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Selbst, WSOP, and Moral Poker Selbst, WSOP, and Moral Poker

07-26-2022 , 07:52 PM
Quote:
Originally Posted by hardinthepaint
You need to get back on your meds, man. Your response to my post is literally just a jumble of words that mean very little. It's worse than postmodern philosophy. If your position is literally that I am equally well off hiring some drooler in my local 8/16 game as a coach who has been losing for decades than I would be hiring someone who has been a consistent winner for decades, you're beyond hope and not at all connected to reality.
What I'm saying is that drooler you are talking about, has one of the best mttsng scores over the longest sample size available online. They are offering coaching to you at the live tables. do you accept?

Last edited by jbouton; 07-26-2022 at 08:06 PM.
Selbst, WSOP, and Moral Poker Quote
07-26-2022 , 07:59 PM
when "5bps of edge" isnt enough...
https://youtu.be/k3REB7RkBbU?t=622
Selbst, WSOP, and Moral Poker Quote
07-26-2022 , 08:01 PM
Quote:
Originally Posted by antialias
Jumping in becaue this sounds like fun and there's a couple pet peeve misconceptions being brought up here. Feel free to ignore.

There's a qualifier that makes this statement iffy. What does 'reasonable' mean in this context?
Of course you can use Chebyshev's inequality and see to what confidence level does an (observed) high win rate correspond with a true edge. While you can never say it with 100% certainty you can get arbitrarily high in this confidence given a large enough sample.That is why when evaluating someone's claim you need both: win rate AND sample size. The cutoff for how you determine the probabilities as acceptable is up to you. There is no mathematical standard for it. (Many scientififc papers use 95% or 90%..but those are arbitrarily chosen and are being used by convention - not for any fundamental reason)
Yes. From a player's perspective 'reasonable' becomes a match of expectation to income etc. We aren't at that question yet.

Reading from your tone, my quess, if you go look at the data available, you will come back and say you agree with me. You are assuming that the sample sizes are 'reasonable'. They are QUOTE OBVIOUSLY too small.



Quote:
On the flip side the entire premise is flawed for two reasons:

1) (as has already been mentioned) It posits a (past) observed win rate - if born out as a (past) edge - translates in a similar (future) expected win rate/edge.
Players improve. This doesn't work because neither the own skill nor the skill of the field is constant. But it also doesn't compeltely invalidate the past win rate and sample size as an indicator. It just means that the age of the hand samples is relevant.
I'm not using this point. Ignore this point for now.

Quote:
2) Sample size is not equally meaningful between stakes. An average win rate of 10bb/100hands at miocrostakes is not the same as 10bb/100 at the highest stakes. If you go to a coach and want to learn mid stakes poker and they show you that they played a million hands with 10bb/100 win rate at miocrostakes over 500k hands then that's an entirely different resume as if they show you 10bb/100 win rate at the highest stakes over the same amount of hands.
Is there a typo there? This doesn't go against anything I have said. The relevant point is that you can hard core skew your stats in mttsng if the tracker site lists "5-15$ games" and you binked a few 15$ games and plyaed the rest in 5$ games.


Quote:
If everyone else was trying to play mathematical poker then: yes. But that is not the case. GTO doesn't mean you win most no matter how others play - just that you will not lose if your opponent plays optimally. Those are two very different things. If you're not prepared to play exploitative when the opportunity presents itself then you're leaving money on the table.

In short: "Best poker play" is not defined by making consistently mathematically best plays but by being most efficient at winning money (again: over a large enough sample size that satisfies your personal level of confidence). There is no prize for style points. Knowing what the mathematically best play is is just a fallback when you're out of ideas how to play exploitative in your current situation at the table. It's the base skill (no one has yet mastered) and only becomes the be all/end all once everyone has mastered it fully.
This is speaking to/against my argument B. It's premised on A. Show me the data available IS sufficient. Or tell me you looked at the data and its enough.

Quote:
Is survivorship bias a thing in coaching? Certainly. You can use the same Chebychev inequality to calculate how many percent of coaches are just deluding themselves (unwittingly). Problem is that it's again a probabilistic game which of all the coaches these are (but that, again, is skewed by their win rate and sample size. So you can make a good - though not perfect - choice when selecting a coach)
If you have 10 games sample, you cannot make a good decision. if you have 100 games sample also can't. if you have 100k games sample you CAN make a good decision. If you have the ACTUALLY available sample you cannot make a good decision.

