Not as questionable as the infamous SM runner-up's, though But the post is going to be a bit light-hearted for sure.

Basically, I once promised to coffeeyay to do research on BRM for spins but didn't attempt to do this until last month.

This is my 2+2 post #10K, and the problem is that Russia has passed a law that forbids VPN and proxy server owners from offering help with bypassing blocks that has come into effect on Nov 1, and though law enforcement is generally lazy here, my access to these forums may be cut off at any time now (unfortunately or not, one of the 2+2'ers has detected my Discord account), so I have to write my 'last word' fast before it's too late, please forgive me for the incompetence and possible incoherence.

And one more warning: I'm on massive chronic life tilt right now, caused by my failure to both study efficiently and think efficiently at small tables, so incoherence is indeed very possible.

Cliffs on cliffs:

In games where the EV ROI converges so lightning fast, skill matters so ldo much more than variance: no BRM will save a -EV player, but a reg will be fine with a few dozen BIs if they choose not to shove themself into the jaws of the higher-ups in the food chain*.

End cliffs on cliffs

* I'm of 6-max SnG origin, not of HU one, who likes sitting in a warm, fun and big company and came to spins (actually, Twisters) just because there'd been no Blast / SpinMax invented yet and 3-max spins were high-variance by 2014 standards and gave a bigger illusion of superiority to my main customers - recs, so I don't care how much you find reg battles necessary. Imo, most of the cases when mutual happiness is possible in poker are those where one of the players is winning and risk-averse and the other is losing but risk-seeking. When two risk-averse players clash, one of them bites the dust.

Cliffs:

- The main function of spin stables nowadays is to teach people to play well; the utility of their variance reduction function is overestimated; I don't see a need to sacrifice a decent portion of the EV just to get insured against the cold deck when most of us will hit a plateau of skill sooner than later anyway and have to study a lot, no matter the BR size, to add the vital few %s to the EV ROI to make the hypothetical hourly at a higher limit bigger than the one at the current limit. The below philosophy only applies to those who own 100% of their action like a boss... so perhaps to almost none of the current experienced regs

- Don't take shots at a higher limit at all if your EV ROI at the current limit is less than 7%, unless your life expenses have become so baller that you can't afford to stay low for long, which is rather a financial management issue than a poker one. I mean, you can take shots just to assess the reg/rec ratio or learn to play if you don't mind putting your EV on fire for the purpose of learning, but if you're a bumhunter at heart, just don't do it.

- Otherwise you normally won't need more than 50 BIs to move up to the limit that you realistically assess as beatable by yourself right now; just bear in mind that your bankroll will be like a yo-yo if you're managing it optimally, and you'll actually spend a lot of time playing the lowest of those limits that allow you to cover your life expenses at all... but it doesn't hurt as long as you're the best in the world at your limits... at your limits.

End cliffs

Life/grindwise, I'm in a worse spot than what I expected 2 months ago, but that's not the topic. For now, let's just assume that I'll be able to get enough help from a neurochemist (a specialist in nootropics and mood stabilisers recommended by fellow Russian grinders) to get myself on track and actually start beating this bloody poker of 2017.

Anyway, what's cool about hypers / spins is that the EV is easy enough to estimate and is quite uncorrelated with the actual winnings. Therefore, a math model where a grinder has fixed true cEVs (going up as the stakes go down) throughout a few months of the career is quite plausible.

I've actually tried reading smth about the forecasting theory to try to predict linear trends of cEV change over time caused by learning or field toughening, but it seems useless to me in the 1-month timeframe because it takes a lot of thousands of games to distinguish the true improvement of skill from just flopping worse than avg, far more games than what it would take to run good enough to start shot-taking or run bad enough to move down to the cozy comfort zone

An obvious issue with my model is that it's hard to estimate by how much your cEV goes down/up when you move up/down. From what I've read on 2+2, I assume that the ballpark estimate for the skill gap between the stakes is 15-20 chips, maybe even 25. If there's a rake jump between the stakes, reduce that by 5 chips.

Remember, one needs to to compare not the EVs of the best regs of given stakes (who're distinct people), but what their own EVs would be if they hypothetically ground higher/lower stakes at the time of the estimation. The EVs at super-low stakes for a HS crusher would be calculated inaccurately under this simplifying assumption, but this doesn't matter much for the BRM, as the crusher isn't too likely to fall that low anyway. What matters most are the current, the adjacent lower and the adjacent higher limits.

