Quote:

Originally Posted by dybboss

http://www.speedyshare.com/d3Q89/ROISimulator.zip

^Mod edit, new link

In addition to this thread i wrote a spreadsheet program that simulates the variance STT results based on your input. You may then review some typical runs and your profit distribution.
For example, here are some results from my 9-player 20+2 STT simulation, 5000 tournaments, ROI=9%:



Furthermore, by performing simulations I obtained some dimensionless graphs that might show variance in a graphical way and is useful for most buyin levels.

1. Profit distribution

The profit distribution is shown as probability density function, which in this case follows a normal distribution (as expected):





Notice variance decrease considerably with increasing ROI and tournaments.

Furthermore, average and standard deviation is calculated which provide quantative statements about confidence intervals. For example, over 5000 tourneys with a 10% ROI the standard deviation is about 0.218*Expected value (which is just the expected profit based on ROI). You may then conclude that:

• There is about 68% chance your profit is between 0.782*EV and 1.218 EV
• There is 2.2% chance your profit is smaller than 0.564*EV
• There is a 0.1% chance your profit is larger than 1.654*EV

Use your own parameters for simulations using the excelsheet to create insight in possible profit distributions. You may want to check wikipedia on normal distribution and confidence intervals.

2. Chance of going broke

The neccessary bankroll for playing SNG's highly depends on your true ROI. The chance of going broke converges with increasing number of tournaments, as is also shown in the following graph. Note that in this case there are no withdrawals.



3. Downswing

I'm currently working on graphing the chance of a downswing of a certain amount of buyins after N tournaments (based on ROI=x%). However, the algorithm of identifying downswings takes an enormous amount of calculation time for lare number of simulations and tourneys.

4. Download

To perform simulations for your own parameters, you can download the spreadsheet. As VB code is used, you may need to enable macros in your Excel security settings.

Excel 2007

Excel 97/2003



Note 1: Nondimensional profit distribution is based on 3 sets of 32000 simulations for each roi and number of tournaments.

Note 2: Nondimensional results are based on a 10% rake situation. Results may change with other rake levels.

Note 3: For the nondimensional simulations the following finish distribution is applied: 40% first, 30% second, 30% third (percentages of ITM part). This is quite a realistic finish distribution for a good player but can be changed in the sheet for your own simulations.

I'm offcially switching to cash games now.

Nice work.

The profit/expected profit plots are a much better way of showing what people playing SNG experience, rather than my typical smart-ass answer about the sample variance in SNG results being almost entirely dictated by the payout structure, and to a small extent by a player's finish distribution.

why is the sample variance almost entirely dictated by the payout structure, and to a small extent by a player's finish distribution?

First form of downswing graph:



Will add 100 buyins and more data points, but the simulations take a lot of time with downswings.

Awesome job, that purple 50BI, roi = 5 is scary. Not for me of course

Why is the light blue, 50 BU, 10 ROI so weirdly shaped? Just a random simulation occurence?

I guess so, for these data points only 1000 simulations are used. I guess the line will converge to normal shape with more simulations and data points (working on it).

Too bad I cant use this. I got Excel with my new laptop but cant find the key somewhere so I cant do anything more than to view it in excel. meh. And it dont work in Open Office.

This reminds me why I play where I have a 15% roi, instead of moving up. Very nice work Shrooma, thanks for the spreadsheet.

Wow awesome (the work, not variance)!
Must have been a LOT of work.

Can anyone explain the profit distribution graph?
What do dot X and Y axis mean?

heres my guess;
Y - probability distribution function
X - the factor you multiply by your mean profit

If you consider the fraction of the area beneath the line that is also below 0 on the X axis, that would be the probability of losing money.

This as well as the spreadsheet is a great contribution that answers alot of questions and solves disputes seen often in the forum. It improves confidence during a downswing and graphically presents the sentiment so many posters are trying to get across here: don't be results oriented.

Whether it's someone declaring greatness after a good run, or sobbing about bad beats and how they run so bad, good posters will remind them that these are STTS and variance is part of it.

With crazy swings like this, it makes me realize how the goal of 'getting better at poker' can be sidetracked by the desire to win money, get out of 'downswings', and even cash in individual tournaments. Thanks shrooma for doing this.

Uh.. I guess I should say distribution of the sample variance. Anyways, people sometimes go on about "Oh my style of play leads to higher varience because I'm so awesomely aggro early on. Why am I in this huge 2k SNG downswing? I was total 25% ROI over my first 300 SNGS!!" In reality, 2 players with the same ROI and a different finish distribution don't end up with vastly different probabilities of certain-sized downswings, break-even streaks, you know... varience. There's not much way to escape the 1.6-1.9 buy-ins per SNG swing derived from a 0.5/0.3/0.2 (or 0.65/0.35 6-max) payout structure no matter what you make the finish distribution.

It's just my way of telling people who are sucking at SNGs to STFU and get better rather than blaming statistics.

Correct, consider it the continuous version of a histogram. To make it suitable for any buyin the profit (x-axis) isn't in dollars but in fractions of your expected profit. Of course your profit has the largest chance to be the expected profit (Profit/expected profit=1).

This is a fantastic job.

Well done, OP.

nice grapg i am experiencing that downswingg

Fantastic job OP.

That 6% chance of 50 BI downswing with a 15% ROI is scary as hell. I guess that's why Irieguy says to stay away from SnGs.

As if 100k breakeven hands is much better

This is worthy of a link in the FAQ, I think it explains why everyone complains of variance more now that ROIs have dropped.

Updated downswing graph:

Dear mods,

-----------> FAQ asap, plz

kthx

forgive the noob question but would upswings be the same graph?

Nice work Shrooma thanks!


pifhluk what do you mean by an upswing graph? I would think as a winning player you should have a very large upswing? I guess a losing player might have a similar upswing graph to our downswing graph?