Let's call the available sample x. You didn't check what x was before you spoke. Go look at x. The highest available sample is too small.

Last edited by jbouton; 07-26-2022 at 08:07 PM.
Selbst, WSOP, and Moral Poker Quote
07-27-2022 , 11:21 AM
Quote:
If you have 10 games sample, you cannot make a good decision. if you have 100 games sample also can't. if you have 100k games sample you CAN make a good decision
You can make a good decision on 10 samples for a personal definition of 'good'. There is no absolute definition/threshold for where 'good' starts. There is some that is used as convention in scientific papers (e.g. how many standard deviations you need before you can claim a discovery) but those thresholds are just convention - not based on any kind of real qualitative difference. An 85% confidence interval is just a quantitative difference to a 95% confidence interval.

What your personal definition of 'good' is depends on what your tolerance for risk (i.e. being wrong) is. Going all-in with QQ against AK is a good decision - but it still turns out 'wrong' around 44% of the time. Yet we would all be satisfied with having made a good decision, no matter how it turns out.

Some side note on coaches: Besides looking simply at the win rates of the coach you could also check on whether the win rate of students of a particular coach have improved, which you could basically add to your sample size.
...And then again there are some things that coaches teach which are independent of the coache's own aptitude for using it in a live setting. Much like there are in any sport coaches who are worse at the sport than the ones they coach. The reason they still provide value is because they understand the math/methods/psychology and can teach those without necessarily being able to employ them under time pressure themselves.

Last edited by antialias; 07-27-2022 at 11:28 AM.
Selbst, WSOP, and Moral Poker Quote
07-27-2022 , 11:56 AM
Quote:
Originally Posted by antialias
You can make a good decision on 10 samples for a personal definition of 'good'. There is no absolute definition/threshold for where 'good' starts. There is some that is used as convention in scientific papers (e.g. how many standard deviations you need before you can claim a discovery) but those thresholds are just convention - not based on any kind of real qualitative difference. An 85% confidence interval is just a quantitative difference to a 95% confidence interval.
I don't think using 10 games to judge the likelihood of a players mtt skill is a good idea.

Quote:
What your personal definition of 'good' is depends on what your tolerance for risk (i.e. being wrong) is. Going all-in with QQ against AK is a good decision - but it still turns out 'wrong' around 44% of the time. Yet we would all be satisfied with having made a good decision, no matter how it turns out.
This is WILDLY not on topic.
Quote:
Some side note on coaches: Besides looking simply at the win rates of the coach you could also check on whether the win rate of students of a particular coach have improved, which you could basically add to your sample size.
If the sample size of the entire field isn't big enough, how would considering only 2 players from the field be big enough?
Quote:
...And then again there are some things that coaches teach which are independent of the coache's own aptitude for using it in a live setting. Much like there are in any sport coaches who are worse at the sport than the ones they coach. The reason they still provide value is because they understand the math/methods/psychology and can teach those without necessarily being able to employ them under time pressure themselves.
Right ic. So if the coach doesn't understand the game or the math of the math game, then their attitude or something makes up for it in poker? I'm a little confused.

What I'm really not understanding is our inability and unwillingness to comment on the actual available data.

edit: put it another way. instead of saying "oh im blind to the stats and im blind to the math involved and blind to what is a good sample or a bad sample. Let's all suggest what might be a reasonable sample for 180 mttsngs and then i'll show you that the available sample is nowhere near what you thought.
Selbst, WSOP, and Moral Poker Quote
07-27-2022 , 04:53 PM
Quote:
Originally Posted by jbouton
I was looking at katie's stats for sng's she played a lot in my field. I think this doesn't really apply to physical sports. I don't know what excuses we want to accept that the partner of the guy that 'wrote the book' on sng's doesn't have strong results in low/mid stakes mttsng environment. Its just one player. I have zero counter examples in the data I looked at.

I looked at mttsng's from around the year of what I posted there (2014).

I'm commenting on the ACTUAL available data and attainable sample sizes. Counterpoints shouldn't really be theoretical in that sense (ie 100k games with 25% roi doesn't help us when no one can achieve that.)

It's not a troll in the sense posters are accusing. I took the data, and I look at it all the best I could. I didn't just think in my head like you guys are doing.