For non-max spins, I have a feeling that the gap between adjacent stakes is no smaller than 20 chips (4% ROI difference) because of how many videos, stables and other signs of civilisation there are. (I however advise against switching to spinmax if you don't know exactly what you're doing. Its theory is nontrivial, and I'm afraid you'd be at risk of breakevenness as Dunning-Kruger might prompt you to study less than you'd have to. Better safe than sorry.)

A corollary is that, if your goal is to minimise the EV of the time needed to achieve a certain monetary goal, then, as Mr Mason Malmuth knows, the bankroll requirement for a limit that you can beat is lower (actually, often up to twice lower), than the requirement given by the Kelly criterion (for spins, the latter would be 250 / ROI BIs, where the EV ROI is taken without 100+ BI JPs; for HUSnGs at division-free stakes, that would be 100 / ROI).

The reason is that the Kelly criterion was discovered for scalable activities like sports betting or stock trading, where it's impossible to attain a higher ROI by betting less. At poker, one achieves a higher ROI by moving down - low stakes act like a safety net.

I understand that not everyone has the same type of objective as me, in particular, people may have short-term goals, but I've found the problem of time-to-ultimate-goal minimisation much easier to solve, as then one's state (prospect) depends on the bankroll size but not on time, thus the HJB equation associated with this problem is an ODE. (The spoilered paragraph is a higher math explanation, may be skipped easily.)A huge assumption in my model, possibly one that makes it too unrealistic is that the player 1) can get a real job (or at least a loan) that covers their life expenses, 2) has a liferoll (not included into the poker BR) big enough to maintain themself while they're looking for a real job if they bust the BR.

I don't yet know how to solve the BRM problem elegantly if this assumption is omitted (I mean, the equation is the same, but the initial condition for it, such as the requirement that the risk of ruin if one starts at BR=$N be 5%, would complicate the calculation of the cutoff bankroll sizes between the limits, as opposed to my assumption that there's a zero-variance profit option at BR=$0). That said, it's always possible to add a smallish safety margin to the BR requirements (add the same $ margin to each) so that, if the variance goes a totally wrong way, one is left with like 100 BIs for $3s (or for whichever limit is needed to cover the expenses in that mysterious first world), so I don't think the assumption of real job availability is too restrictive.

And anyway, just like for a live poker pro, it pays off to cut the life expenses to the bone until one is comfortably beating the midstakes.

Let me give you an example. Assume that someone who's crushing $30s has minimum life expenses of about $3.50 per hour of grind ($600 a month), can do a real job for $3.60 an hour if necessary, plays 20 spins an hour and has ROIs as outlined below (I assume that the chests just about compensate for the deficiency of 100+ BI JPs), then they'll have the following requirements for moving up/down.

BI	ROI	BR, $	BR, BIs
$3	14%	$0	0
$7	12%	$210	30
$15	9.5%	$450	30
$30	6.5%	$1K	33
$60	3.50%	$3K	50
$100	study	booty	off

The fact that the requirement for $15s in BI terms is the same as for $7s is explained by the pressure of the life expenses at the bottom end of the stake range.

You must be puzzled right now. But I know how swings work, I've been to the park. As I said above, Hero will have to spend a lot of time playing $3s or jumping from $3s to $30s and back like a yo-yo before he hits a really good heater.

No, I wouldn't be able to withstand the yo-yo psychologically if I weren't sure of my maths. Actually, I haven't yet got to the task of withstanding it because I'm yet to sit on my booty a bit to ensure that I have bearable EV ROIs at spinmax micros, and you'll probably never learn about the results of my grind according to my model***, but rest assured that I'll be using it, incl. of course moving down religiously to the comfort zone of the micros whenever things go a bit wrong outside it.

Use with caution.



*** Well, at this very moment, my actual spinmax BRM is as simple as it can get:

BI	ROI	BR, $	BR, BIs
$3	fml%	w/e	w/e
$7	create	HUD	at last
$15	study	booty	off
$30	booty	and	heater
$60	solver	and	bink
$100	forget	about	it

Peace and GL!

first

Oops, in case it's not obvious from what I wrote, I have to mention that I assume that the life expenses are being subtracted from the BR continuously at a constant rate, and if cashouts are made seldom, one should still subtract the expenses from the BR mentally despite not subtracting them physically. This may be somewhat confusing. Oh, and of course, my assumption is that any surplus income from the real job (income minus life expenses) is pumped into poker; this of course only works if one indeed has a positive EV ROI and is just temporarily out of luck. The estimated skill and the actual earnings are rather uncorrelated in hypers / spins in the short term, as I've mentioned.

