Why would you not apply Bayes inference against hard data when the hard data is from the population?

Your example doesn't make any sense to me. The guy having a sick stache has no bearing on the flip where as the population data does have a direct bearing on whether or not this player is a nit.

I'm mostly concerned with the first question because if your data is from the population, how is the population data not relevant?

I'll try and explain in reference to Tombos post, since he first posted Bayes theorem first.

He used it to break down three data sets (winning players, losing players, overall pop), and really, since you don't know the player at all, overall population is the best to generate a std deviation from. What the population data point he's looking at is the avg VPIP and PFR, and then based on that mean, creating a likely VPIP and PFR if the sample size is increased to a normalization point.

Adding population player types on top of this, doesn't really make sense, because you don't know anything about this player. All we want to know is, based on average VPIP/PFR of the population, how likely is it that the person playing didn't get a hand distribution that is X% of the top hands that the population plays.

Again, maybe there's some Bayesian inference adjustment that can be made to that using additional player type break-downs of the population, but I don't think it's necessary. We just want to know how off this player is from the VPIP/PFR average, given a larger sample size.

Okay I'm following you but we do know that there are no 11/11 players in the population correct?

How does the population sample not play into us getting more accurate information?

I guess where I am losing you is why we wouldn't add population player types on top of this because that will help us narrow down if this is an outlier or a common case.

In tombos more detailed analysis he disagreed with you that this is a likely nit and said the odds of him being <20 VPIP is less than 15%. Do you agree with that or disagree with that?

There's a second post from Tombos but it's in DDP's blog

I think that's what's causing the confusion. Both posts just use different methods for integrating population data I don't think they're stacked.

It doesn't really matter, because we're not concluding this player is 11/11.

We're saying he has a likely VPIP of between 12 and 22. Which is everything from a total NIT to a tighter reg. Our mean again, being 17. The reason this makes the most sense to just take the population at whole is because when you start creating subsets of data w/ varying sample sizes, it can vastly skew this data. I'm sure Tombo or someone versed in this can explain this as well. If you have 100k population sample, and you happen to have 1 player that plays say 16/16 over 10k hands in that sample, it's going to vastly skew your conclusion.

It's better to just take the entire population when you're trying to create these likely hand ranges w/ small samples. I think you're going to get more accurate data, and hence make better conclusions.

You can just validate this in your own play as well. How often after 35+ hands are you playing w/ a VPIP of 11 or less in a 6max cash game?

Yeah I know that is what Tombo's said initially but he wasn't taking into account the fact that this is not a random sample, it is a sample from the population.

And he said the VPIP was only a 14.3% chance of being <20 not that the VPIP is likely between 12 and 22 in my PGC.

I don't know enough about statistics to counter your argument so I'll ask some other people and I'm hoping Tombo's can respond as well to elucidate his thought process.

I read your blog. I don't think you should reduce the population to players <30 VPIP and then run a bayes theorem from there trying to figure out a players likely VPIP/PFR range. I don't think that's the most accurate way to look at this data.

I think I've kind of exhausted my point, so I'll just leave it there.

Can't find the ref so i concede!


That said, that article by Costa seems all over the place to me. Agree with the main argument he ends up with (exploits all the way baby), but what exactly is he on about here?

huh??? how does what he’s saying in that paragraph rebuke the 'deviation is optimal' critique? Which he then goes on himself to recommend anyway? I'm legit confusedo

I think that criticism still stands. If you run private bot v bot data and compare it to regs to explain your reasoning the argument is inherently flawed. Two main reasons:

1) It entirely discounts the fact high stakes crushers might be luring opponents into more profitable nodes by taking suboptimal lines on previous streets [I know this is true because Alvin teaches it in his exploit course - calls it leading your opponent into the forest]

2) This cropped up recently in a half joking bot thread. Apparently new GTOw AI is comparatively decimating its peers using a) greater accuracy (bandwidth/tree size/Nash distance etc) AND b) some kind of as yet undisclosed AI/neural net magic that is able to calculate and factor in future EV that isn't realised in the traditional solve.

[My wild sepculation is that it's mimicing what high stakes players might call 'intuitive' factors (i.e. a sense for what mistakes their opponent might be making elsewhere that yields greater EV) - but given i am essentially a theory dunce this is mostly devil's advocate speculation in the hope of correction]


But I think the main point stands. Private bot v bot data doesn't confirm high stakes players are playing suboptimal. You can't just look at MDA ubiquitously for one street/decision and conclude it's the incorrect/suboptimal line. Not least if you're using suboptimal and outdated bots as your baseline. And the only way you could make this claim is on a hand by hand basis using strenuous reasoning based on the holistic strategy (that yes, may or may not include MDA on any/all streets). Make sense?

unlikely fish have static ranges that are able to run card dead for even that long they'd rather vpip somehow somewhere before only playing 4 hands in 20-25mins or so

The article isn't judging whether nosebleed regs are playing well

"I’m not gonna tell you in this post if those adjustments are good or not. What I wanted to do with this week’s post was to show you a piece of truth that can save you a lot of time and effort in your poker career. I wanted to demonstrate to you that perhaps the current obsession of the community with GTO strategies actually does more harm than good."

Really? He has titled it 'Are Nosebleed Players GTO?'.

how is that (and the subsequent breakdown between regs and his bot v bot GTO) not adjudicating/evaluating high stakes pool strategy?