Varience differnce in Full Ring vs SH, NL vs Limit

[Piz0wn0reD!!!!!!]

i dont have huge sample sizes, but this is interesting:

A friends stats:

37k hands at full ring 5/10 = SD of 14.3BB/100

88k hands at SH 5/10 = SD of 15.5BB/100

my stats at NL:

84k hands at 100NL Full Ring (2$ Bblind) = SD of 33.4BB/100 (133$/100)

17k hands at 100NL SH (2$ Bblind) = SD of 25.4BB/100 (102$/100)


How can this be? Are my sample sizes too small? Does WR play a large roll in this?

You math guys please tell me what is going on here.

[Piz0wn0reD!!!!!!]

sklansky, malmuth..... where you at brothas???

[Piz0wn0reD!!!!!!]

Miller??? anyone?

[SomethingClever]

Um. 2+2=4.

POWN

[gaming_mouse]

I think it's possible, though somewhat unlikely, that the discrepancy is due to your sample size.

It's more likely due to differences between your playings style and your friends. Is he hyper-aggressive short handed?

Also, it seems that your results are more in line with what we should expect, based on the article in the other thread.

gm

[Piz0wn0reD!!!!!!]

[ QUOTE ]
I think it's possible, though somewhat unlikely, that the discrepancy is due to your sample size.

It's more likely due to differences between your playings style and your friends. Is he hyper-aggressive short handed?

Also, it seems that your results are more in line with what we should expect, based on the article in the other thread.

gm

[/ QUOTE ]

We are both hyper-aggro. I think that this trend is because the players in NL 6max make way more mistakes in big bet situations, thus i push a bigger edge more often than in a limit game. This is just my hypothesis, and i am very curious as to what is actually happening here.

[Piz0wn0reD!!!!!!]

PS. i dont think its my sample size. My SD has not moved more than 1/2 a BB in the last 15k hands or so.

[gaming_mouse]

[ QUOTE ]
PS. i dont think its my sample size. My SD has not moved more than 1/2 a BB in the last 15k hands or so.

[/ QUOTE ]

Yeah, I didn't think it was either.

Also, the article about how SH-variance is usually smaller was for limit games. It may, or may not, carry over to no limit. However, your friend's stats seem to be an anomaly, though hyper-aggressive play helps exlain them.

As for what you're seeing in the NL games, I think your explanation is as good as any I can think of. But who know for sure? It's a complex beast to understand. But whatever the reasons are, your sample size is big enough to trust your stats pretty well, as you said.

PS: Who is your avatar a picture of?

[Piz0wn0reD!!!!!!]

I was always under the impperesion that limit SH did have higher varience than its full ring counterpart.

my avatar is just some little girl on the internet that i jokingly claim i would have sex with. Prolly too poor taste for 1/2 of 2+2. ill change it soon.

[gaming_mouse]

[ QUOTE ]
I was always under the impperesion that limit SH did have higher varience than its full ring counterpart.

[/ QUOTE ]

We had this discussion already, but I'm still convinced that impression is wrong.

[ QUOTE ]
my avatar is just some little girl on the internet that i jokingly claim i would have sex with. Prolly too poor taste for 1/2 of 2+2. ill change it soon.

[/ QUOTE ]

Nonesense. Play to the elite among your audience, not the rabble.

[Piz0wn0reD!!!!!!]

[ QUOTE ]
Play to the elite among your audience, not the rabble.

[/ QUOTE ]
good call.

[Piz0wn0reD!!!!!!]

I am not satisfied!!!!! chime in math guys!!!!

[gaming_mouse]

[ QUOTE ]
I am not satisfied!!!!! chime in math guys!!!!

[/ QUOTE ]

It's not really a "math guy" thing. There is no "solution" to your question, only explanations of the sort that you offered yourself.

Not to say that someone here might not have an insightful one, but it seems like you're looking for hard and fast answers where there are none. Things like variance are affected by playing style. Those effects can take various forms and degrees of intensity. Your results don't seem all that strange considering this basic fact....

[jtr]

Not really a math guy, but I've got a pet theory about why the typical non-mathematical player's understanding of variance is potentially inaccurate. This theory doesn't explain the interesting numbers you quote above (and my own are similar but with an even smaller sample size). But it might explain why we have certain truisms about variance floating around (e.g., SH is higher variance) when they're not necessarily true.

Here's the theory. The variance we get excited about is the variance that causes us to have downswings over a significant number of hands. If variance causes only a few peaks and troughs in a healthy upward trend then we don't mind it too much.

So, let's suppose for a minute that a certain player in a short-handed game actually has the same variance that he would in a full-table game. If it's the case that the short-handed game causes him to have to make more tough decisions, e.g., calling down when he's unsure if his hand is good, etc., then it may be he'll experience a lower winrate in BB/100 than he would at the full-table game. This will lead to the variance feeling more significant, because, for example, he's much more likely to be in the red after 5000 hands, etc. Of course, in our little scenario the variance is not to blame but the lower winrate is.

I first thought this up when trying to figure out I (and others) found NL games to feel more "low variance" than playing limit, even when the numbers indicate that they plainly are not. At least in my case, better winrates in the NL games lead to a feeling of doing well at the game, which leads to not really noticing the variance.

Hope this is of some use.

