win $1.1k risking $5 and the odds are 199:1, so obv a good bet." You could also say that even if you had 0 equity - i.e. you could look into the future and see you were going to lose the coinflip despite it still being a random occurrence - the most you could lose is $5. But you'd be wrong on both counts. Even though you are spending $5 for the opportunity to make a +ev wager later on, your gross cost is still greater than $5 and therefore you are liable to lose more than $5 if your equity were zero. In this particular lottery, your gross cost is $7, so if you were to never win a coinflip you'd lose more than the initial cost, despite the only future decision being +ev.

On an unrelated note, running this lottery would be worth $0.50 per ticket sold.

I never said anything about playing bad. You seem to be implying that net negative implieds do not exist for a player who plays well, which is certainly wrong. The fact is, net negative implieds exist, even if you are a winning player. It has nothing to do with making bad plays; it's just a random statistical situation that occurs in poker, and sometimes players, even winning ones, through a combination of somewhat random occurrences (i.e. the ordering of the deck and action of opponents) find themselves in it. And when we do, our average gross loss will be greater than our original call.

i don't understand what you're trying to say, but the EV of the $5 initial cost is -$5 and the EV of the 1 in 100 chance at getting $1100:$200 on a coinflip is $4.5. putting the $5 is a bad bet. you have implied odds (which allow you to recover, on average, $4.5 of the $5 you bet originally). this is not a reverse implied odds situation.


no

It was simply meant to illustrate how you can lose more on average than your initial investment, even if all future investments are placed at +ev.

The calc I did for Justin's hand makes it possible for the ev of the play to be less than -1 sb. If you think that's impossible then where is the mistake iyo?

i will find it.

There easily could be. :/ Thanks for checking.

Oh man. Thanks for forcing me to go over the calc again. I forgot a whole step in this process, though it isn't necessarily related to it being possible to come out with a result of less than -1 sb. It will increase the ev of the play though once I make the changes. Hold on..

Okay, so I forgot to discount -0.9 for the times we put in that avg 0.9 bb on the turn and then get there on the river. So we find the average number of outs we have for the 24 cards by taking the weighted b/d outs we came up with at the beginning and finding an average. In this case, we'll have an average of 6.3083 outs on the turn when we vpip.

6.3083 / 46 = 0.1371
0.1371 * -0.9 bb = 0.1234 bb

So we get back ~14% of our bet(s) on the turn on average, and since our average bets put in on the turn is 0.9 bb, we get back 0.1234 bb.

-0.9 + 0.1234 = -0.7766 bb
-0.7766 * 24 = -18.6384 bb

So take my initial turn bet total and add 2.96 bb we get these:

+3.954 bb on turn per 47
+5.6015 bb on river per 47
-18.6384 bb on turn per 47
-1.7279 bb on river per 47
Sum = -10.8108 bb per 47

-21.622 sb per 47 implied
+2.425 sb per 47 immediate
Sum = -19.197 per 47 net

EV of flop call = -0.4084 sb

Also just realized I made a mistake in labeling outs. Ugh. Will correct in a bit.

Agreed, if there's a decent chance at a free card on the turn, go ahead and peal one if you want. Otherwise, i say fold, who cares about this pot. It's so close either way. Go ahead and fold, unless youre really really feeling a runner runner moment. Plus, the Problem with hoping for a free card is that when you do get one and you make your hand , chances are youre not getting paid much on the end. If at all. (Above, if you enjoy having a tight solid image)

Call and if you catch a dream turn, 7, J, or even 6 or Q of your suit. Perfect spot for a play, maybe they'll fold (c/r), or maybe you'll spike your hand and set someone on tilt. (Above, action, loose image.)

Either way, this feels like chasing a little to much for me. Muck it prolly.

ps. have a nice day

I made a stupid counting error in vpip cards to give us outs and had 2 more than what we actually have.

After correction:

EV of flop call = -0.332 sb

Math is for nerds. Nothing's funner...

daver is a nerd

Not me.

