Holy variance batman! (500th post)

[Outlaw]

For my 500th post I wanted to focus on something that I think most beginning and intermediate players simply do not understand. Variance and how much this game can suck over the short term.

There have been posts like this before, I know, but I think the dead horse needs beating in this instance. I have been reading a lot of posts lately about how people are running good/bad or are "beating" a stake. Then they post a graph with 2,000-20,000 hands and think this is a good sample.

Its not.

Let's take a look at some graphs that include 10 players each with the same winrate and standard deviation.

Graph #1: 10,000 hands is not a good sample.




Graph #2: 50,000 hands is not a good sample.




Graph #3: 100,000 hands is not a good sample.




Graph #4: 500,000 hands is a better sample.




Graph #5: 1,000,000 hands is an okay sample, but still isn't going to tell the whole picture.





Graph #6: 2,000,000 hands.. now things are becoming clearer.




Graph #7: 10,000,000 hands. Okay, now you are probably pretty close to knowing your true winrate. But oh wait.. you probably learned something over the past 10 million hands. Please start over so we can see how good your really are. See you in 10 more years.

Each graph is based on 10 players with the same winrate and same standard deviation. I used http://pokervariancesimulator.fr/ to create these. Money won per player is in the left column and the graph is a visual representation of each players winrate.

Notes:
1. One of the most important things any player can learn is that shit can happen for a long long time.
2. Positive variance over the short term (<500k hands) can make us think we are better than we really are. (see http://www.flopturnriver.com/phpBB2/...ath-t9214.html)
3. We need rakeback to keep us going during negative variance.
4. We need to focus only on making good plays and forget the results. (stop looking at PT/HM every 30 seconds!)
5. Over 100k hands we can be winning players and either make a buttload of cash or lose our ass if we don't exercise proper BR management.
6. Even over one million hands we still could running 50% under our true winrate or 50% over it.
7. (I will add to this as people comment.)

So now that we know we have no control over variance no matter how good we are, all we have to do is apply this knowledge to our games. How do we do this?

Feel free to either discuss the subject or post links to other posts who have addressed issues related to this.

[Vinland]

Wow.....I mean, wow!
Love those graphs, thats awesome stuff.

For me, positive variance makes me more confident and helps me enjoy the ride but I also feel that I dont begin to overplay my cards or really change my game much.

Negative variance on the other hand really turns me into a wuss. I start thinking that even though I should be raising preflop with my good holecards, I dont want to b/c I know that 2 players will join in the pot with me and I'll just have to muck my cards when I miss the flop (notice its "when I miss", not "if I miss") so I might as well just limp behind or fold now...

[shyguy03533]

those r some sic graphis
they actually help me put my game on a much grander scale

[wonderland]

Mother of christ this has changed my life.

QUESTION!!!

Where did you get this data from???

[Kijjo]

read the fine print at the bottom of the last graph, he tells you where he made those graphs.
good post. reminds me of a book I was reading (maybe Lou Krieger?) where he talks about that we always say the good players will win in the logrun, but statistically until internet poker, it was possible for a person to play 40hrs/week for a lifetime and never actually make it to the "longrun".

[wonderland]

hmmm, i motion to sticky this in the beginner's digest. Those in favour?

[dranger7070]

NH SIR

Puts things in perspective, and lets me know how fortunate I really have been over the last 5 months.

[surviva316]

i second the sticky. how many tens of millions hands have you played? congrats on 500 posts

[Sasquach991]

At my current rate of about 1000 hands per day,

it will take me over 27 years to get 10,000,000 hands.

Call me when I'm 75 and I'll tell you if I'm good at poker.

Maybe I'll be back up to 25NL by then.

Nice graphs

If I was still a losing player by the time I hit 100k hands, I would have quit.

[caddie444]

Which standard deviation did you use and how did you come to the conclusion to use that particular one?

It's just that I have a hard time believing that 100,000 hands is not at the very least a good indicator or your true winrate

[wonderland]

balls, i don't think PT3 has standard deviation feature.

anyone, anyone? bueller.... bueller.... bueller...

[meeloche]

This is such a good post. Take a good look everybody. If you're serious about this poker thing that is something you have to expect and be able to handle.

[Outlaw]

Which standard deviation did you use and how did you come to the conclusion to use that particular one?

It's just that I have a hard time believing that 100,000 hands is not at the very least a good indicator or your true winrate

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.

Wait until you have a 100k break even stretch or a losing streak that long. It will happen to you multiple times if you play enough.

It only gets worse as you move up. I'm sure there are plenty of people here with more experience than me who can attest to this.

Here is a variance graph of what a winrate of about 8BB/100 would look like (based off of my 5NL 24 tabling stats)



I would probably win around $750 in 100k hands at that winrate... but could win as little as $113 or as much as $958.. depending on variance.

