Author: Dann Corbit
Date: 17:21:54 07/15/00
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On July 15, 2000 at 20:15:48, pete wrote: >On July 15, 2000 at 20:08:29, Dann Corbit wrote: > >>On July 15, 2000 at 19:39:10, Ralf Elvsén wrote: >>[snip] >>>Why are there 2^101 outcomes in total? Just curious. >>It's easy! Just count them. >>Actually, I was wrong, it's only 2^100. That's because 100 1 bits is only 2^100 >>-1, and the all zero bits makes a total of 2^100. >> >>Consider each toss as a binary digit. Each digit can be 0 = heads or 1 = tails. >>The number you get will be anything between >>0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 >>and >>1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 >> >>As you can imagine, every combination of bits is possible, and each bit (with a >>fair coin) is equally likely. > >I just stumbled over a past post of Uri Blass where he already explained the >correct statistical experience for the question originally discussed : > >a.) coin fair ? >b.) coin unfair ? > >If you get 100 1's the hypothesis of equal chances ( or worse ) is statistically >just completely unlikely . > >I wonder why you object as you seem to know what you are talking about , I have >no idea in fact .. You will get about half heads and half tails with a large number of trials. That is what I am arguing for. A large number of trials. The point I made is that each of the different combinations is equally likely. And, you can get a large number of "sports" to start off with. The more trials you run, the more likely that the results are correct. Again, a coin is not a great model, because the chess players learn from the previous trials. In such a scenario, sports at the beginning are actually what we would expect to see, wouldn't we? Simplifying. I have a penny. I toss it twice. Heads, heads. I toss it twice Heads, heads. I toss it twice Tails, heads. I toss it twice Heads, tails. I count them up. Heads are stronger than tails. My conclusion is faulty. Why? Because I did not gather enough data. In the case of chess games, as the GM's learn from previous mistakes, the true strength of the program will be revealed. The same would be true of a human player. Given enough games, they will settle down to their true strength. With a computer, which is more deterministic than a human and if it learns, does not learn nearly so well, the effect of more games will be far more devastating. At least according to the model I am imagining. But models can be wrong, or imprecise.
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