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 /images/graemlins/wink.gif

[SuitedSixes]

I've hit for the cycle (1,2,3,4) a few times and even the Bridesmaid Slam once (4,4,4,4).

[Irieguy]

You haven't truly lived until you've had a "Prisoner's Welcome."

That's 4 10ths in a 4-table session aptly named after how you would feel following your first night in a county jail holding cell.

Irieguy

[SuitedSixes]

[ QUOTE ]
You haven't truly lived until you've had a "Prisoner's Welcome."

That's 4 10ths in a 4-table session aptly named after how you would feel following your first night in a county jail holding cell.

Irieguy

[/ QUOTE ]

lonely?

[Slim Pickens]

This has probably been done before, but I made one that takes an actual finish distribution as input. Does anyone care to look at it? It was cool to see some simulated runs using my actual finishes.

Slim

[AleoMagus]

Ok, the better and actual SNG result based variance demo

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

the variance demo2.xls file

I'm not sure if there is an easy auto refresh technique, but all I do is take an empty cell, type the number 1 in it (or anything for that matter) and hit enter. it changes all the random results.

Regards
Brad S

[Slim Pickens]

Thanks. Yours looks way nicer than mine. BTW, "F2" and enter will get a refresh without danger of changing a cell value.

Slim

[SumZero]

You're a pretty decent player if you hit the holy grail every 1,875,000 sessions on average (where each session is a start up of 8 simultaneous SNGs). That would mean you win first about 16.44% of the time. Even a small drop to 1st ever 15% of the time means every 3,901,844 or so times. To put that in perspective you expect the grand slam to occur every 1975 sessions or so if you are the 15% player. If you were a breakeven player (1/9 of the time 1st, 1/9 2nd, 1/9 3rd) you'd need 43,046,721 times to get the holy grail!

If each SNG session takes 1 hour and you play every hour of every day of every month of every year it would still take you more than 200 years to hit the holy grail with the 16.44% win rate.

[SuitedSixes]

That is depressing.

[Mammux]

Has anyone compared sng rois to ring game bb/100? I would like to know whether I should play ring games or tourneys if I seek to maximize my profit. I have approximate roi and bb/100 values for a couple of limits / buyins.

-Magnus

[Nottom]

F9 will refresh all the values.

[1C5]

Congrats on the grand slam!!! /images/graemlins/cool.gif

[AleoMagus]

Bored while playing a multi this morning and added a ROI/ITM progression as well to variance demo 2.

Had to cut it down to 400 SNGs to fit it on that site though.

I would encourage the excel familiar to expand the graphs out to 2000+ SNgs. It's interesting to see how long it takes for results to actually converge with your 'Actual' expectation.

Regards
Brad S

[bball904]

[ QUOTE ]
3A) If you don't know what your standard deviation is per tournament, it is safe to guess 1.8 * Buy In Amount.


[/ QUOTE ]

ROFLMAO. Absolutely brilliant statistical analysis contained in this thread. Lorinda, consider yourself the exception to this touch of sarcasm.

[Nottom]

[ QUOTE ]
[ QUOTE ]
3A) If you don't know what your standard deviation is per tournament, it is safe to guess 1.8 * Buy In Amount.


[/ QUOTE ]

ROFLMAO. Absolutely brilliant statistical analysis contained in this thread. Lorinda, consider yourself the exception to this touch of sarcasm.

[/ QUOTE ]

Why the hate?

[bball904]

No hate here.... "it's safe to guess" when alluding to standard deviation was one of my most used phrases on the way to a statistics degree.

Seriously, though, I find it more entertaining than anything, and don't have hate for anyone.

[AleoMagus]

You know, I can't figure you out...

You once claimed to not ever want to discuss stats again, then chimed in with protest in another thread, only to be debated with again (to which you claimed that another poster was to blame because he disagreed with you).

In a PM to me you made a diplomatic attempt to 'agree to disagree', but here we are again hearing dissent about some of these statistical ideas.

Is it just the Buy-in*1.8 estimate that has you bothered this time? Because I actually think for a winning player that is a safe estimate. I would have said 1.7 though. the point is, it's unlikely to be outside of 1.65-1.85 for any realistic real world sample, and for the purposes we have here, that's close enough.

Or are you still troubled by the normal distibution assumption, becasue I get the sense that you want to debate it a little more ...or maybe I do, who knows?

Regards
Brad S

[ericlambi]

Aleo,

Don't mess with bball. His powers of debate are only exceeded by his mastery of statistics.

[rachelwxm]

[ QUOTE ]

Or are you still troubled by the normal distibution assumption, becasue I get the sense that you want to debate it a little more ...or maybe I do, who knows?


[/ QUOTE ]

LOL.