Imagine playing 100k hands of 5NL break even... it could happen, even if you are soundly beating the games.

[grnydrowave2]

This almost makes not want to play poker ever again.

[TAGurit]

what a post! i...third?...the sticky nomination

[tyrn]

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.

This is your problem, what kind of player is going to have a $2/100 win rate and $27/100 variance? you wont even be breaking even on rake if your variance is this large with such a low win rate.

$2/100 win rate is 10ptBB/100 at 10NL and $27/100 std dev is 135ptBB/100. So for every 100 hands, the player with these stats is between 280 and -260 ptBB 95% of the time, or between $56 and -$52 at 10nl in only 100 hands.

Try a more reasonable $2/100 win rate with $6/100 variance

[grnydrowave2]

Try a more reasonable $2/100 win rate with $6/100 variance

I just tried this, and the 50k graph now looks like OP's 2 million graph. My faith has been restored.

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.

This is your problem, what kind of player is going to have a $2/100 win rate and $27/100 variance? you wont even be breaking even on rake if your variance is this large with such a low win rate.

$2/100 win rate is 10ptBB/100 at 10NL and $27/100 std dev is 135ptBB/100. So for every 100 hands, the player with these stats is between 280 and -260 ptBB 95% of the time, or between $56 and -$52 at 10nl in only 100 hands.

Try a more reasonable $2/100 win rate with $6/100 variance

First of all, variance is standard deviation squared, they're not the same thing. Second of all, the standard deviation is more like 20ptBB/100. They had that statistic in PT2, but they failed at putting it in PT3 (unless they did it already)

[wonderland]

yeah i was starting to wonder if there's any point playing if on the whims of variance we could be pro players yet not pay our bills for two months, randomly. This aint black jack!

SD is they key factor here, i hope everyone can agree on what a sensible figure is or the whole thing starts to fall apart a bit.

Again... little help... poker tracker 3 doesn't seem to have standard deviation.... ??

also, yeah i was starting to wonder if there's any point playing if on the whims of variance we could be pro players yet not pay our bills for two months, randomly. This aint black jack!

SD is they key factor here, i hope everyone can agree on what a sensible figure is or the whole thing starts to fall apart a bit.

25ptBB/100 is sensible
40ptBB/100 is probably right

but here, read this:
http://archives1.twoplustwo.com/show...ue#Post9901246

[wonderland]

ok, i think i'm almost there now.

So... when you said 25BB/100 i put the number 25 into the calculator and it went apeshit.... then i realised it said $/100. So am i right in saying that the math formula should be:

25 x bb (in my case 0.05c) x 2 (ptbb) ?

My stats are 0.80c/100 hands so i put in 0.8 and 2.5 but the graph went MENTAL @ 20k hands (where i'm at currently), so i tried to make it look like my graph somewhat and it took 4 as the sweet spot, so i'd say the 40ptBB/100 is more likely.

so i think folk should test it to see if it matches their current graph with 10 variations or so.

40 x bb x 2 in the SD box.

THEN we can see if we're going somewhere in half a million hands time.

well, the higher the standard deviation number, the wilder the graph will be
but of course you could just hit a weird graph if you run enough of them

[Outlaw]

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.

This is your problem, what kind of player is going to have a $2/100 win rate and $27/100 variance? you wont even be breaking even on rake if your variance is this large with such a low win rate.

$2/100 win rate is 10ptBB/100 at 10NL and $27/100 std dev is 135ptBB/100. So for every 100 hands, the player with these stats is between 280 and -260 ptBB 95% of the time, or between $56 and -$52 at 10nl in only 100 hands.

Try a more reasonable $2/100 win rate with $6/100 variance

I think you are off on your math here. A $2/100 winrate with a SD of $6/100 would be like winning at 100NL for 20BB/100 or something like that. Keep dreaming.

The whole point of the post was to show how bad variance can be over a small sample like 100k hands.. but how it becomes less of a factor the more hands you do play.

Any people with a ton of hands feel free to plug their $/100 hands winrate and SD ($/100 hands) into the simulator and see what you come up with over 100k hands. Post them here if you like. The url for the simulator is here: http://pokervariancesimulator.fr/

(I believe the default figures on the simulator were like running 1.5-2.5BB/100... which is pretty awesome over a lifetime for a good winning player... feel free to show otherwise, math people)

[Outlaw]

This almost makes not want to play poker ever again.

Almost being the operative word. I think its better to have this info, at least now peeps can stop tilting during a long downswing or break even stretch... which will help our win rate in the long run.

Staying off tilt will add xBB/100 to your lifetime winrate.