Can someone take the data and show me what I did wrong? I'll start playing poker again maybe.
Fair enough, thanks for the response. You sound educated enough that you can understand why I want to check methodology and why I ask for someone to show their work. (I still don't know what Dozier's actual win rate is, but at least you confirmed you based your statement from her SNGs specifically.)

Incidentally, you can credit/blame my best friend growing up for these questions. He co-founded an organization that promotes transparency when it comes to research in an effort to improve integrity and reproducibility. As one would guess, many a "scientific study" comes out with some surprising statement, and the trigger-happy media tends to report those findings before anyone gets a good look under the hood. Whether it's due to bad science or bad reporting, unreliable conclusions often make their way into the zeitgeist.

Consequently, he has me and most of his friends pretty well-trained at asking a lot of questions at almost any claim. (And as a PIO, I already have a trained eye/ear for media bias, etc.) So apologies if I sound like I'm attacking your integrity or something.
Selbst, WSOP, and Moral Poker Quote
07-28-2022 , 01:04 PM
Quote:
Originally Posted by Wilbury Twist
Fair enough, thanks for the response. You sound educated enough that you can understand why I want to check methodology and why I ask for someone to show their work. (I still don't know what Dozier's actual win rate is, but at least you confirmed you based your statement from her SNGs specifically.)

Incidentally, you can credit/blame my best friend growing up for these questions. He co-founded an organization that promotes transparency when it comes to research in an effort to improve integrity and reproducibility. As one would guess, many a "scientific study" comes out with some surprising statement, and the trigger-happy media tends to report those findings before anyone gets a good look under the hood. Whether it's due to bad science or bad reporting, unreliable conclusions often make their way into the zeitgeist.

Consequently, he has me and most of his friends pretty well-trained at asking a lot of questions at almost any claim. (And as a PIO, I already have a trained eye/ear for media bias, etc.) So apologies if I sound like I'm attacking your integrity or something.
Fair enough...maybe...I think I was a little un-motivated to sort of prove that, expecting people want to check for themselves anyway etc. I forgot I had my original thoughts still in a past blog so I have the details I was going on. I still feel like no one will comment on the numbers but will just say I'm a crazy idiot. Do you mean to call me out but not really care when I show my homework anyways?:

Quote:
Observations on 180 Man Turbo MTTSNG Variance: Comparing 2013 with 2014 Leaderboards
My observations given I used the calculator properly, is that in any given year almost all players will not have enough empirical data to know their own winrate [with any decent confidence].

Notes on the Spreadsheet Layout:
Quote:
View the spreadsheet here.

We might be able to make some useful observations even if we don’t have all the information we need. The OP from the forum post seems to be lacking the pictures. For now we will concentrate on the numbers from the spreadsheet. There are 2 years: 2013 on the left half and 2014 on the right half. Each side is again split into $2-$5 stakes on the left and $5-$15 stakes on the right. Once more each of the separated stakes is divided into top 20 profits on the left and top 20 counts on the right.

For each $2-$5 section there is the players name, profit, count, roi%, and avg stake. For each $5 -$15 there is the player’s name, profit or count, and then another separate count, profit and roi for each of the $8 stakes and the $15 stakes in order that we may see what a player’s separate 8’s or 15’s stats are.

Along the bottom are some sums and averages not much (or at all) referred to.
Observations:
Quote:
It doesn’t seem to be a big enough sample size to truly compare year to year and decide whether or not the overall profitability of the game has changed. By the numbers it almost seems the game hasn’t changed much or has gotten slightly better, but it’s doubtful anyone would agree with that (other than Dnegs and PS). There are many reasons such a comparison might not be accurate-for now we’ll have to make other smaller observations and see if there is any conclusion to be made that way.

2013/2014 $2-$5 top 20 profits
We will largely ignore the possibility of $2 stake games in our data, although, for example in 2013 there is one player with an average stake of 5 that might play a mix of 2’s or possibly not re-buy very frequently, but it shouldn’t bother our analysis to ignore the difference. In 2014 one player has an average stake of $5 as well.

In 2013 the top two profits for $2-$5 stakes were 63k and 56k respectively compared to 48k and 43k for 2014 The 1st place player for both years is “opted-out” and the 2nd place player had 15k games for 2013 and 11k games for 2014 (none are the same players for each year and rarely is this ever the case so we might assume as such unless otherwise stated). The total profits for the top 20 of 2013 was $740k for about 37k games for the average player. In 2014 the total profit was $729k for about 36k games on average.

