Hi

I don't think I understand how the pokerdope variance calculator works...or what exactly it tells you.

Look at these 2 data sets:

The first one is for a winrate (17.58BB/100)and standard deviation I achieved over about 8600 hands of 2nl ZOOM.

the 2nd is for 2k hand heater I had today at the end of the larger 8600 hand sample, where my winrate was over 37BB/100, with a somewhat lower standard deviation.

For the first set, the 95% confidence interval shows that my true winrate never going below 15.86BB/100.

In the 2nd, the 95% confidence interval says my winrate never falls below 35.42BB/100.

For both, I ran the simulation for 1 million hands.

How can the bottom end of my possible winrate be so divergent over 1 million hands? I really don't know much at all about statistics or how this calculator works, but these results seem useless. Is there some crucial piece of information I've overlooked and so I've done this all wrong?

Again, I'm terrible at math, but I don't understand how this can be accurate if you aren't even entering a sample size of any kind.

Any help very much appreciated.

You're not running a simulation. "number of hands" is the number of hands in your sample, so, 8600 for the first one.

You told it you won at 17.58bb/100 for a million hands and so it was like "yeah, that's probably pretty close then"

Actually I don't think I'm interpreting the calculator quite right either. I think maybe it's answering the question of "if my true EV is Xbb/100, and I play for Y hands, what can I expect to see in the terms of results"

But still, by choosing a million hands, you're asking it for very long term results. This calculator isn't to estimate how likely it is that your win rate is X given an observed win rate of Y over Z hands. It's telling you the range of results to expect *given* a specified win rate/stdev over a period of hands.

The variance calculator tells you the following:
IF your true winrate is 17.58BB with a standard deviation of 85.9BB/100 THEN your winrate for a random 1 mio hand sample will be within 15.86-19.30BB/100 in 95% of trials.

But that's probably answering a question you are not interested in.

What you appear to be looking for seems more along the lines of: After observing a 17.58BB/100 winrate with SD 85.9BB/100 over a sample of 8600 hands, what is the 95% confidence interval for my winrate?

If you assume that your sample SD 85.9BB/100 is somewhat close to your true SD, then you could calculate the lowest/highest true winrate that would still give you a minimum of e.g. p=5% of producing a sample at least as good/bad as the one you observed.

p 5%: 2.34 - 32.82BB/100.
p 1%: -3.97 - 39.13BB/100.

This tells you:
IF your true winrate is below 2.34BB/100 THEN there is a less than 5% chance of observing a winrate of >=17.58BB/100 over a sample of 8600 hands.
IF your true winrate is above 32.82BB/100 THEN there is a less than 5% chance of observing a winrate of <=17.58BB/100 over a sample of 8600 hands.
etc

As you can see, a 8600 hands sample is not exactly giving you a good idea here. [My statistics are rusty, I apologize if I screwed up somewhere.]

Ok thank you! That is definitely NOT what I thought it was telling me. And it is definitely not the question I was interesting in trying to answer.

However the information you provided:

p 5%: 2.34 - 32.82BB/100.
p 1%: -3.97 - 39.13BB/100.


is exactly what I was looking to understand!

You have already helped me alot, but if you have an equation you can share that will allow me to do this myself with other samples, I'd really appreciate it.

Thank You So Much

You'll need some statistic package like R, or Excel probably works too.

Online R console:
http://www.r-fiddle.org/#/fiddle?id=GoCAdnG7

Basically, in that example you are calculating the bottom 1% result if the observed winrate were your true winrate. That comes out as -3.97BB/100.

Since the normal distribution is symmetrical, that means that the observed winrate of 17.58BB/100 would be the top 1% of results on a 8600 hands sample if your true winrate were -3.97BB.

Thank You Very Much.

I used to have a calculator for stuff like this online, but my site is long since dead and I doubt I'll ever revive it. The calculations are fairly simple, you can definitely do them in excel. I'm not feelin it right now but maybe I'll put together a google sheet or something, unless I can find an online calculator for it. My favorite calculator, and the one I based my own off of, was uDevil's online calculator, but that's long gone too.