[gaming_mouse]

jtr,

Very nice post and good insight.

gm

[Piz0wn0reD!!!!!!]

good show. However i belive that one would attain a HIGHER WR and SH. This i am not sure of tho, and im sure there are other variables that could show diff results. Also, from past experiences and compairng my stats to my friends limit stats: limit DOES have longer lasting swings than NL. While we do have large sample sizes for this, they are still not large enough to draw cut and dry conclusions.

As i understand it V=SD^2 which, according to my stats, shows less varience in the SH vs full. I also am under the imppression that SD becomes accurate reletivly fast.



maybe we should get a bunch of people stats, pool them and take a look.

[gaming_mouse]

[ QUOTE ]
As i understand it V=SD^2 which, according to my stats, shows less varience in the SH vs full. I also am under the imppression that SD becomes accurate reletivly fast.

[/ QUOTE ]

i'd always had the same impression, and i think it does become reasonably accurate fairly quickly.

however, the convergence is not as fast as we usually assume. there were some threads by jason1990 a few weeks back about the topic. it is actually quite complex. He discusses how to calculate an SD for your SD. And the convergence, if i remember, is pretty slow.

[pzhon]

[ QUOTE ]
I first thought this up when trying to figure out I (and others) found NL games to feel more "low variance" than playing limit, even when the numbers indicate that they plainly are not. At least in my case, better winrates in the NL games lead to a feeling of doing well at the game, which leads to not really noticing the variance.

[/ QUOTE ]
There is a meaningful sense in which NL games have a much lower variance than limit games. For a fixed size of the big blind, NL has a much larger variance, but for a fixed win rate of a decent player, limit has a larger variance.

The NL $100 full game with a $2 big blind had a standard deviation of only $133/100, just under the standard deviation of a $5-$10 limit game. However, good NL players typically win more from $100 NL than good limit players win from $5-$10 limit. That means downswings are shorter in NL than in limit, and for a fixed bankroll, you can safely win more per table-hour playing NL than limit.

[uuDevil]

FWIW, poster grisgra did some polls to collect SD data in the micro, ss, and sh forums a while ago:

SH Poll (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=headsup&Number=1362508&For um=All_Forums&Words=deviation&Searchpage=0&Limit=2 5&Main=1362508&Search=true&where=bodysub&Name=1538 4&daterange=1&newerval=1&newertype=y&olderval=&old ertype=&bodyprev=#Post1362508)

Micro Poll (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=micro&Number=1362540&Forum =All_Forums&Words=deviation&Searchpage=0&Limit=25& Main=1362540&Search=true&where=bodysub&Name=15384& daterange=1&newerval=1&newertype=y&olderval=&older type=&bodyprev=#Post1362540)

SS Poll (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=smallholdem&Number=1362524 &Forum=All_Forums&Words=deviation&Searchpage=0&Lim it=25&Main=1362524&Search=true&where=bodysub&Name= 15384&daterange=1&newerval=1&newertype=y&olderval= &oldertype=&bodyprev=#Post1362524)

I think there are some problems with these polls, but if someone has time to make a comparison, please post your thoughts.

[Piz0wn0reD!!!!!!]

[ QUOTE ]
[ QUOTE ]
I first thought this up when trying to figure out I (and others) found NL games to feel more "low variance" than playing limit, even when the numbers indicate that they plainly are not. At least in my case, better winrates in the NL games lead to a feeling of doing well at the game, which leads to not really noticing the variance.

[/ QUOTE ]
There is a meaningful sense in which NL games have a much lower variance than limit games. For a fixed size of the big blind, NL has a much larger variance, but for a fixed win rate of a decent player, limit has a larger variance.

The NL $100 full game with a $2 big blind had a standard deviation of only $133/100, just under the standard deviation of a $5-$10 limit game. However, good NL players typically win more from $100 NL than good limit players win from $5-$10 limit. That means downswings are shorter in NL than in limit, and for a fixed bankroll, you can safely win more per table-hour playing NL than limit.

[/ QUOTE ]

that is how i always understood it. However why would fewer players decrease the varience in NL? In limit it goes up?!?! Is this because my WR goes up in SH NL?

[jtr]

Thanks, pzhon: this is a really useful way of looking at the limit / NL difference.

And piz (etc., damned if I can spell your login name) yes, I agree that in practice a strong, aggressive player's SH winrate is often higher. That's a weak point in my theory, for sure.

Still: not being a hugely strong player myself, I have had a few experiences in the past where I dipped my toe into the short-handed versions of NL games in which I'd done fine at the full-table version, and my WR certainly suffered as I was much too tight and lost a fortune in the blinds. So these games felt "swingy" to me despite similar SDs to my full-table games.

Not expecting one anecdotal example to prove the point, just thought I'd mention it.

[jason1990]

[ QUOTE ]
There is a meaningful sense in which NL games have a much lower variance than limit games. For a fixed size of the big blind, NL has a much larger variance, but for a fixed win rate of a decent player, limit has a larger variance.

[/ QUOTE ]
Hi pzhon,

You seem to know something about this. Can you answer my question in this thread (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2013443&page=0&view=c ollapsed&sb=5&o=14&fpart=1)? Are there typical winrates and SDs for winning small stakes NL players, just as there are for winning limit players? If so, what are they?

Thanks,
Jason

[Piz0wn0reD!!!!!!]

wow, this thread is old.