Another obstacle to using the model in its pure form is that it's hard to keep an eye on the account balance when multitabling (let alone that most grinders don't want to see the balance at all), and precise execution of the BRM would involve loading sets of mixed buy-in if the BR is borderline between two limits, and ideally, even deciding which table to load depending on how good one is running in the ongoing spins

Such execution would deliver fun and headache at the same time, I've actually never tried it, though I have some experience with adding lower buy-in spins to a set when I had a VIP goal not allowing to end the session altogether (which isn't very relevant in the chest reward era) while my game quality was admittedly too bad to allow loading the tables from the same limit.

This is actually an interesting point, and one I've never seen by anyone applying Kelly to poker.

On the other hand, trying to apply this to your games seems like madness, especially if you care about "life quality" at all

Also not sure about your micro ev assumptions -- I haven't seen any guys beating them for 10%+ ever, but ymmv? if you're actually a $30 spin crusher playing $3s

Well, I don't know about any precedent of a $30 crusher proceeding to play $3s for long enough. That's for a couple of reasons:

1. If he's staked, then the stable has a quasi-infinite (for practical purposes) BR and simply puts him at the limit that maximises its $EV*.

2. If he's not staked, then he probably has a tight (hundreds of BIs) BRM, which means that once he's established himself at $30s, going all the way down to $3s is too improbable.

One thing to note about EV measurement is that, under my model, it's normally based on a sample for all the shots combined; each of those shots may last for a small number of games depending on the card distribution. I don't find it necessary to play several K games in a row at the same limit to measure the EV because the population of each limit changes quite slowly relatively to the frequency of moving up/down. These required Ks of games can be put in as dozens of short series on highly random dates (whenever the RNG brings me up for a little while) and then combined into a sample. This of course assumes that the previous limit has already been comfortably beat EV-wise.

* Actually, the longterm EV that the stable gets from a player is not always proportional to the player's EV in the games. I'm seeing some stables refuse to promote people who attain 70-80 chips at $1s, despite the promotion being ldo +EV in terms of winnings at the tables, which, apparently, happens because of ecological considerations - the stable doesn't want to reg-infest higher stakes too fast at its own peril and give secret coaching materials to too many people unless they're really talented.

That's actually one of the downsides of being staked - one loses control over their ability to move up to maximise their own hourly $EV.

Wait, what?

Amazing thread btw.

What other explanations are there for this phenomenon?

Perhaps those stables use overly tight risk management strategies involving confidence intervals, e.g. if a horse attains 80 cEV in a 1000-game block, they focus too much on the fact that he might, in some cases, have a 'true' cEV of 65 but be flopping good in that sample, while missing out on a ton of EV by not promoting someone whose true cEV is 90 but who was flopping bad... well, confidence intervals are just a suboptimal framework. Bayesian inference is much better, i.e. it helps to look up the historical data about which cEVs the past horses with similar work ethics would have at $3s after attaining X cEV at $1s and being moved up.

It's even worse when divisions use the fact that some poker players are fishes at Bayesian inference* as an excuse to deny entry to those who don't run good enough EV-wise over small samples in battles to satisfy the cEV criterion based on confidence intervals. * Or, rather, they abuse the information asymmetry - by pooling the data from many battles, divisions have more info than the individual candidates do about the apriori probability distributions of cEVs that the plethora of candidates that have previously battled tended to attain.

I'm willing to try this, as a 'fun' challenge. If I'd start at 1's with 50BI and move up to 3's with 30BI's would that make sense? How would you suggest studying to improve fast enough to be able to go from beating 1/3 pretty hard (70ish cev) to taking those 1k roll shots at the 30s?

Volume goals?

I can't advise on how to maximise your fun because I generally fail to understand what makes people have fun.

If you're beating the 3s with 70 cEV, then I wouldn't recommend you to play higher than 7s at all until you have 70 cEv at the 7s in a sample of 2K+ games, unless you play spins primarily for fun.

My scheme doesn't impose a minimum bankroll requirement for the lowest stake that one is OK with playing. As soon as you have any spare cash that you don't mind losing, use it to play 1s or whichever limit is the lowest of those where you can earn more money than from non-spin sources. (I.e. if you have a real job that pays >$10 an hour or can play another form of poker with such profit, it's probably a waste of time to ever play the 7s even.) Of course you need a non-spin source for that spare cash.

The primary motivation for my research was to maximise the probability of securing my third-world retirement before online poker dies as a profession. Also, I had Spin & Go Max in mind when researching, that appears to have lower skill gaps between the limits, to allow for rapid expansion up to the 30s before too many thinking regs would get there. (Maybe it's too late already, or maybe I'm seeing ghosts.) I'll be applying similar BRM frameworks to any interesting new poker format that Stars will roll out in the future.

