I hope it helped. Is it what your looking for? R is tricky...

I'm not going to have a big value raising range against the recreational player on the turn, because his hand range is; hand distribution = bluff > semibluff > nuts.

Realistically, I could profitably raise any two here. I think that I gain more value by calling strongish made hands to induce a river bluff. But raising a large part of my distribution on the turn to charge his draws is also a viable strategy. Its hard to go wrong when his range is so weak...

Time Stamp?

I disagree that those two ideas are inconsistent. I open up 45% on the button, but my opposition often times opens up close to 70%.

Board: Empty

Range 1: A8o
Range 2 (70%): AA-22,AKs-A2s,KQs-K2s,QJs-Q2s,JTs-J2s,T9s-T2s,98s-92s,87s-84s,76s-74s,65s-63s,54s-53s,43s,AKo-A2o,KQo-K2o,QJo-Q3o,JTo-J5o,T9o-T6o,98o-96o,87o-86o,76o

Equity 1: 57.306% Win 1: 55.305% Tie 1: 4.001%
Equity 2: 42.694% Win 2: 40.694% Tie 2: 4.001%

It seems preposterous to fold a hand with 57% hot/cold equity against my opponents range.

When is the last time you folded 99 in CO to an UTG raise?

Board: Empty

Range 1: 99
Range 2 (15%): AA-55,AKs-A7s,KQs-K9s,QJs-QTs,JTs,AKo-ATo,KQo-KJo,QJo

Equity 1: 52.904% Win 1: 52.421% Tie 1: 0.965%
Equity 2: 47.096% Win 2: 46.613% Tie 2: 0.965%

5min

No, I was concerned that even a weaker player would realize that his 8x was no good after I overcalled the flop.

In some ways his line is more consistent with a faceup King than an 8. He looks really strong betting into two players on that river. Its also very hard for him to be bluffing. Leading me to the conclusion that he has a lot of kings along with some percentage of "mistaken" bets.

You don't think a rec player would go for greedier sizing with trips or raise flop/donk turn?

On what hand does the rec put the bettor and me on when the river hits?
It is very obvious to most players that somebody has TT+. Hence the rec's small betsize.

And yes, we can contrive a player type that always has an 8 at that betsize then bet/calls it on the river but I can't infer that from an uneven stacksize. Which is basically all the information I had in the hand.

I should note that you are much better off raising this hand at play money/microstakes. Mainly because the players don't care about the chips and will bet/call 100% of their betting ranges. As people develop bet /folding ranges, raising goes way down in value.

Yeah, I'll fix that problem in my next shoot.

I took most combos of KJ, KT out of his range in my mind. King high tries to make it to showdown a lot.

Also I need more than my immediate odds to call the turn, because he's going to continue bluffing on the river with most of his bluffs (all?). I don't remember the exact number, but I should need at least 40% for me to able to call the turn profitability.

I've got the next 4 videos shot, but I'd certainly be willing to model this in cardrunners EV in a future video.

Great vid Tyler. I agree that KJ KT might be discounted some, but if we fold A4 here, with the heart of without, it feels we are probably overfolding. If we fold this, I assume we also fold A2-A7 (a7 blocks 76 t7). So our continuing range is AT and then A8 A9 98 Q9 JT? we dont have the sets or AQ in our range, so it feels we will fold too much... he will be cbetting this board with a range advantage, escp for a small sizing, with a very wide range. so he can easily double barrel here with a ton of semi bluffs. like T6s T5s J7s J6s J5s 75s 76s 65s and then a lot of heart combos given small flop sizing

lol i kept watching and here u admit u deviated from gto, whoops lol

Hey Fivebet,

I hadn't considered the small suited hands in the calculation. Including them would certainly make this a much easier call.

Thanks for the suggestion!

Next time Ugur. Next time.

Hi Yoyo,

The advantage to adding more suited connectors is board coverage/bluffs on some run outs we normally wouldn't hit.
But as we add more suited connectors to our range, our average hand strength decreases on most boards. This means we'll either bluff more or check/fold more. Our opponent will have more equity in every pot we play.

To get maximum advantage of board coverage/bluffs, I prefer to have equal parts of 43s+, 53s+ in my range UTG, which requires that I fold some of the combos. This keeps the advantage of board coverage without the disadvantage of overall range weakness. The GTO limit bot, Cepheus, uses similar logic to design its ranges.

Thanks Andrew!

I think finding good ways to approximate R is one of the next big ideas in poker. The current equity approach is inaccurate in a lot situations.

Hi Zach,

Thanks for taking the time to write out your thoughts. I'm going to elaborate a little bit about how I see this problem. Feel free to point out anything inconsistent or questionable.

Common Assumption:

1. There should be consistent relationship between equity and winnings. e.g. constant * equity = R = winnings. The domain for this function should be any poker hand, i.e. 44's 50% equity is equal to A8o's 50% equity.

.

Why It's Wrong:

As you point out set-mining (or implied odds) grossly violates this logic. E, the constant, is not 920% for every hand! As every poker player knows 44 makes more money A8o. This is because having nut equity or bluffing equity (44) is more valuable than having a constant bluffcatching equity (A8o). Equity is created unequal! Because equity is unequal, R does not hold for any poker hand.

.

Can we use R situationally?

Yes, we should be able to find a constant relationship between equity and winnings with two qualifications.

.
Qualification 2. Our hand range is the same. If in the 55 set example, we only jam 55, and our opponent knows this and folds. Our R changes value significantly.

As I said in the prior post, getting the right function as R is quick way to nosebleeds. I doubt anyone has a complete model at this point.