There are 5 players count missing from 2013, the 1st, 3rd, 4th, 14th, and 15. The total games for the 15 players remaining is 177,033 and the average of them is 11,802 games. The 1st, 4th, and 10th, players count are missing from 2014. The total games for the 17 players is 192,877 for an average of 11,346 games.

The average stake seems to represent some amount of re-buying. Most players most likely double re-buy initially, always add on, and always double re-buy when if they bust before the add-on. This should amount to a rebuy of 10+. For 2013 the Avg stake ranges from 5 to 10 with most top regs around 9 or 10. The average seems to be about 8 for 2013 and 8.8 for 2014.

Roi ranges from the 30’s to 40’s mostly and can go below or above however these numbers aren’t very useful without proper weight. Some players have 10k-20k games which might be useful for analysis but many have less than 10k which is probably not a very decent sample with 20 players total to choose from. A 30%+ roi might give a strong enough sample but it’s tough to suggest these are real numbers (players would never load the alternative). What is likely is the roi is down close to the 8’s and 15’s level but sharkscope’s re-buy tracking does not account properly.

2013/214 $2-$5 top 20 count
Less telling for our re-buy’s since most of the $2-$5 counts will involve players from the 2’s stakes either mixing or only playing $2 games. Fried liver, in 16th place has 15k games in 2013 while holding the 2nd place in profits for the same year. Vasily has an avg. stake of 5 and so likely either mixes 2’s with re-buy’s or doesn’t re-buy with the above stated strategy, yet did in fact make the top 20 profits. madaAK with 15k games made 16th in the profits. In 2014 Fried liver didn’t make the count leaderboard but did make 5th spot on the profits board. For the most part players on the profit boards of the $2-$5 stakes for each year are not on the count. The bottom count for each year is 11k and 15k (this suggests not many other players sample sizes are valid since they are not either on the profit board or have a decent sample at a lower roi).

2013/2014 $5-$15 top 20 profits
We divided each of the $5-$15 stakes (profits or count) again further into 8’s and 15’s in order to get an idea of what the “combined” statistic is made up of. In 2013 the top profit is $34k by a player that is opted out and $35k by lijey in 2014. Lijey played about 13.5 games and slightly over half were 8’s (the rest 15’s). Their roi for each was 24% and 23%, for 13.5k games it might not be a perfect sample but this player is seemingly strong in the field (perhaps unnoticed as well).

2nd in 2013 to MrNorberto with $26k profits and 11k games (1st place stats not available). MrNorberto played almost 16k games, over 10k of which were 8’s with an roi of 16% (19% for 15’s). 10k games is a decent sample with 16% roi but the 15’s sample is lacking and these two players are the top and so can easily be outliers. What is noticeable is the $10k difference between 1st and 2nd, we would need to have a count for the 1st player but what is likely is they had a great (exceptional) run that year regardless. 2nd place in 2014 is closer to 1st this time with $32k (vs $35 for 1st) with about 2k games less (11k). 3rd place in 2014 made nearly $8k less with almost the same number of games

In 2013 the profits drop off at a fairly normal seeming rate. What is noticeable is I AmLegend11 with 24k games and $21k profits (roi of 14% and 4%) who comes somewhere around 10th spot amongst many players with half the count but nearly the same profits Boon79s is in the nearly the same boat with a few thousand less in profits and games and further down the line forboon isn’t far behind. Other than that most players seem to have around 10-12 games. The same non pattern exists in 2014, which many players with ~20k games count are interleaved with players that played ~10k games.

For 2014 Lijey and Dany871 have the best Roi combinations 24/23 and 20/23 and about 13k games a piece each fairly evenly distributed between 8’s and 15’s. This might be a minimum sample size although again these are the two top players of the year and they do seem to be outliers. No-else seems to come near to 20% roi with a decent sample size close to 10k. It SEEMS like somewhere between 10%-15% with a 10k+ sample size is about the norm and attainable roi%. However being the top 20 profits in the field it may very well be at least even a few points behind this with an even bigger sample size by at least a few thousands more games than that..

2013 is the same and possibly there are no equivalent scores to the top 2 from 2014 (again 1st for 2013 is hidden). What is plain to see is there are no players with a strong sample that shows a 20% roi is attainable. There is little evidence even 15%-20% is a reasonable expectation over a decent sample. Its difficult to tell what amount of players might achieve 10-15%.