How to study is still a grey area for me, and the answer depends on whether you play usual (3-max) spins or Spin & Go Max (the latter requires a 1.3-1.5 (?) times higher bankroll if one has the same ROIs, btw).

The problem with 3-max spins is that they're already being heavily studied with the use of postflop solvers. If you intend to make a profit at the 30s without being staked, you'll need to invest money and time into one of the solvers and the hardware or cloud server required to run simulations within bearable timeframes. Fortunately, the damage done to the bankroll by such purchases will be likely recovered reasonably fast due to the softness of the low stakes.

But I don't intend to play a high volume of 3-max spins ever again, so you'd better wait until the 3-max gurus correct me and give their advice.

As to Spin & Go Max, the same methods as in usual spins allow to gain some edge in winner-take-all tourneys, though the gain will be smaller because of the lower average stack size, but as to tourneys with a bubble, I find ICM inaccurate in some spots, so I do some calcs in my head (to take a rest from the laptop screen), on paper or, better, in Excel.

As for volume... I intend to play for as many hours as my random mood allows me (i.e. not many), and as many tables as my brain can realistically handle without overload.

I'm (prrrretty) drunk so I read 'wait until you have around d 70 cev at a limit and then move up'.

I have sufficient side income so I don't have to care about the roll until I get to the 30's for now.

Monday or Tuesday I will reset my roll to $50 and start at 1's. Care to follow me? Or you'll be off 2+2 soon?

Yes, I do expect to be off 2+2 soon...

I'm generally not a fan of setting up an 'artificial' roll and doing artificial challenges... my roll is basically my liquid net worth minus 2 months' worth of life expenses (so that I have enough time to sell some of my belongings if the poker goes wrong). The struggle is real.

In your case, where you have a large non-poker hourly profit and just don't have enough skill for serious stakes yet, don't worry at all about wins/losses during the learning until you're good enough for the 30s. Start at the 1s, then, after collecting a +EV sample there, move up to 3s; once you crush them EV-wise, move up to 7s regardless of how much you've actually won/lost.

What would you consider to be crushing stats cev and roi wise?

Oops, my wording was bad, I meant smth more like 'satisfactory' instead of 'crushing'. I meant 7% ROI, which corresponds to 70 cEV at the 15s (which is indeed a very good result); for lower stakes, add 5 chips per 1% extra of rake to the requirement, i.e. 75 for the 7s, 80 for the 1s-3s, though it's not the maximum of what a grinder can achieve at those micros.

But it's just a wild guess, let others give a preciser estimate.

I've never been in a situation where I'd put in volume at adjacent stakes on the same network (because iPoker's Twister limits were capped at €10 until the summer of 2016, and pre-MPN PKR's biggest limit was $12; I was splashing the cash back then, but not to an extent where I'd dare to be a reg in higher PS / FTP games).

My best estimate of the difference between the adjacent stakes is 15 chips / 3% ROI - between the €5 and €10 Twister in the middle of 2015 (8% and 5% ROI after rakeback) - but my sample for the €5s is too small, and the difference was probably affected by the abundancy of rakeracers at the €10s.

[Of course a lot has changed since then, so these numbers aren't representative of what's happening on iPoker right now (I've read on a Russian forum that good regs of €50 Twister have 35-40 cEVs / 4-5% EV ROIs currently, all coming from rakeback and races, which is a good result considering the 2-minute blind levels and the antes, but if they fail to hit 100x+ JPs, their actual ROIs may be merely 1-2%, so the iPoker grind is now a risky business).]

So it makes sense to me to move up from a limit where I'd have a 7% ROI to one where I'd have 4% (as 4*2 > 7) but not move up if I merely had 6% at the lower limit.

I could do a 'if my cev is 70 and my roll is at least x BI for next limit I will move up' at the 1-3's and the higher I'd go the lower the cev and perhaps higher amount of BI. I will put something together on Monday and post it here.

Does this make any sense?

1-30s challenge

$1:
90cEV over 2k sample and 30BI for 3s ($90)
$3:
80cEV over 2k sample and 40BI for 7s ($280)
$7:
70cEV over 2k sample and 45BI for 15s ($675)
$15:
60cEV over 2k sample and 50BI for 30s ($1500)

This does make sense because you're not at risk of starvation and your goal so far is just to learn, so there's no need for you to move up from $1 to $3 asap, and you can hone your 'anti-fish game' (exploitation of recreational opponents) at $1 with little risk.

