Variance Simulations

[ThrillCory90]

This is in my blog but since I spent almost 3 hours working on this I kinda wanted more people to see it.

I'm doing a little project on variance. I'm trying to learn what to expect in terms of variance in different games such as hu, 6max, FR, MTTs, MTSNGS, etc.

I started at HUNL since it is my main game. I googled a lot and looked at a lot of peoples stats. By far the best thing I found was this

(Theory) - Amazing Bankroll/Variance Post - Heads-Up No Limit Poker Strategy - Heads Up No Limit Poker Forum

The highlight from this post is this gem of information

At 100k hands the average person crushing their stakes are still +/- 4-6 PTBB/100 hands off their true winrate. To get winrate resolution of +/- 1 PTBB/100 it takes well north of 1 million hands given that the average Standard Deviation (SD) is much higher in HU cash.

Some consequences of this:

If you only play 1 table at a time, 100k hands is close to 700hours of playing poker!!!

If you 2 table HU you will see about 300hands/hour. If you do this for 20 hours a week, you will see this many hands in about 4 months. If you play 5-10 as your main game, your winnings after 4 months will be +/- $80,000 of what they should be!!!! That's a lot of "luck factor"

So I looked at a lot of HEM stats random people posted to try to get an idea of what a typical winning HU player is like. This is what I came up with.

Generic 100nl Good Winning Reg's stats:

55VPIP
13%-3bet so standard TAG, more on the aggro side.

Winrate: $8/100 hands
Standard Deviation: $100/100hands

2 tables
5 days a week
4 hours a day

Using these stats we can model what this players graph may look like after so many hands. I found a good variance simulator
Poker variance simulator
And modeled this over 1 Week of play, 1 month of play, and 1 year of play. I assumed this player would be 2tabling for 4 hours a day (1200hands/day and 20 hours a week (6000hands/week) (2600hands/week) (312000hands/year).

On each graph the simulator produced 50 random simulations of what may happen. The red line is the expected outcome. This is what The simulator produced.

1 Day:


1Week


1Month


1 Year


Even over a year of playing 20 hours a week your results can be way off of what they should be!!!!

Variance is even sicker than I thought.

[Chipless Wonder]

Wow. What a cool thread. Very interesting information!

[Clover23]

Very nice post... these are interesting to look at and sometimes scary to look at

[ThrillCory90]

4 Years!!!! Over 1 Million hands!!!! Massive Gap between the 2 outliers.

[otbdave]

Great topic, very interesting to see. I am a true beneficiary of the ultimate 1 day life heater.

[rryu87]

Great topic, very interesting to see. I am a true beneficiary of the ultimate 1 day life heater.

haha so close tho. did you play any circuit events in hammond? what would durrr's variance graph look like? I am really curious to see his noshow $.

[pegboy1]

Wow!! very interesting. This really proves that "variance is a bitch"..

very interesting to see the gap between hot and cold. Its huge!!!!

[otbdave]

Cory,

Not to tax you, but if you do have the free time...

It would be interesting to see similar simulations with different games, such as SH cash, FR cash, SNG, and MTT. The Standard Devs. would of course be guesses, but maybe some reasonable information is out there?

[ThrillCory90]

Cory,

Not to tax you, but if you do have the free time...

It would be interesting to see similar simulations with different games, such as SH cash, FR cash, SNG, and MTT. The Standard Devs. would of course be guesses, but maybe some reasonable information is out there?

Someone like you or GoMukYaSelf probabally has a big enough sample size of FR hands to come up with a good idea of what a typical Standard Deviation for FR is.

[ozzy]

What a good thread. Im waiting to hear more responses