Small FAQ on Variance

[dmmikkel]

To be honest I haven't read much here, so someone might have posted something similar before, but since I see so many people who really don't have a clue about variance.

Also keep in mind this is v0.1 =) I didn't even bother reading through it myself.

What is variance?
Variance is how your results variates from your expected value or winrate.
If that wasn't simple enough: It's how bad/good you can run.

So, how bad/good can I run?
Quick answer: Bad, really bad.
Long answer: Standard deviation (SD) are used to describe this. In SNGs we use SD/tourney. Your results are 70% likely to be within one SD and 95% to be within two SDs. I usually calculate using two SDs, because you're rarely outside that.

Say you play 10+1 SNGs at 15% ROI (yeah i know it's low) and you're SD/tourney is around 19. If you play 500 SNGs (you might think this is alot, but I'll prove it is not) you're total SD would be sqrt(500)*19. Thats about 425. With 15% ROI you should have $825. Your results are 70% likely to be $825 +/- $425 and 95% to be $825 +/- $850. My point is that you can play a lot (in this case 500) of SNGs and still not be in the positive.

Now I think being about break even after 500 SNGs is running really bad, but it says alot about poker and SNGs. First of all it tells you a winning player can have a really bad run, but it also tells you 500 SNGs isn't really that much. One of the most interesting part of this is that a losing player, can run really good for over several hundred SNGs, which again explain why so many are fooled into thinking they're better than they actually are.

How many SNGs do I have to play to know if I'm winning?
You should have a good idea after 500, but i would play atleast 1000 if you're planning to quit your job.

How many SNGs do I need to know my ROI?
As I have already proved, 500 hardly says anything. For a rough estimate I would play 1000. If you want to be pretty sure, I would play 3-5 times that.

How big bankroll should I keep?
As with everything in poker: It depends.
If you're planning to make a living of SNGs you should know this yourself. If you don't I wouldn't quit my job if I were you.
If you're planning to build a bankroll, 30 buyins should be fine as long as you drop down if you run bad.
If you don't want to drop down I would keep 100 buyins just in case.

I have 30%+ ROI at the XXs
No you don't.

The point of this post was to maybe (but i have a feeling it won't help) get down on the number of "Look at my first 100 SNGs"-posts. 100 SNGs is nothing. Period.

[dfscott]

nh

[Nick M]

I'd read this thread...it's long (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=singletable&Number=230 2700&Forum=,All_Forums,&Words=&Searchpage=0&Limit= 25&Main=2302700&Search=true&where=&Name=15228&date range=&newerval=&newertype=&olderval=&oldertype=&b odyprev=#Post2302700)

[dmmikkel]

ty

[dmmikkel]

I did read it, before I posted this.

He has a experience look at things, I have a mathematical look at things.

[TStokes]

nice post thanks

[AleoMagus]

I posted this a while back which gives a pretty concise intro to calculations involving confidence and variance. It is worth looking at for those who'd actually like to perform some of these calculations for themselves:

Confidence Calculations (http://forumserver.twoplustwo.com/favlinker.php?Cat=&Entry=54096&F_Board=singletable &Thread=1373360&partnumber=&postmarker=)

Also, I have a few cool spreadsheets for calculating and simulating these kinds of things

Spreadsheets (http://www.aleomagus.freeservers.com/spreadsheet)

Specifically, one might be interested in the following files:

Confidence calculator - Automatically performs these calculations as well as ROR Calcs.

Variance Demo - Graphs a simulation of a players progress over hundreds of SNGs. It's pretty humbling to refresh the simulation and watch short term (Hundreds of SNGs) fluctuations in the negative. If you play with it long enough you can see some truly horrifying results that 'winning' players can achieve.

Regards
Brad S

[Scuba Chuck]

[ QUOTE ]
How many SNGs do I have to play to know if I'm winning?
You should have a good idea after 500, but i would play atleast 1000 if you're planning to quit your job.

[/ QUOTE ]

LMFAO

[curtains]

Id say 2500-3000, but ok 1000 can usually give you a good estimate as to whether or not you can win, however your win rate might still be quite a bit less than your results.

[Slim Pickens]

Nice try, but the people who don't want to believe you will still question you no matter how simply and clearly your post explains variance. I get it though. Well put.

Slim

[dmmikkel]

That's the point. I said you need more to figure out winrate, but you shouldn't have to play alot more than 1000 to know if you're a winner. Or do anyone have different thoughts?

[Jman28]

[ QUOTE ]
That's the point. I said you need more to figure out winrate, but you shouldn't have to play alot more than 1000 to know if you're a winner. Or do anyone have different thoughts?

[/ QUOTE ]

Well, after 1k or even 4k, you may not know how you might deal with a huge downswing when it hits. You may not know if you can handle playing poker day in and day out. You may not know if you can keep up the motivation level you started with.