The only thing that I'd change is raise the cEV requirement at the 15s to 70 because I'm afraid of a somewhat large strength gap between the populations of the 15s and 30s (as the latter is the lowest limit where serious developed-world regs' egos allow them to stay for long).

I mean, if you merely have 60 cEV at the 15s, you'll be toast at the 30s (earning less per hour than at the 15s) until your strength improves by 10 chips.

Let me emphasise it once more: my approach is to move up not because I'm in the top Y% of the current limit's population by strength, but simply when I assess that I'd be earning more $ per hour at the next limit, taking the population skill gap into account (and I monitor the assessment continuously and move back down if I find out that I was initially wrong). The reason why some regs move up too soon is their egos. My approach is not to copy other regs but to check my ego at the door.

Makes sense. My game VS recs is already fairly decent, while VS regs I'm lost and terrible (unbalanced) most of the time. So I can foresee some trouble coming up there. I will put some thought in a moving down 'strategy' and how to study to improve my weaknesses and I'll be good to go.

1-30s challenge

$1:
+ 90cEV over 2k sample and 30BI for 3s ($90)
- back to $1 if <$66

$3:
+ 80cEV over 2k sample and 40BI for 7s ($280)
- back to $3 if <$150

$7:
+ 75cEV over 2k sample and 45BI for 15s ($675)
- back to $7 if <$375

$15:
+ 70cEV over 2k sample and 50BI for 30s ($1500)
- back to $15 if <$1030

Looks good.

Again, if the goal were to maximise the profit, I'd advise to move back down at the same bankroll point (plus-minus 2 BIs so that limits not be mixed within sets of games) as the one for moving up, but as your goal is to learn and you probably want to have more connected (uninterrupted by moving up/down all the time) samples per limit, giving yourself some leeway instead of moving down immediately is fine in your case.

did i understand correctly, that your assumption is that for each BI level your cEV drops by 20? that seems like far too important a variable than to make such an assumption, i believe. did you use any data to back this up?

I don't have much data about this, see the latter half of post #13 ITT. Again, please note that I don't compare the cEVs of the best regs (who're different people for different limits) nor the cEV that one has currently with what he'd have after moving up and collecting a large sample while learning at the same time, but the cEV that one has currently with what he'd have immediately after moving up, without learning. In this setting, I'm afraid that the 15-chip difference is an underestimate.

That's why, in my own career, I'll start by playing decently sized samples at the 1s and 3s and assessing the cEV gap between them, then I'll take a shot at the 7s assuming that the gap is similar, then update my assessment basing on the data from the 7s, and so on. I think that hardly anyone has such data for Spin & Go Max yet anyway.

This is one of the advantages of the Yo-Yo BRM (aka the Schrödingrinder BRM if you wish, coined so because the grinder is randomly found at one of a wide range of limits) - by playing different stakes in the same week, I'll be able to remove the influence of learning from the assessment of the population skill gap between the stakes because learning will affect the cEVs at all the played limits about equally.

A faster way to assess the gap, though, is to measure the reg/rec ratios at each limit and then regress the cEV data on the reg/rec ratio. Measuring the cEVs vs the rec population and vs the reg population separately also helps. I haven't heard about any research quantifying how the ratio affects the cEV yet; mind that I've never had a Spinlyzer account, and now it's too late to extract data from there (and I'd actually still refrain from doing so because Stars are now attentively monitoring spin regs for possible T&C violations).

But I think that stables with a lot of past and current horses have enough data for such an assessment. They can do something like double exponential smoothing to estimate how fast people learn and gain cEV, then they can subtract the learning factor to determine the negative jump in the current 'true' cEV that a typical horse experiences immediately after being moved up.

How fast, IYO, does a reg with a good work ethic gain cEV by learning? The rate of 2 cEV per 1K games looks realistic, doesn't it?

I guess I can incorporate the linear (in time) growth of skill into the model if I make the inaccurate assumption that the learning rate is independent of the limit that I'm playing. The addition of a positive learning rate will likely lower the BR requirements further but won't change the fact that I should never move up if my current hourly at the next limit is estimated to be smaller than the one at the current limit.

As for the incorporation of a heterogeneous skill growth rate that does increase when one steps out of the comfort zone (i.e. moves up prematurely), I don't think I can elegantly solve the stochastic control problem in that case without an advanced simulator.

The many cups of tea that I've had don't seem to have had an effect on my brain yet, so I might be mistaken in this post.