We're definitely on the same page. I think R = constant * equity scope of application is very limited. We really need to compare situations where other factors are static.

In no limit, future equity matters more than current equity which leads to the right model being "Future Equity Realization (FER)" to model situations. Unfortunately hands improve at a different rates postflop and live in different hand ranges. Making FER a much more difficult modeling technique, but also much more rewarding. If you're good at this, you will be playing nosebleeds.

My video demonstrated a basic form of FER by using our past winrates with future street hand strengths to model future hand performance.

Thanks again Zach for writing such detailed posts.

I appreciate you weighting in on this Zachary. Your posts have given me a lot to think about and learn from. Although I don't understand them 100% yet.

'If our calcs have us winning .5BB with JTs then the equity realized is 3.5E-2(1-E)=.5BB ' Coefficient for E should be 4.5??Raise(3)+SB(.5)+BB(1)=4.5?

I'd raise 43s, 54s, 65s, 87s, 67s but I'd only raise them when each one was hearts. I'd fold 43s, 54s, 65s, 87s, 67s, of diamonds, spades, clubs. (Disclaimer: not my actual randomiser). My hand range then covers a lot of boards without weighting my hand disproportionately to 8 high or worse.

Hey Garrett,

I was curious about your name and googled it. I graduated in '06. That was a tough beat yesterday by NC State.

Thanks for finishing my logic for me. It's hard to chew gum and walk at the same time.
Small bets are super tough to balance which is why I think you see so few of them. There's good chance that the optimal strategy for QT there is "bet small some %" and "check/call some %." Because the range "bet small some %" needs to have some % nut hands in it, some % medium strength, some lower % bluffs. Its really to complicated to do well as human, but a GTO computer does it easily.

Hi Deal888,

Its awesome you're excited about it too! The method should be applicable to any big bet game.

Hey Deal,

You can use the ProPokerTools website to query for handstrength, though Odds Oracle is easier to use. The spreadsheet, itself was super easy. If you have any questions, shoot me a pm and I'll help you.

Tyler

Good Luck, I'm rooting for you!

You'll just have to do it for 3-bet pots.

Hey BangBang!

@KQ1 It's a bluffcatcher. It'll going to be read dependent or it'll be 1-A. Off the top of my head, in a vacuum, I'm probably calling up to pot.

@KQ2 In my database, its been a consistent money loser for me in this spot whether I 3-bet or cold call. You certainly can play it. It's probably user-error on my part. I tend to pay off too often with it (and not get payed off in return).

HM2 is ugly this way. You have to select the "not" button below, then select everything except high cards/no straight draw/no flush draw. That'll take out everything except high cards with no draws.

Looks good! You might recheck your flushdraw numbers for the hand, because its a one card flush draw and probably won't win as much as the two card variety.

No prob

Hey Konselieri,

For sure, variance is a big deal in particular poker hands. I didn't come to my decision lightly. I looked at similar hands in my hand range in my 3 million hand database extended those hands over similar situations (say button vs sb or bb vs mp) and came to my decision. I'm comfortable with it.

Obviously other people have to come to different conclusions. And who knows, I might be playing it a year from now when I've figured out I was wrong :)

Hi Raphael!
It's awesome you liked the video! I'm not sure what you mean when you say "gives a more appropriate result". What are we measuring?

From what I have seen in your video and in my db, poker samples for specific spots doesn't seem to follow a normal distribution. Usually you see a distribution that have heavy tails and using the confidence intervals for the normal distribution may lead into an error.

I don't have your sample but you can graph it and I expect it to have a very low density on the mean. I never saw something specific to treat this type of samples but my expectation is that the average will lead into a result that have poor relevance through the sample. The median may have a better result but I can't test it without your sample or one as large as yours for the spot.

The distribution meets all the criteria of the central limit theorem, so its normally distributed.Central Limit Theorem.

Since I was trying to approximate the mean winrate of the hand, using a confidence intervals to see if my result was a possible mean winrate is an easy way to check my work. What you are doing with median is outside the purview of this video.

The generation of the sample isn't independent (you can have more than one entries vs same villain and another possible bias) and you don't have a large number of entries, so CLT won't work. Well, this doesn't have much to do with poker, so I may just get back to pro poker tools and playing.

Thanks for bringing some new ideas to the videos, really good to think more on super clear spots for most people that we are probably not making tons of money.

You need more than 30 samples for the CLT to apply. (Source: Boston University ).
Here's the wiki definition for statistical independence:

"In probability theory, to say that two events are independent (alternatively called statistically independent or stochastically independent) means that the occurrence of one does not affect the probability of the other. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other."
WikiPage

Poker hands have to be independent. Otherwise, I would need to talk about my past hands to deal with every situation. A dependent poker hand would sound like this "I flopped a flush last time with 54s and won $10, so I need to fold this time ($0) because i've already flopped flush with 54s in this game and I won't flop another."

If you need something more rigorous, can we do it by pm?

I am totally fine with the way you did it, I don't "need" anything more rigorous and I see your approach as good. The only problem is that when I first saw that you are making 1.27bb/100 flatting JTs there and the variance is around 15bb/100. The approximation 1.27bb/100 doesn't seem to tell us much about the sample and I thought that there must be a way to treat this two heavy tails samples in a better way than average. I found nothing on the internet and my best guess was the median.

Dependancy would happen if you have the same villain for two entries which might be the case but I am not sure.

I think its the most profitable option against his wide opening range. I'm well ahead of his 3-bet call range (and get 4-bet rarely).