I can't decide whether I'm more appreciative of the effort which resulted in your first post in this thread or for the time you took to think about the equation and then make corrections: TWICE.

Either way, thanks for the EV calculation.

I'm actually going to try to understand GoT. Guy, I hope you don't mind explaining a few things --

Can you explain where the 43.705 comes from?

Isn't this just the sum of the turn cards that will improve your hand to cause you to call a turn card? Shouldn't it be 26 based on the outs in the beginning of this calculation?

Edit: GoT, I think you already noticed this error.

There are (roughly) 47 unknowns after the flop, so if we have determined we have the equivalent of 3.295 outs after discounting, we will win 3.295 times out of 47 and lose 43.705 times. I saw "roughly" because really we are putting all our opponents on at least some semblance of a range, especially the PFR, and ideally should be weighting whatever ranges we are using into how many unknowns are left in the deck. If we had perfect information, i.e. both opponents hands were face-up to us, we would have 43 unknowns, but because we have imperfect information we really have somewhere between 43 and 47 unknowns. Doing the Bayesian analysis and weighting for this would take enough time for a small enough difference that I don't think it's worth it, for the most part, and I rarely make the effort, though it would allow for much more precision in determining outs and out reductions. The biggest problem with doing it in this hand is how wide the blind's range is.


Isn't this just the sum of the turn cards that will improve Actually I gave us 2 too many outs to vpip the turn. I didn't label the outs when I listed them and probably should have, since even I made a mistake and I'm the one who wrote them down. I discounted 2 off that list initially because they are over-lapping. You'll note I lumped all 10 flush cards together and discounted off of the number 9, when in reality 4 of those flush cards also give me straight draws. Those extra outs are accounted for in 2 outs for 6 and 2 outs for 3. When I went back to count how many cards to vpip, I knew I had overlap, but only discounted 2 instead of 4, so my number should've been 22.

Folding and calling are both fine, they have about the same ev closing the action here. Getting 14 to 1, the outs you need are about 45/14, which are probably close to what your adjusted number is. I'm dividing by 45 here with 47 cards remaining because I'm taking out the two running cards that help our hand and then dividing by pot odds.

The thing that may swing this in favor of a call is that the probability of getting by the turn for free is not zero. If we knew for certain we were getting two card for the price it would be an easy call. On the other hand, if we know for certain that he is betting the turn, then our pot odds are 16 to 1, as the pot will be bigger by two small bets. And we get to see the turn card before deciding whether to put in the turn bet.

BTW: i do outs the more easy, Ed Miller way. The top end of a no gapped backdoor straight is about 1.5 outs, and a backdoor flush is worth about 1.5. So you have about 3 adjusted outs. So you have 3 outs getting 14 to 1. What should you have?

47-3=44
44/14= 3.14

It is right there, and a call considering implied odds. And you either have implied odds or a free card, one or the other.

emerson, serious question: did you read the thread before posting this?

GoT, I went through and redid the calcs as well, albeit in a slight less rigorous way, and came away with a similar ball park figure of a flop call being a fraction of a sb mistake (-0.35ish). Thanks for taking the time to explain things on here as I've honestly never sat down and really thought about reverse implied odds in a quantitative way before.

Serious answer: no, I read only the initial post and your response. I am now going through and reading some of the other responses. I did the edit after reading one of the later posts.

Edit: I have now read the thread and it makes me question how to value backdoors.

Something of note that hasn't been mentioned:

Our hand is much, much better if the flop contains the A instead of the 8, as it would mean discounting flush outs quite a bit less. I'd probably go 10 outs to 8.8 outs, which would mean 0.457 outs more than we have with the 8. That results in 0.197 sb worth of extra EV, which is quite a bit for such a small detail, and that doesn't include reducing our river reverse implieds. If we were to assume that our river loss when we got there and were no good remained at the assume 2.8 bb*, the reduced reverse implieds on the newly discounted flush outs is worth an extra 0.053 sb.

