Quote:
Originally Posted by FatedToPretend
I might as well be honest with you argentina. I didn't really know 'variance' was something you could quantify and say 'my variance is this.'
Can you explain to me, (without biting my head off) an example of how you would do this ?
Well, I suppose it would be a good exercise for me to try to explain it to you...so, why not? Poker is such a lonely business :/ I will try not to bit your head off with my answer. I will assume that you don't know anything about variance, so I will explain the whole process:
Let's say you play about the same number of hands every day. You always play the same level (if not, you can divide how much money you made/lost in a day by looking at the amount of BB instead of the amount of $). You make a table where you list how much money you made/lost each day. You can calculate how much money you are earning on average: you add all the money for each day and you divide it for the number of days. There you have your average return per day, AR. Does that mean that you are going to make that amount tomorrow when you play your usual game? No, it doesn't, you know that by experience. You want to know what to expect though, and how confident you can be in making/losing a certain amount (so you can plan ahead). So you do the following: you look at how much each particular day differs from that average. You do that by substracting your return in a particular day from this average. You will now have a table like this:
date | amount won/lost | difference d
day1 X1 d1 (= X1 - AR)
day2 X2 d2 (= X2 - AR)
.
.
.
day N XN dN (=XN - AR)
Now you want to know how far (in average) you are from that AR. It doesn't matter if that is below or above AR. You want to know how FAR. You get that by doing (d*d) (which is noted d^2=d*d). That gets rid of the sign. It makes more important the ones that were far from AR, but that is ok. You can now calculate an average of those d^2, so you add them all up and divide it by the number of days. This gives you what is called the variance. If you have some data that is very far from the AR, you get a big number. var = ( d1^2 + d2^2 + ....+ dN^2)/N
If you now take sqt(var), you get what is called the standard deviation (sd = sqrt[( d1^2 + d2^2 + ....+ dN^2)/N]=sqrt(var)) (or 'sigma'). You can look at this quantity as some kind of measure of how far away, on average, your results are from your AR, a measure of distance.
If you assume that your daily returns are normally distributed (i.e., they have a particular bell shape when you plot them
in a histogram form), then in terms of this sigma, you can find the probability of getting a result that is a given distance apart for your AR. For example, if this measurement reflects your true distribution, the probability that tomorrow your return will be 3 sigmas above or below your AR is about 0.3%
(3 in 1000).
Once you understood that, there is something else to consider. Imagine you do this a second year, and a 3rd year, and N years. You will have again, a table for each year you played. In this table you can list
Year1 | ARy1
This is: your average return that year. These amounts, again will not be the same every year. They will have a distribution. The different ARs will hover around your 'true' AR. How spread? The dispersion of the data you measure are related to the spread of your true distribution by
Sigmatrue = Sigmameasured/sqrt(N)
The dispersion of your results for AR (Sigmameasured) is like a margin of error in your estimation.
The more you measure, the higher the N, the smaller the error, the closer your average will be to your true AR. Knowing your sigmaM will give you limits for your trueAR within a certain confidence interval.
So you can say things like: I am 95% sure that my trueAR < measAr + 2*truesigma and trueAR > measAr - 2*truesigma. Voila.
I recommend you read the entry in wikipedia:
http://en.wikipedia.org/wiki/Standard_deviation
and in case you don't get to the bottom of the page, check their link to Standard deviation - an explanation without maths. There are many other links to easy explanations:
http://en.wikipedia.org/wiki/Standar...External_links
I didn't check the forums here, but I am sure you will find an infinite number of posts with plenty of info on the subject. It is really fundamental to your livelihood as a poker player, using some of your words. There is a probability forum:
http://forumserver.twoplustwo.com/25/probability/
There is a poker beats, brags, and variance forum (now hopefully you know what variance is)
http://forumserver.twoplustwo.com/54...rags-variance/
And hopefully you now realise how important it is to know your numbers, and in particular to have a software program like PT or HM. Not only this. You can also analyse particular hands. For example, how many times I got aces, I went all in preflop, they called me with 22, and see how many of those times you won and how many you lost, and compare that measured probability of winning with the calculated one.
S.
Last edited by argentina71; 05-29-2010 at 04:40 AM.