I don't use HEM or PT3, have been using Poker CoPilot for mac. Is there any way to figure out my SD by calculations? Sorry if this was already discussed, I just scimmed through the posts.

look up the central limit theorem

dont forget winrates are way bigger in live games, since regs can only play one table instead of 12, and casinos tend to attract worse players anyway

1st simulation I did:



So I can expect to go on a $100k+ downswing in 30k hands on 5/10NL while being a 3ptbb/100 winner with a somewhat standart SD? Sick...

Square Root of variance.

variance is a scientific term. colloquially it means "swinginess" on 2+2 but more accurately it is this and standard deviation is this.


having a higher win rate will lessen how in the red you are likely to dip during a downswing but that is not bc your variance or SD have changed but rather because your coefficient of variation has changed due to your winrate (mean) being higher.

That's sick good thanks maven.

How can I tell what my SD is?

Here is my variance simulator. Click on the spoiler to simulate variance.

It's Tom Dwan and Isildur1

holy sht how has no one pointed out the idiocy in this: hes asking you where you get the actual numbers to calculate std dev. we all know it is the sqrtVAR but that doesnt tell you anything. you get it by adding up the squares of the differences between actual results and mean results of all the results in your sample (i.e. [win per each 100 hands/expected win per 100 hnds]^2. this says NOTHING about how winrate affects it.

winrate most definitely affects variance. the higher your winrate, the better you are reading hands, the more often you are getting in as an overwhelming favorite, the less often you are getting in as a big dog.

the variance of a fair coinflip is higher than the variance of a coin weighted 90% to one side.

please forward all 1000$ wagers.

wow...... i'm speechless how terrifying this is...

this bottom line is like unbelievable omg

i wrote one of these too, also displays winrate distribution and large downswing frequencies. http://www.evplusplus.com/poker_tool...nce_simulator/



You can increase the number of trials and plot the worst/best runs from those trials:



The frequency of having a downswing of at least X bb:



The above is a cumulative histogram of the distribution of largest downswings from all the runs. The far left (probability of 1) represents the smallest downswing from all the runs (ie. everyone will experience a downswing at least this big). The far right (probability close to zero) represents the largest downswing from all runs.


And the distribution of all winrates for the simulated runs:

That's why we look at bb/100 instead of bb/1. The results per 100 hands are much closer to a normal distribution (look up central limit theorem). I have actually tested whether bb/100 is normally distributed. This was not exactly the case, to be exact: the empirical distribution formed by my hands was more leptokurtic. Therefore results from this simulation should be taken with a grain of salt, but it does give a decent indication. By the grain of salt I mean that if you solely base your BR management on these kind of simulations, you will be subject to model risk.

Hey, neko, do you want to maybe talk a little about the math behind how you came up with this? How do you deal with the fact that every jump is not independent of the one before it? And how is the random part of the jump distributed?

Hey Gospy,

A quick explanation of how it works:

There are a couple of assumptions you have to make:
a) Game conditions, the players mood/skill level/tilt level and hence their expected winrate never change.
b) Your results in a 100 hand block are distributed normally around your true winrate.

These assumptions clearly make the simulation naive one since in reality a) will never be satisfied. (I'm not sure about b).

So given these two assumptions the simulation works by picking a series of random values distributed normally around your winrate (with the input standard deviation), and then the chart is created by plotting the cumulative sum of those values vs the length of the series (i.e. the number of hands/100).

For example If we were to do a 500 hand sample with a winrate of 10bb/100 then you might get results that look like this

Trial	Win	Cumulative
1	30	30
2	50	80
3	-120	-40
4	70	30
5	-20	10

Let me know if that doesn't make sense.

edit: to answer your question, each jump is considered independent of previous ones.
edit 2: I am no statistics expert

is there any way to use this and input what limit it is for?

ie NL2c or NL10c or NL100 etc.

The cool part about this is that if you run like 1000 of these at a time it looks like one of those Magic Eye things

I see several hundred crushed souls when I cross my eyes juuuuuuust right

answer to this thread: play a million million hands.

The one on my website (posted earlier in this thread) uses bb/100 as the units so if you wanted to look at results for NL10c then you would just multiply the results by 0.1.

It's doesn't work anymore.

mine does:

http://www.evplusplus.com/poker_tool...nce_simulator/

Awesome tool, have one question though:

What does the vertical line represent in both these graphs?




If I understand the second one correctly, I should have about a 20% chance of a 20BI downswing over this sample? If thats correct I still dont understand the fist one.

Thanks!

Your understanding of the second one is correct.

The labeling of the first one is misleading and needs to be changed.

It is generated by dividing up the range of winrates into 50 bins, so the bins might look like

bin 1: 0.0bb/100 to 0.3bb/100
bin 2: 0.3bb/100 to 0.6bb/100
bin 3: 0.6bb/100 to 0.9bb/100
etc
bin 50:15.7bb/100 to 16bb/100

You then run through every player and and add 1 to the bin their winrate falls in. So if a player had a winrate of 15.8 bb/100 you would add 1 to the last bin, if they had a winrate of 0.8bb/100 you would add 1 to the 3rd bin and so on.

The whole thing is then normalized so that the area under the curve is 1. This is just to give a consistent plot where all the values fall between 0 and 1 for all simulations.


Make sense?

Absolutely. Thanks!