The question seems simple enough, however it's something that I've wrestled with for some time now. Before we get into the world of poker, let me frame the discussion with a concept that is more familiar to me. In finance, most investors are not focused on maximizing expected return, rather they will try to optimize the Sharpe Ratio of their portfolio - a measurement of incremental return per unit of risk. It is calculated by taking the expected return, less the risk-free rate, divided by the standard deviation. Now of course each investor has their own utility curve and typically investors have unique utility curves; rational investors are typically risk adverse - of course I do recognize the irony in that poker is inherently a risk seeking game. Perhaps more relevant to poker would be an aversion to spending time grinding away? Regardless, I have yet to really come across this in discussions around bankroll management, expected returns or even around the ability/willingness for one to move up or down in stakes.

To give a specific example, let's say over the course of 100k hands (a reasonable, but not infinite set) a fantastic player might expect to make 8bb/100 at 5NL. Should they move up to 10NL if they can make 4.5bb? Probably since time is finite, but it depends on their bank roll and an acceptable risk of ruin. If you gave me the choice of being 7bb/100 vs 8bb/100 with twice as much risk, I could give you multiple justifications for preferring the former. The interesting question to me, is what is an acceptable level of variance of one's green line to justify a player being fantastic?

As a new player who has played only 26k hands and is average at best, what is the appropriate level of variance? How often should I be stacking off? Now of course the answer is "It depends", I know. But considering very few people probably play more than a million hands (realistically, I don't know if I will be one of those - and those that do, probably play many many more) I would say that even if I knew my skill, or lack there of, would cap me at most to 8bb/100 then there probably is a maximum acceptable level of variance over time for me.

I might say if you knew ex-post what your true equity in every pot you played (fold equity, pot equity as well as implied odds at each point in time) then you could calculate your expected return. In fact, some of you here are probably quite good at estimating this ex-ante with a fair degree of certainty. Realistically, I can't (at least well, but I am trying to improve). Thus, at some point it might be valid to say that I'm stacking off in poor spots far too often (or building pots far too quickly, putting me in a situation requiring me to stack off) and I am better off trying to control variance by being less aggressive and folding more. Thoughts?

TLDR; in poker as in life you don't know what you don't know. It's impossible to know what your exact fold equity is, or even what your opponents exact range is - especially if you are a relatively new player (though I admit there are those that are quite good at estimating these numbers). Is there any point you are better off trying to purposefully mitigate variance in situations that are probably +EV? Maybe a better way to put it is how thin is too thin (especially when it requires stacking off) for a new player?

Game: 100bb 6-max (usually cash out before I get too deep)
# hands: 26,357
bb/100: 4.22
VPIP/PFR/3bet: 21.6/18.4/6.59
WTSD%: 27.7
W$SD%: 51.9
Agg: 2.42
# of hands won >80bb: 57
# of these hands w/ $EV diff -80bb or lower: 8
# of hands loss >80bb: 44
# of these hands w/ $EV diff +80bb or higher: 7

Sometimes it feels like I am an aggro fish and I stack off far too frequently, but honestly I have no clue. If anyone needs other stats I am happy to provide them. Thank you all for your thoughts! I hope this wasn't too much of a rambling first post.

this is all a bunch of mental masturbation.

Read the theory of poker about the fundamental theorem of poker.

lol def this ^

the book Professional No Limit Holdem also comes to mind with all the SPR discussion

There are ways to play hands that have roughly the same EV but with less variance. Generally that is keeping pots small and choosing the passive action versus the aggressive action. However the most important aspect of keeping the variance below insanity levels is to win at a high rate. Who cares if you have 100bb/100 or 200bb/100 stdev when you win at 10bb/100.

If you want to use a similar metric I guess you could divide the winrate by stdev in units of bb/100 divided by bb/100, which is dimensionless. Depending on what type of games you play that may be good or bad. Winning more typically involved fish spewing and more variance. I guess at higher stakes these things may come in handy but at lower stakes just try to win a lot. The only reason live poker is possibly is because of high winrates to compensate for the low volume.

Thank you both for the thoughtful responses - I have read both of these books. FTP acknowledges that perfect information would help a player to make +EV decisions. It in no way discusses variance beyond the fact that it implicitly promotes it when one is ahead. SPR is simply a tool to tell you how committed you are to a pot and useful in how to either build a pot or select hands depending on your stack size; not sure I understand how this is relevant when discussing frequency of stacking off - especially when you have full stacks.

I think ultimately you are right; when games are low enough stakes that there are fish spewing constantly, that will be the largest governor of win rate. I'm sure many times when I stack off aggressively with draws, I'm becoming the fish by over valuing the fold equity. Honestly finding the fold button myself would probably help me a lot hah.

Would love to hear the thoughts of others; especially with regards to the number of occurrences that I've stacked off - is 0.4% of the time too often? I mean with a 20 VPIP that's like 2% of all hands played.

ROR is really a bankroll issue. Can you afford to play the stakes you're playing at, or are you "scared money"? If you have zero ROR (for example, if you have a day job that pays all your bills, and just play 1/2 for fun) you are free to take the most +EV moves, even if they are highly speculative. Obviously you can't jam every time you're a 55/45 favorite if your entire life roll is on the table without running into serious problems.

But this is going to be very player dependent. There isn't math answer to it. In investing, you're generally dealing with a situation where you don't have an external source of funding. If you run your mutual fund to zero with boom/bust strategy, there is no guarantee you'll get future investors.

Short answer: maximize EV, but don't play at stakes where a bit of runbad will backrupt you, especially if you have no other source of income.

there is a stat called standard deviation/100 hands in HM, you can compare yours with some players you consider good to see where you stand. Havent used it in a while, bad I think something like 80-120 bb was standard for 6max nlhe, 160-ish for HU

in general, correct way to play poker is A LOT higher variance and involves A LOT more stacking off that most beginner players think. Beginners and losing players attribute emotional value to not losing stacks, thus affecting their play very negatively.

another general rule is that being being risk-prone in poker tends to be much less bad than being risk-averse, since population of bad players tends to be risk averse.

the above of course applies to in-game decisions, not bankroll management

Both very helpful! Especially the stat STDV/100bb stat in HM - I was surprised that I came out in a reasonable range of 85.7 over my sample set. It would be interesting to think about if I am correctly balancing aggressive play with number of times stacking off. How often should you be getting stacks in when you are waaaaay ahead at in the micros?

How often should you be playing for stacks? As often as you are able to with your strong hands.

How often are you actually able to play for stacks in the real world? Rarely these days. It's very rare to get your sets and other big hands paid off for 3 streets of value in today's online games.