[kfaess]

Nice post outlaw, def gave me some insight into variance, however

I think these graphs are being misconstrued slightly. The point of the graphs is to show that your true winrate might not be accurate until a very large sample of hands. But my question is, how significant is this? If you are making good decisions and are a winning player then you will know you're winning/make money much before 10,000,000 hands. The thing most of us care about is beating a level and making some cash (at least thats what I care about) and less about what our true winrate is. If you work hard on your game and start plugging leaks then this will be affect your winrate and the amount of money you win long before 2,000,000 hands are played.

This is why I don't think the graphs should discourage anyone, which is what happened to me when I initially read the thread. Look at the graphs after 100k hands. All the graphs have winnings between approx 1500-2500 except for 1. What are the chances of a 100k breakeven stretch/downswing? Probably pretty darn small.

Look at all the small/mid stakes players on FTR. How many hands did it take each of them in any given level before moving up? Look at all the current micro stakes grinders and how fast they are able to move through the levels. I'm not that experienced in poker yet at all but I think its realistic for a player to play 50k hands at each of 2nl, 5nl, 10nl, 25nl and each time beat the level and move up.

I was gonna say more but some people just showed up at my house so I'll cut it short.

[dranger7070]

For kfaess,

I think that 50k hands would be a lil bit of overkill for all levels except maybe 25nl. I beat 2nl (starting at $10 finishing at $100) in 22k hands, 5nl in 15k hands (I may have moved up a little too soon (i had 20 BI's tho...) but it worked out) and I'm almost to the point where I can move up to 25nl at 22k hands at 10nl. I'll definitely be spending some time at 25nl tho.

[wonderland]

I think more to his point. He's saying that the sample size is too big.

I beat 2 for 12k, i have technically beat 5 for less than 10k but this variance flu has caught up with me and now i've decided to lay off moving up until it passes, just breaking even atm (dranger you know all this but for the sake of whoever).

And god knows how long i'll be breaking even for. There is a point though that SOME of us will be hitting that variance bitch hard and will be on those lower curves, some the opposite.

I just wonder why there are set 'periods' for getting repeatedly riverred in the anus over... and over... and over... and over...

But it seams there are.

Mooooon riiiver... wiiider than a miiile.

[Cougar]

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Robb contributed an awesome post about how to use this to calculate your personal variance stats in February.

http://www.flopturnriver.com/phpBB2/...ight=deviation

[Outlaw]

Nice post outlaw, def gave me some insight into variance, however

I think these graphs are being misconstrued slightly. The point of the graphs is to show that your true winrate might not be accurate until a very large sample of hands. But my question is, how significant is this? If you are making good decisions and are a winning player then you will know you're winning/make money much before 10,000,000 hands. The thing most of us care about is beating a level and making some cash (at least thats what I care about) and less about what our true winrate is. If you work hard on your game and start plugging leaks then this will be affect your winrate and the amount of money you win long before 2,000,000 hands are played.

This is why I don't think the graphs should discourage anyone, which is what happened to me when I initially read the thread. Look at the graphs after 100k hands. All the graphs have winnings between approx 1500-2500 except for 1. What are the chances of a 100k breakeven stretch/downswing? Probably pretty darn small.

Look at all the small/mid stakes players on FTR. How many hands did it take each of them in any given level before moving up? Look at all the current micro stakes grinders and how fast they are able to move through the levels. I'm not that experienced in poker yet at all but I think its realistic for a player to play 50k hands at each of 2nl, 5nl, 10nl, 25nl and each time beat the level and move up.

I was gonna say more but some people just showed up at my house so I'll cut it short.

I think we would typically be in the middle area of each graph.. however the extremes are possible due to variance. The graphs are actually meant to encourage people who might have had a big downswing recently. If you are solidly winning I doubt this post will discourage you. It might make you learn to appreciate running good a bit more though

[Outlaw]

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Robb contributed an awesome post about how to use this to calculate your personal variance stats in February.

http://www.flopturnriver.com/phpBB2/...ight=deviation

Thanks for posting this. I am not sure how I missed it back in February.

This should definitely clear up the SD thing.

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Where's "More Detail"

[dranger7070]

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Where's "More Detail"

lol

[daven]

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.
.

make sure of the winrates you are presenting here. Also confirm the logic - just cos it's on some website doesn't make it truth... I would like to see the results over 50k hands for a player with a 2.5ptBB/100 winrate. Then 100k, 200k. Standard deviation used is probably fine.

also

5. Over 100k hands we can be winning players and either make a buttload of cash or lose our ass.

this isn't true. We don't lose our ass - that's what bankroll management is for. Get it?

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Where's "More Detail"

lol

Where is it

[dranger7070]

I have no clue, I don't have PT3. I just thought it was funny lol.

[Outlaw]

PT3 has Standard Deviation metrics in the "Sessions"->"More Detail" tab.

