For the stats obsessed: Let's look at variance (long but worth it)

[SuitedSixes]

I just won my 100th SNG since I've been keeping track of these things. This is also significant because victory #100 was my 4th win in a 4 table session (never hit a Grand Slam before). What is even more significant is it was my 5th win in a row, after 10 OTMs. Variance is a bitch.

In a post earlier today, Irieguy said,
[ QUOTE ]
Managing variance is really a psychological endeavor. You just need to keep your head straight while you run badly so that you are in action and playing well when you start running better than average. A few times a year you will run really, really well and make a ton of money. The mistake most of us make is to allow our perspective to change during these hot runs and we redefine our expectations. It's difficult to wrap your mind around this concept, but making $10 a SNG means that you actually make $1 a SNG for several weeks, and then $50 a SNG for a few days.

[/ QUOTE ]

I thought it might be fun, and useful to get a look at what variance is supposed to look like so we can "wrap" our mind around the concept.

(Disclaimer: I got this from another forum a few months ago, so I don't really know all of the math that goes into it. It was originally designed to illustrate hours of playing hold 'em ring games, the numbers won't be exact possibilities for tournaments, but on average, they will be correct.)

Ok, step by step:
1) Create a new spreadsheet in Excel
2) In cell A1 enter <font color="red">=RAND()</font>
3) In cell B1 enter <font color="red">=(X*NORMSINV(A1))+Y</font>, where X is your SD/tourn and Y is your profit per tournament. This converts the random number to your win for that tournament.
3A) If you don't know what your standard deviation is per tournament, it is safe to guess 1.8 * Buy In Amount.
4) Copy cells A1 and B1 through A500 and B500.
5) In cell C1 enter <font color="red">=B1</font>
6) In cell C2 enter <font color="red">=C1+B2</font>
7) Copy C2 through C500
8) Select the entire C column and click on the '$' in the tool bar, this will convert the random # amount won or loss to dollars.
9) Select C1 through C100 (or whatever range you want) and make a line graph. This will give you an idea of the range of swings that you can expect over 100 tournaments (or whatever range you selected.
10) If you want to see how much things can change even within 100 tournaments, save the spreadsheet. Every time you save, the random numbers will change and give you another view of what our friend variance can do.

The next time you're running bad, just open up this spreadsheet and remind yourself that this is variance. This is normal.

[AleoMagus]

But wait a minute... How do we know that SNGs results are independent or obey a normal distribution!!!!!?

kidding.

Seriously though, nice post. I'm going to do a nice version of this with insertable ROI values, buy-in values, etc... and I'll provide a link for my freeservers site.

Regards
Brad S

[lorinda]

But wait a minute... How do we know that SNGs results are independent or obey a normal distribution!!!!!?

I'm aware of the arguments on this.

I would imagine that results of sets of sngs (whether it be 3 or 4) would follow a normal distribution, however I would think that games within a set are probably quite a way off it.

I have many people that I've only seen 3 times in PT, and those people have often played 3 games against me at once.

Lori

[SuitedSixes]

Way to one up me, AM! Just kidding, I was going to run it by you first, but figured you were tired of excel related matters. So since you started it: Do you know how to make it so that the random numbers would be an appropriate distribution of -11, +9, +19, +39, or a factor thereof?

[Irieguy]

[ QUOTE ]


The next time you're running bad, just open up this spreadsheet and remind yourself that this is variance. This is normal.

[/ QUOTE ]

I just use my own spreadsheet and get the same effect.

Irieguy

PS- Congratulations on the grand slam! Revel in it while you can, it is rare. 8 out of 8 wins while 8-tabling is called the "Holy Grail." Please brag out there if anyone has found it. I have not.

[AleoMagus]

Ok, that was easy

http://www.aleomagus.freeservers.com/spreadsheet

the variance demo.xls file

it's not very fancy, but it only took a second to realize that I can do a much better version that calculates actual finish results with associated prizes by just making an 'if' statement that associates the random numbers with finishes. For example:

0-0.15 = +127
0.15-0.30 = +57
0.30-0.45 = +27
0.45-1 = -33
(or whatever)

This is ok for now

Regards
Brad S

[SuitedSixes]

Nice. Isn't there an easier way to refresh the random numbers? I thought it was F4, but that doesn't do it.

[AleoMagus]

Sadly, I have not found even a grand slam yet

I do have a few 1,1,1,2 and 1,1,2,2 sets... but the grand slam is a tricky accomplishment

The 'holy grail' seems like something you could search a lifetime for and still not find.

Regards
Brad S

[Irieguy]

[ QUOTE ]

The 'holy grail' seems like something you could search a lifetime for and still not find.

Regards
Brad S

[/ QUOTE ]

C'mon, Aleo. That's a little imprecise. I was expecting:

"You can expect to find the Holy Grail once every 1,875,000 8-tabling sessions... on average."

Irieguy

[Mr_J]

I managed the grand slam in around 100 sngs. That was part of 7 wins in 12 sngs. Isn't it great to experience the healthy side of variance when you start out [img]/images/graemlins/wink.gif[/img]