Because of this, I'd wait a long time before quitting my job.

[dmmikkel]

I agree 100%

I didn't want anyone to quit their job after 1000 sngs, but there are people considering for a smaller sample size and they are way off.

You want to be a winner before you quit your job, and you just won't know that until you have played 1000.

If you consider quitting your job after only 1000 sngs you need to be very confident that you can beat the game and handle the variance.

[Jman28]

Yeah. We're in agreement then. Good post, by the way.

[dmmikkel]

ty =) you mean except for all my horrible spelling and writing =)

[Degen]

great post

[multifast1]

[ QUOTE ]
Say you play 10+1 SNGs at 15% ROI (yeah i know it's low) and you're SD/tourney is around 19. If you play 500 SNGs (you might think this is alot, but I'll prove it is not) you're total SD would be sqrt(500)*19.

[/ QUOTE ]
OK, could you explain where/how you calculate 19 as the SD/tourney? And if that is the SD/tourney wouldn't you're overall SD be just 500*19 instead of sqrt(500)*19 ?

[ QUOTE ]
How big bankroll should I keep?
As with everything in poker: It depends.
If you're planning to make a living of SNGs you should know this yourself. If you don't I wouldn't quit my job if I were you.
If you're planning to build a bankroll, 30 buyins should be fine as long as you drop down if you run bad.
If you don't want to drop down I would keep 100 buyins just in case.

[/ QUOTE ]
Don't most players "tweak" their style a bit when they're running bad.. even if not realising it? This combined with dropping down levels when in a bad run will lower your overall variance and therefore your SD. So how do these factors affect your SD/tourney calculation?

[ QUOTE ]
I have 30%+ ROI at the XXs
No you don't.

[/ QUOTE ]
Ummmm.... yes you do. It may not be sustainable or expected long term, but it's what you have at that moment for how ever many SnG's you've played..

Good post. Got me thinking for sure.

[multifast1]

bump.

Can anyone help explain where the variance equations come from? Looking at AleoMagus's spreadsheets, some of the formulas just don't make sense to me. Do they come from some probability and statistics handbook? Anyhow, I'd really like to understand this better. Thanks in advance.

[eastbay]

[ QUOTE ]

I have 30%+ ROI at the XXs
No you don't.


[/ QUOTE ]

That's a little too categorical for my tastes. I don't think it's impossible to get >30% in some games.

eastbay

[wiggs73]

[ QUOTE ]
I have 30%+ ROI at the XXs
No you don't.

[/ QUOTE ]

one of the funnier things i've read in a while on here.

nice post man.

[dmmikkel]

I have never seen anyone sustain this over a significant samplesize. I'm sure someone might be able to sustain this at lower buyins at other sites than party, but I don't think its possible at party.

[dmmikkel]

thats just the way you calculate it =) I'm really not sure, but I would think it had something to do with SD being the sqrt of variance.


I used 19 because that was what I had at the moment i wrote it =) It didn't seem way off

[ QUOTE ]
Don't most players "tweak" their style a bit when they're running bad.. even if not realising it? This combined with dropping down levels when in a bad run will lower your overall variance and therefore your SD. So how do these factors affect your SD/tourney calculation?

[/ QUOTE ]

You're absolutely right, changing your style of play would affect both EV and variance. These are not perfect calculations, but more a way of proving mathematically that you can run pretty damn bad =)

And for the ROI of 30%+ I'm thinking of EV and not winrate over 10 SNGs

[dmmikkel]

Your totalt SD = SD/Tourney * sqrt(number of tourneys)

SD = sqrt(variance)
do some searching and you should find how to calculate variance too =)

[eastbay]

[ QUOTE ]
I have never seen anyone sustain this over a significant samplesize. I'm sure someone might be able to sustain this at lower buyins at other sites than party, but I don't think its possible at party.

[/ QUOTE ]

Maybe no one has, but that's only because when people get results like this:

http://sitngo-analyzer.com/poker/ROI-33.PNG

...they move up. Was this a hot run? Sure. Was it so hot that 30% is impossible? I'm not confident of that.

eastbay

[Messy_Jesse]

I'm not sure its impossible- I've been running well, I'm sure, but still, this is over almost 450 tournaments at the 55s, 8-tabling. Im sure that if someone were 2 tabling or even 4-tabling, this could be even higher.

Jess


Poker summary 55s

ROI 32.8%

ITM 42.9%

Total Tourneys 436
Multitable utilization 8.50
Total entries $23,980.00
Total prizes $31,850.00
SNG Profit $7,870.00

$/Tourney $14.31
# hrs 51.29
$/hr $153.43
Avg Finish 5.56
Bubble % +/- 7.2%