So if the flop is the A our EV is 0.250 sb better and the EV of the flop call would be -0.082 sb getting 14:1 closing the action with these two opponents. All else being equal, the EV hits neutral at 15.027:1, whereas it doesn't hit neutral until 18.736:1 as is.

*Note that it could be argued the number 2.8 should be larger in this new scenario since we should be more apt to go more bets on the river on average if our opponents have less hands that beat us less often. This would have a negative impact on our EV, albeit relatively small compared to the impact on our positive EV side (as shown by how our reverse implieds odds were impacted ~25% as much as our immediate odds). Because our two pair and trips being beaten is also a consideration, the consequences of changing this number would take a bit more time than it's worth for illustrating the point I'm trying to make - namely, that small details can often have a larger than intuitively expected impact on our EV, even on decisions which aren't very close at all (I would call the flop fold not close in OP's hand at -0.332 sb).

I didn't go over all the math, but there is one thing I didn't like about your initial calculation. This was the inclusion of the draws to two pair or trips. We will not have the pot odds to draw to a four outer on the turn and should thus eliminate this. Its inclusion adds negative ev to the prospects of calling. If we include it then it is a free draw as it will be folded to a bet on the turn. Perhaps I didn't follow it far enough. Do you assume calling turn bets after making a pair?

It was too late to edit, but I have the same comment concerning your outs to a gut shot. These too should be ignored. We won't have the pot odds to draw to a gut shot. The total number of favorable cards we might catch, which will cause us to call a possible turn bet, is 16. Right?

I may or may not have touched on this in earlier posts (I think I did), but I took some shortcuts along the way. One of them was in my discounting of outs, I simplified by only discounting the latter number and kept the original number the same, as you can see in the first set of numbers in my first post.

The more accurate way would've been to discount both numbers slightly, but for simplicity's sake I just discounted the latter number and compensated that number accordingly. I double checked one of these (the b/d flush draw deduction) by using an unweighted hand range for the PFR and a Bayesian analysis and it was pretty close to spot on, and I have a lot of faith in my ability to estimate outs anyway, having spent a lot of time doing different calcs for different situations, some of which are pretty similar to this one.

Long story short, the 6 outs to make 4.0 that I listed to represent our b/d 2 pair and trips outs would more accurate be described as 5.x outs to make 4.y outs, but I chose not to list it that way for simplicity's sake, since I didn't take the time to actually figure out what 5.x should be, or any of the other former numbers in that list. In reality, we have, imo, greater than 4.0 outs, enough so that we will have the pot odds to justify a turn call for one bet. Another shortcut I took was not discounting the turn cards to vpip for times when we pick up a pair on the turn but are faced with two bets. I kept those numbers whole and undiscounted, though if I wanted to do a thorough calc I would have to discount them based on a weighted hand range of both players, most importantly the blind, whose range is very wide and adding in that step would take a lot of work that I don't think is really worth it here. If I wanted to estimate, I'd give us 5.7 outs to make 4.2 and adjust the calc accordingly.

As for gutshots, I did not include them at all, except in cases where we also had a flush draw. Justin pointed out that he would prob call with them if the blind stayed around on the turn, and he's right. I did not include any part of that in my calc though, mostly because of laziness. Determining how often the blind calls the turn would take a lot of effort, and the added benefit of a slight number of outs and better river implieds compared to the cons of having more slightly more cards to vpip with on the turn is going to come out to not make play a smaller factor than other of the others I used. Basically, I didn't think it was worth it.

The difference between what I'd give 3.9 outs and 4.2 is not that big, but imo 4.2 is just enough to make a turn call even if the blind drops. Just estimating roughly and not weighting anything, we'd need to make ~1.4 bb net on the river on average when we hit to make a turn call neutral EV assuming we're HU, and I think we have that. With 3.9 outs you'd need ~2.3 on the river on avg if we're HU on the turn facing a bet, which we are not going to have.

PS. Suck it daver.