For 2013 the only sample for 15’s above 14k games returned a 4% roi, for 11k, 10k, 10k and 11k games respectively for 8’s players had 16%, 14%, 15%, and 6% roi’s. In 2014 no players played 10k games in 15’s and the highest sample was 8100 with an roi of 11%. For 8’s there was 10k, 10k, 12k, and 10k games samples with 10%, 8%, 12%, and 13% roi’s respectively.

2013/214 $5-$15 top 20 count
Count might not be useful in the same way but it is worth observing. We might wish to look for habitual donators in some games but probably here mostly (and unfortunately) this won’t be the case. We expect to find a lot of winning players and break even players mass tabling.

Count for 2013 ranges from 27k to 13k games with the highest total profit MrNorberto at 26k, I AmLegend11 21k, booone79s 19k, and redhot0007 at 17k (nearly all from 6k 15s). In 2014 the author is still waiting on 15’s stats for 1st place and hotjenny314. Some of the notables are MtZK $24k, Mikwej $18k, lijey with $34k, Dany871 $32k, N.Ionas $24k.

The least count for 2013 was 13k and 11k games for 2014. Both seemed to have the same average amount of games although with missing players its seemingly not a very accurate sample.
Problems
There are many issues with this analysis most of which is the obvious lack of information and large enough sample sizes. Some of the information is not available because players are blocked/opted-out. The re-buy’s don’t seem very accurate, and the author will look to other players in the field for further explanation. Most of what can be shown is really just that there is a lack of information.

Conclusion
It’s difficult to make solid over all conclusions with such little information on the overall field, however, there are some important and helpful observations that can be made. It seems nobody has an roi of 20% or higher with any decent sample size. The 2 players that came close are anomaly and outliers. Perhaps they are of those players often encompassed with the statement “Anyone that get’s good at 180’s just moves on anyways”, however its difficult to suggest such an roi is attainable or reasonable when only 2 players have come close and not with a reasonable sample.

Some other observation can be made as well. There are not a lot of player showing up year after year in the top 20 (fried liver). Also profits are never related to count in an stable manner. No players serve as solid reference points as some will do great in 8’s and poorly in 15’s or in 3’s or vice versa. There might be good or better players not on these tables however then they must have had less than the lowest top count or profits and so at best they cannot have a decent sample to suggest such a thing. OOmekatzoOO1 and lijey did show up on both profit boards in 2014 though.

What remains remarkably clear to the author is the overall empirical evidence for 180’s does not at all show whether or not the game is profitable or sustainable and increasing or decreasing over time. What we do hope to show, if it is true, is that clearly one cannot establish an roi with any decent confidence (at least in a years time; even two for most) or at least that there is no evidence to show this.

Players with decent roi’s but with small and bad sample sizes seem to be making the reverse judgement that because of such a high roi, one doesn’t need a high sample. But without knowing the sample size needed, it is not correct to think that one’s roi is a representative of one’s true roi. This does seem to be the great mistake, and its not hard to see how players would talk themselves into such self fulling “prophecy”.
Selbst, WSOP, and Moral Poker Quote
07-28-2022 , 02:50 PM
Quote:
I don't think using 10 games to judge the likelihood of a players mtt skill is a good idea.
And I agree. But it would still be better than judging someone on 0 games. I was not disagreeing with you that a small sample size is problematic and that someone shouöld buy their coaching just based on that. I'm saying any sample size is better than no sample size. Whether it's good enough is up to the one wanting to sink their money into said coaching.

...because what you are arguing is that even though some people are having a win rate with a small sample size that they MUST be outliers (i.e. that none of them is possibly a winner due to edge)..and that's an entirely different thing to prove.
Selbst, WSOP, and Moral Poker Quote
07-29-2022 , 12:33 AM
Quote:
Originally Posted by antialias
And I agree. But it would still be better than judging someone on 0 games. I was not disagreeing with you that a small sample size is problematic and that someone shouöld buy their coaching just based on that. I'm saying any sample size is better than no sample size. Whether it's good enough is up to the one wanting to sink their money into said coaching.
I played poker full time for some years. There is no decision I can think of that a 10 game sample size affected and certainly not one that is worth bringing up as a 'counter point' to anything I have said. I am talking about useful sample sizes versus sample sizes that aren't useful. 10 games is not useful for anything else give an example please.

