8 SNG set probabilities

[AleoMagus]

Well, this likely only interests me, but I'll post it here anyways in case someone else cares.

I calculated probabilities for, and graphed every unique $ finish possible in a set of 8 SNGs (as this is my daily regiment these days)

This is actually pretty cool, because it is an exact combinatoric calculation, and gives a confidence result, but without relying on Normal distribution assumptions.

an excel file called 'sng set probabilities' can be found at:

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

You can fiddle around with the input values at the top so that it refects your individual finish breakdown. It is currently set for $22 SNGs, (I've been 4-tabling those twice a day). If you change it for another buy in, you should adjust the scales on the charts to accommodate min and max values for your particular buy-in. Hopefully you'll see what I mean.

I think it I find some time, I am going to do this for an even larger set of SNG outcomes. 20 would be about the most I'd ever want to do on excel because the combinatorics get crazily huge after a while. Still, even with a 20 SNG set, it would give a much clearer picture of how the actual SNG results curve compares with standard normal distribution estimates. Actually, even this little 8 SNG sample does that to some extent.

What I really should do is learn to program and write something that would do much larger samles automatically. It really would not be out of the question for a fast computer to do these same kinds of calculations for a 100 or even 1000 SNG sample. In this way it would be possible to give EXACT confidence figures for even very large samples and predict confidence values exactly for future results over an upcoming sample that may also be very large.

Anyways, hopefully this interests someone
Any questions/thoughts?

Regards
Brad S

[ThorGoT]

Wow. This is way cool. I admit I don't fully understand it, but it is still way cool.

[AleoMagus]

Just in case anybody is having trouble figuring it all out, I'll offer a bit more explanation.

In the first graph, each point represents a possible $ outcome of a 8 SNG set. This is represented by a $ amount on the x-axis (you profit or loss) and a probability value on the y-axis.

In the 2nd and 3rd graphs, each point still represents a $ amount as an outcome, but the probability values are now the probability of that result AND every result better (or worse, depending on the graph).

It is possible to see then your odds of 'making the money' after an 8-SNG set, and other things like your odds of making more than $100 etc...

What is most interesting about this is that unlike my confidence calculator, this does not rely on normal standard distribution assumptions. This is simply a combinatorics calculation based on the respective probabilities of every possible outcome.

AND, where this gets really interesting is in the potential to expand this for a much larger and more useful SNG set.

It effectively gives confidence values that are not approximations at all.

Regards
Brad S
For example

[poboys]

I could write a perl script that takes the following variables Pr(1st), Pr(2nd), Pr(3rd), the %-Juice (eg. 0.10 for $55 and below SnGs), and the # of SnGs.

The result would be a .csv file that you could import and graph in Excel (or OpenOffice). If you are really interrested, PM me and we can talk about the specifics.

[Daliman]

[ QUOTE ]
I could write a perl script that takes the following variables Pr(1st), Pr(2nd), Pr(3rd), the %-Juice (eg. 0.10 for $55 and below SnGs), and the # of SnGs.

The result would be a .csv file that you could import and graph in Excel (or OpenOffice). If you are really interrested, PM me and we can talk about the specifics.

[/ QUOTE ]

Bah on both of you. Find a program that tells you RAISE! [img]/images/graemlins/laugh.gif[/img]

J/K, pretty cool, if obtuse to laymen such as I, stuff.

[tallstack]

Brad,

I have been playing around with your exact combinatoric calculation idea in VB and I have a crude program that will spit out the probability and winnings data pairs for sets up to about 160 games. Anything more than that and the combination values are out of range for the double precision variable types. I am not a programmer so maybe there is another variable that will let it go higher. Either way, this should be high enough to show convergence with any normal distribution model.

I don't have any webhosting, so if you are interested then send me a PM and I will forward it to you. If you like it then feel free to post it.

Dave S

[Irieguy]

Dude, thank you. I just started 8-tabling, so it's nice for me to be able to have a firm grasp on the frequencies of my respective session outcomes.

I would love to see the same for bigger numbers. Multiples of 8, of course, would be ideal since you also play 8-game sessions.

Thank you very much.

Irieguy

[eastbay]

I just wanted to say: very nice work, Aleo.

eastbay

[stupidsucker]

Thanks much.

[AleoMagus]

Ok, Dave (tallstack) did some excellent work and sent it to me and I have put it up on that site also.

It is the 'Setsof 8to50SNGs(1)' file (or something like that)

As it's title states, his file contains the same graphs of 8,12,20 and 50 SNG sets. It's pretty interesting. I cannot believe how smooth the 50 SNG set curve is. I know that people have been saying the normal distribution calculations are a good estimate for a while now, but I just didn't really believe it for some reason. I am starting to now. At least between the 10-90% range, it looks spot on. Those are my first glance assessments anyways.

The next step is graphing the same normal distribution results and comparing them. Who knows. We may be in for a surprise yet.

Anyways. Great work Dave.

Regards
Brad S