for Gorilla Player, I DON'T GET

gorilla player:

"Posted By: gorilla player
Date: 28 Oct 04, 7:34 am

In Response To: Yes... (doppelganger)

The other point that often gets overlooked is that while the probability of two consecutive losses is (say) .57^2, in a long series of play, the probability of two consecutive losses happening somewhere in the series approaches 1.0.

That often gets missed. IE the first time you try to test a random number generator (as a student) and you learn all the various randomness tests such as the poker test, the runs test, the test for unformity, etc, you begin to get a little insight into this issue. IE if your RNG produces the numbers 1,2,3,4,5,6,7,8,9,10 at some point, students first assume "wow, this is not as random as I thought". The point is, however, is that if you _don't_ get that at some point, your RNG is no good, it is "too random" (to use a horrible phrase) because consecutive strings like the above are necessarily going to happen if you do enough trials.

So often, here, we end up in discussing the same probability test, such as two consecutive losses, and it is possible to have two different probabilities. One, the probability of a particular outcome in two consecutive trials, and two, the probability of a particular outcome in two consecutive trials, somewhere in a much longer test series. The first is small, the second is near 1.0...

As the saying goes, "a statistician is someone that can use numbers to prove anything they want." :)"

Count Blackjackcula:

GORILLA PLAYER, I took statistics 6 times and droped, finally getting a great instructor and tudor to pull a 'B'.

But how in the world can the 2nd trial be closer to one?

Sure glad there are stat guys out their that really comprehend this well!

The idea is this. If you want to know the probability of flipping a coin twice and getting two heads in a row, it is P(head) ^ number_of_trials. In the above, that is P(.5)^2 which is .25 or one out of four. Makes sense?

Now you flip a coin an infinite number of times. What is the probability that you will find two consecutive heads somewhere in that? An easy way to think about it is this: What is the probability that we will get H-T-H-T-H-T for the entire series? Use the math above and you get P(.5)^infinity which is zero. So if the probability of getting H-T-H-T forever is zero, then obviously the probability of getting two heads or tails in a row must be 1.0.

That is very loose probability theory. If you want the actual probability formula for the above, I can dig it up in one of my books here. The point is that in a long series of trials, you expect variance. The more trials, the more likely you are to see some odd occurrence once. IE if you do a trial of 1000 coin tosses, what is the probability if you repeat that trial an infinite number of times, that on one of those trials you get all heads or tails? 1.0... The idea is that strange things _will_ happen given enough tests. I suppose that if you flip a coin an infinite number of times, and let it hit on a hard flat surface, the probability of it landing on the "edge" once is also going to be 1.0 for a really strange idea...

That is why the idea of "patterns" is basically flawed. Once you run a long test, you can look at the results and see lots of patterns. But if you notice a pattern, and then try to use it to predict something further down the trial, it doesn't work. As an old probability instructor once told me in class, "patterns can be observed easily, but they can not be predicted." That was just a clever way of saying that you don't know you had a pattern until the pattern has already ended.