Quote:
...because what you are arguing is that even though some people are having a win rate with a small sample size that they MUST be outliers (i.e. that none of them is possibly a winner due to edge)..and that's an entirely different thing to prove.
I have no idea how you would think I am arguing that and can only think that you have created a stawman.

Think of 3 types of profitability a player can consider:

1) whether or not a player could reasonably afford their own expenses at their winrate. (at no point here am I arguing sites owe players this and I will reference this bolded if someone responds that I am)
2) whether pots and prizes are awarded/distributed/paid fairly etc ie whether or not sites cheat the prize pools-this we aren't considering.

3) whether or not the players playing the most profitable strategies have an expectation of profitability (ie is the rake and effective rake so high that no players have a profitable expectation).

We want to consider 3) and the range/degrees of the field/time considered. I'm saying you can't measure/observe/analyze this even in the most liquid games of the most liquid times.


It's not something to be an opponent of me for saying, or call me crazy. If you disagree...I posted the numbers...reference them at least.

Last edited by jbouton; 07-29-2022 at 12:51 AM.
Selbst, WSOP, and Moral Poker Quote
07-30-2022 , 11:46 AM
"More specifically I'm thinking of a time when Daniel Negreanu headed a poker stars campaign that tried to convince the players that higher rake was better for the game. The basic idea being there is some subset of players that YOU the reader belongs to, that benefits from 'low rake seeking players' leaving the site for more profitable games."


Daniel said this because he's dog s hit. He knows this is stupid. He basically sold out
to the poker world massively. Probably as the highest endorsed poker player in the world
at that time, or at least top 5.

But only a few players on 2+2 and Doug Polk called him out.

When I guy whose not top 100 in the world, and is probably top 5 in endorsements,
sells out like that. I mean you may as well give up hope. Imagine what this guy
would do or say if he really needed money and was broke!

So its pointless to police or call out anyone. The average human is just too pathetic.
Selbst, WSOP, and Moral Poker Quote
07-30-2022 , 04:21 PM
Quote:
Originally Posted by fasterlearner
So its pointless to police or call out anyone. The average human is just too pathetic.
Ah, no.
Selbst, WSOP, and Moral Poker Quote
07-30-2022 , 07:35 PM
Very productive discussion itt. I love to read endless opinions about variance and gto/exploitation
Selbst, WSOP, and Moral Poker Quote
07-31-2022 , 01:40 PM
Quote:
Originally Posted by fasterlearner
But only a few players on 2+2 and Doug Polk called him out.

...

So its pointless to police or call out anyone. The average human is just too pathetic.
Bobo Fett casts doubt I believe. And yes there were only a few of us. I hope people remember what Polk did back then (and Joey iirc). I do remember as well a type of poster that would always break into the general complaints against raising rake to proclaim: "POKER SITE DON'T OWE YOU A LIVING". I maintain that such a player archetype is self-inconsistent and cannot exist from a game theoretical point of view as a (game theoretically-rational) player. Not that I mean to say poker sites do owe players a living, but rather that the best players should expect non-zero non-negative profits(else where does the money go?!).

I've put up the numbers, I put them in a spreadsheet, I "parsed" them to the best I could, and I summarized them. Then I summarized my summary.

Since we are poker players and interested in reducing probabilistic type data into finite conclusions/decisions I think that my point "A" should stand at least until someone references the actual data I put up. Or at least conjecturally we can start to understand how this would shape our understanding of the game as it has evolved.

Putting this another way, by now we should be able to have (or at least want) a sample size to view empirically whether or not Dnegs claim that raising the rake would make the game more profitable for the player archetype he was referring/preaching to (ie 2p2 regs!). But of course we run into an intrinsic difficulty here in that the games must be less liquid than at the time when mttsng 180's were at their peak (or we can test this) and if that is the case then if "A" is true, that there was at the highest liquid times not enough data to prove profitability of the games for the best players, then it must be that you also cannot discern this for today's game.

Then we would have shown that there is no way to prove Dnegs claim wrong, even if it were wildly so.

Here tho is where we again highlight that line that is alluded to in the OP:

Quote:
It was the observation of a new “line" that has become popular with those responsible for “raked" functions relating to national poker sites that gave us the idea for the study of “asymptotically rakeless" poker.
And we can see how it creates an assumption for us that is implicit but useful for the observation that there cannot actually BE an (empirical) observation.
Selbst, WSOP, and Moral Poker Quote

      
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