AleoMagus, I remember you did some empirical analysis of normal assumption of SNG results for a big sample, where is the link? /images/graemlins/cool.gif

[Irieguy]

Here the explanation for why that estimate for SD is accurate:

why SD is 1.5-2.0 buy-in for SNGs (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&amp;Board=singletable&amp;Number=147 9432&amp;Forum=f22&amp;Words=%2Bwhy%20%2Bstandard%20%2Bdev iation&amp;Searchpage=0&amp;Limit=25&amp;Main=1479432&amp;Search=t rue&amp;where=bodysub&amp;Name=15228&amp;daterange=1&amp;newerval= 3&amp;newertype=m&amp;olderval=1&amp;oldertype=m&amp;bodyprev=#Pos t1479432)

This is NOT a statistical proof. It is a conceptual explanation by a non-statistician for all the non-statisticians on this forum. But, I believe Aleo does chime in with some real calculations to support my theoretical argument.

Irieguy

[bball904]

Thank you, I did find it slightly amusing.

[uaw420rook]

how do you increase it to 2000 or more tourneys.Im not real Excel literate

[bball904]

[ QUOTE ]
You know, I can't figure you out...

You once claimed to not ever want to discuss stats again, then chimed in with protest in another thread, only to be debated with again (to which you claimed that another poster was to blame because he disagreed with you).

In a PM to me you made a diplomatic attempt to 'agree to disagree', but here we are again hearing dissent about some of these statistical ideas.

Is it just the Buy-in*1.8 estimate that has you bothered this time? Because I actually think for a winning player that is a safe estimate. I would have said 1.7 though. the point is, it's unlikely to be outside of 1.65-1.85 for any realistic real world sample, and for the purposes we have here, that's close enough.

Or are you still troubled by the normal distibution assumption, becasue I get the sense that you want to debate it a little more ...or maybe I do, who knows?

Regards
Brad S

[/ QUOTE ]

Aleo, please don't misread my sarcastic "dissent" as wanting to debate this further. That ship has sailed.

I know you're smart enough to realize that the assumptions you break with your analysis probably invalidate them from a purely "scientific" perspective, but you can choose to continue to use them as what you feel are close approximations if that floats your boat. I reserve the right and will continue to provide snide remarks to such "analysis" in the future.

[Irieguy]

[ QUOTE ]

Aleo, please don't misread my sarcastic "dissent" as wanting to debate this further. That ship has sailed.

I know you're smart enough to realize that the assumptions you break with your analysis probably invalidate them from a purely "scientific" perspective, but you can choose to continue to use them as what you feel are close approximations if that floats your boat. I reserve the right and will continue to provide snide remarks to such "analysis" in the future.

[/ QUOTE ]

It is hard to be patronizing, condescending, and narcissistic to any significant degree using only 4 sentences of text. (I know, I often try it.) But you are able to pull it off with a frequency that is worthy of recognition.

You couldn't possibly have learned that from your undergraduate statistics coursework. Those skills can only become finely polished by working for somebody for years that you think is less intelligent and less deserving than yourself.

Irieguy

[tallstack]

[ QUOTE ]
I would encourage the excel familiar to expand the graphs out to 2000+ SNgs. It's interesting to see how long it takes for results to actually converge with your 'Actual' expectation.


[/ QUOTE ]

I played with sample sizes up to 10000 games (this is where it first started to lag on the refresh time). For an assumed 20% ROI player (.135/.135/.12 distribution for money finishes), the simulated ROI for 10000 games was generally between 18% and 22%. After 1000 games it was generally 10% to 30%.

I also added in some cells to track the maximum dip during the samples for the 20% ROI player, and was surprised with how often large dips occurred. Over the 10000 game samples, maximum drops of 30-50 buy-ins were the norm. The worst dip I saw was 87 buy-ins. That would hurt! For the multi-tabling, full-time players 10000 games should be little more than a year of play, so large drops &gt;50 buy-ins should unfortunately be hitting some of the players on this board a lot more often than I would have thought. I will never feel that safe with a 30 buy-in bankroll again.

Dave S

[tallstack]

SuitedSixes,

Thanks for kick-starting this thread! I don't think that anything else I have read on this forum is as therapeutic as watching my simulated player go through some brutal short term runs as I hit the refresh button over and over, while watching his bankroll always rebound nicely over the large sample sizes. The worse the run I put him through, the better I feel about the ones I have gone through.

This idea is gold!

Dave S

[SuitedSixes]

You're welcome, Tall Stack. It did turn out to be a pretty good thread with arguing, name calling, silliness, vocabulary flexing, and good spirited discussion. We hear all the time here "your sample size is too small" and "it takes a large sample to get a true ROI" but seeing the graph of our sample player over huge samples really is eye-opening. Of course, it won't keep most of us from doubting ourselves after an 0 for 11 run. That really is the difficult thing about playing poker after being enlightened by 2+2, you can never really be confident that you're that good. As humans, we're programmed to adapt, and it is difficult to adapt when playing correctly does not always transate it to a win.

[Nottom]

For anyone who may be interested, there was a post in the prob. forum (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&amp;Number=1711139&amp;page=0&amp;view=c ollapsed&amp;sb=5&amp;o=14&amp;vc=1) that had another method for charting the variance you may see in SNGs.

Its a bit more complicated but probably represents the actual swings a little better.

[SumZero]

Yeah, that was my spread sheet code. It is really fun to hit F9 and watch the chart change. Especially for a low (5-10%) ROI player. If you aren't a 25+% ROI player, the 30 buyin "rule" is too little (unless you are quick to move down levels when needed).