Where's "More Detail"

Click on the drop down window where it currently says sessions-by time.. there is another drop down called sessions-details. It breaks down the SD by BB.

[Outlaw]

27, the default one. Its based off of a winrate of $2/100 hands. I'd guess that this is a player with a winrate of about 4BB/100 or so.
.

make sure of the winrates you are presenting here. Also confirm the logic - just cos it's on some website doesn't make it truth... I would like to see the results over 50k hands for a player with a 2.5ptBB/100 winrate. Then 100k, 200k. Standard deviation used is probably fine.

also

5. Over 100k hands we can be winning players and either make a buttload of cash or lose our ass.

this isn't true. We don't lose our ass - that's what bankroll management is for. Get it?

100k break even stretches are possible for any solid winning player at any stakes. I've seen the graphs on here more than once.

I updated the post to clarify that. Of course we practice good BR manage, what I meant is that you can lose your ass as in being stuck in neutral.. which for a winning player, sucks big time.

[Outlaw]

Anyone got any graphs to post showing your experiences with variance?

[dranger7070]

Um, I lost 8 BI's at 25nl in around 1.5k hands. Too lazy to post garph at the moment

[daven]

Um, I lost 8 BI's at 25nl in around 1.5k hands. Too lazy to post garph at the moment

people are too quick to pull out the -ve variance explanation. I could show you 20 buy-in downswings etc, but there is a common theme - the losses are -ve variance compounded by bad play.
My advice: Know about variance, take it into consideration when planning your bankroll management and game-play approach, forget variance (cos it is now irrelevant).

[grnydrowave2]

My advice: Know about variance, take it into consideration when planning your bankroll management and game-play approach, forget variance (cos it is now irrelevant).

Great advice. Allow me to memefy it.

1. Know about variance.
2. Consider it when managing bankroll and playstyle.
3. Forget about variance.
4. ????
5. Profit!

[dranger7070]

lol I'm not saying i didnt play bad, cuz i definitely didn't play my best, but I assure u, losing KK < 96o AIPF is variance. KK < AA, AA < JJ, etc is all variance. Stuff like that. Also, I know 8 BI's aint shit, which is another reason y i didnt post garf, ez game.

[TonyB73]

(sorry, double post - see following)

[TonyB73]

Um, I lost 8 BI's at 25nl in around 1.5k hands. Too lazy to post garph at the moment

people are too quick to pull out the -ve variance explanation. I could show you 20 buy-in downswings etc, but there is a common theme - the losses are -ve variance compounded by bad play.

Very true.

Case in point: I thought I was well on my way back from a 16-odd buy-in downswing at 50NL, until last night I sat down at a couple of the juiciest tables you will ever see and proceeded to drop 6 buy-ins in a 3-hour session. Now I'm back down at the bottom again.

At the time I thought I had been completely and utterly butt-f*cked by the poker gods - again - but after a painful post-session review I realised that while I had copped my fair share of coolers and suckouts, in truth the loss should and would have been substantially less had I maintained my focus and discipline.

I'm going to post about it more fully in the BC when I get a chance, because from what I've been reading around here lately I think some people might be able to learn from my experience. I certainly hope I (finally) do.

[Outlaw]

I just went through a month of running like ass and thought I'd bump this to cheer myself up.

[Gobbatino]

<3

I had never seen this post. Definitely a good thing to read through after what November did to my ass/bankroll.

[tomato paste carnage]

nice graph

Your posts are relevant to my interests














But seriously. This puts some perspective onto why some of my graphs look donked out; small sample sizes, and I'm a donk.

[Carroters]

This post is enlightening. I actually thought I had a reasonable grasp on variance up until I read this.

Maybe my 50k BE stretch at 50NL isn't as bad as it looks. Yay, I don't need to work on my game, I'll just wait for 2,000,000 hands and profit baby.

[Outlaw]

Uploaded with ImageShack.us

25NL so far this year. If I ran equally as bad as I did good, that's a difference of 80+ buy-ins. This over a "big" sample by some people's standards.

On another note, apparently I suck worse than I thought

[givememyleg]

Nice post, Outlaw. I'm sure you've been asked before but when do you plan to move up? Can't stay at 25nl for life amirite?

[Outlaw]

Nice post, Outlaw. I'm sure you've been asked before but when do you plan to move up? Can't stay at 25nl for life amirite?

I moved up in February, ran like 4BB/100 at 50NL for a week or so then hit a 16 buy-in downswing, got scared, and moved back down. So I changed by BR management requirements to 50bbs.

Then like an idiot, I cashed out 3k to buy some stuff (TV, blue ray, etc) and started back over at the beginning of 25NL.

I did move back up to 50NL yesterday though.. I feel like I'm a much better player now and hopefully am there to stay.