I've been trying to find a theoretical basis for game selection aka 'taking shots'. The empirical knowledge is as follows.

This_Passing's Theorem (my interpretation). The certainty equivalent of the hourly post-cashback profit (2 * winrate * net_worth - variance) from a single poker variant is maximised by selecting games from a stake range where the highest stake is 4-7 times higher than the lowest one.

So someone who's adequately rolled should play at one (or maybe more) limit above their 'working limit' (but only at its softest tables because the variance slaughters otherwise) and (at least) one limit below it (again, only its finest tables as otherwise the hourly winrate is suboptimal while variance is more negligible).

For someone who's, like me, overliferolled but inconfident of the skill level, including all players below PLO20 where a living can hardly be made, the explanation is that it's too easy to get slaughtered at the high end of the stake range if the edge estimate proves false, while at its low end the games are overraked or the leap in their softness is not big enough to ensure the same dollar winrate. (I mean, why on earth are there tables full of regs at PLO10 at the same time as I sit with 5 recreationals at a FR PLO50 table?)

Intuitively, this stems from the fact that the expected edge at a table varies vastly on its lineup. There are often too few tables soft enough at a single stake, where by 'soft enough' I mean that post-cbk winnings are close to optimal: the lower the cbk % is at a site (cough, cough, puke), the fishier the lineup of a table needs to be to make it playable, and the difficulty of lobby navigation is also a consideration.

However, I'm struggling with proving or disproving this, as the following questions have to be answered (feel free to provide estimates for certain sites and stakes in replies).

1) What's the law of growth of attainable post-cbk hourly dollar winrates as stakes grow? (It's certainly slower than linear because games get tougher.)

2) What's the law of growth of variance as stakes grow? (Surprisingly enough, in my DB it's flatter than quadratic, i.e. the standard deviation of a hand in bb's doesn't grow, because either games get more nit-infested or I become nittier myself at the higher end of the stake range.)

3) How big can the relative difference between attainable post-cbk table winrates at a single stake be, depending on the table lineup?

While 2) is the easiest of these questions (players can just share their variance data over large samples), 1) requires review of winrates of a lot of opponents, which has already been attempted many times and run into problems because of small sample sizes, and 3) requires grouping personal winrates by table lineups, which is quite a work in PT4 and hard to be precise as it varies so much on table dynamics, relative positions and the nature of certain players' strengths and weaknesses.

Even if the theorem is true, the proof is too large to fit on the margin anyway, so I'll put the issue off (seek some reasoning in my later posts itt when they appear) as I made my 3332nd post too early and want to make a few posts elsewhere before I have energy and time to elaborate on this topic.

Thanks for discussing!

the theorem definitely seems to make sense to me and one key observation i have is that the skill difference between stakes is vastly exaggerated here. check some multistake high volume players on tableratings and this will be confirmed. i am playing a theory oriented style though so more exploitatively playing low stakes players might have more problems at higher limits i guess.
over the course of my poker career my winrates expressed in big blinds have been mostly independent of the stake i have played, in fact they are higher at higher stakes, but that is probably more due to the fact that i table select stricter there and also might play a little more focused there (also rake is a smaller issue).

Can you post the his op?

good post tony. and yea the main idea comes from simply not playing just one limit. mid and high stakes players deploy this concept almost out of necessity because of too few tables running at just $2kplo or just $600plo - they'll spread like $400-$2k or $1k-$10k, etc.

whereas a lot of micro and small stakes players will only play one limit because of the amount of games running at their limit + tying themselves to a strict bankroll idea for a specific reason that they haven't quite thought about too much + maybe other reasons like being "above" playing a smaller limit because it's for n00bies or being scared to play a higher limit because johan5390 is at the table or something

interested to see what others want to contribute to these ideas. and yea it does seem like a fancy way of saying "bumhunting" but there's obv times where u wanna make money and times when u wanna challenge yourself more to move up in stakes, this one just focuses on the former

Erm, this theorem is folklore; I think even the author doesn't remember where he first posted it, if posted publicly at all - it's been spread by word of mouth in Skype groups. The 4-7 relative stake range width clarification was added by me because mixing 4-5 limits at once intuitively just doesn't feel right at the micros - my maximum width was more than 16 times (from $10 to £100) in a recent morning session and I feel I spewed at $10 because of undermotivation to think and the pressure of £100 (the fear of playing shamefully bad rather than of losing money) - though I endorse such a wide range for high stakes where regs just flock to any table where a mark sits.

Ok, so yday morning i mangled about 4 different post attempts in this thread via mobile technology. And my new turned leaf of trying to be more strat orientated failed miserably!! Luckily Napsus saw my pm plea for help and deleted the posts in here, i am just glad no one derailed the thread as a result!!

To me this seems like solid "Fluid BRM Theory" relative to the climate of today's games (haha.. i said solid fluid). The game has outgrown the days of conventional BRM which I believe spawned from Limit>No Limit>PLO.......? Subsequently, the PLO days of Xbi per stake stinks of stale panties !! That said, I do think that a few other factors need to be included in the tPassing Theorem mix though.

• Player pool depth by stakes play a huge factor
• Player pool fish factor
• Hero's objective which can be segmented by stake groupings, ie high stakes, mid stakes, <small stakes

I think there is a good place for me to stop for now, I have some other thoughts as well but just want to book a winning session in terms of posts and not end up writing a tl:dr post that gets cut short via poor tech!!! I might cry if that happens again

Well, the statement of the theorem doesn't aim to describe the whole process of table selection, which includes the factors you've mentioned, it just concentrates laymen's attention on the counterintuitive fact that a single stake (frankly speaking, even a single network) is not enough.

Hmmm, ok, yeh I see where your coming from. The player pool fish factor should really be an inherent sub-bullet point of player pool depth by stake with less onus, as it will be intrinsically connected to the size of player pool. Smaller the pool, the more the need to spread a range of stakes/sites.

I still think Hero objective is relevant though and should trump everything really.

<Small Stakes Hero = Net depositor, breakeven or loser. Never withdraws. Objective: Become a net withdrawer
Mid Stakes Hero = Net withdrawer, winner, never needs to deposit. Objective: Has salary and wants to increase it.
High Stakes Hero = Net Withdrawer, winner, never deps. Objective: Wants to win everything in sight very fast.

Or... Maybe I am being a bit shortsighted by thinking about stakes that are too low to apply this theorem thing as it is intended!!

What I'm looking for is prompting all small stakes heroes to adopt the midstakes hero mindset for our mutual benefit

Yep and to do that you need to tell them that their current BRM strategy is inept imo.

¡P0krParty! theorem imo

/thread

Found an old post I made ~8 months ago

Play in good games at a lower limit than the one you're a "reg" at?



Sometimes it's best to replay a level and set a new high score