Only Chess
06 Mar 08
15 Mar 08
Originally posted by KeplerTo take the analogy further:
What you are simulating here is a random walk. Intuition says the distance from zero should be low and should get closer to zero for larger numbers of trials. As so often with probability, intuition is just plain wrong. In fact the average distance from zero is approximately 0.8 square root n where n is the number of trials. So for 1000 tosses of the coin the ...[text shortened]... 25. Some of the distances involved in 1000 trials could be large without implying a dodgy coin.
For Heads= 1, Tails = 0, the standard deviation is sqrt(n)/2 for n trials.
So for 1000 throws, a result of 516 would be over one standard deviation from the mean. A result of 532 would be over 2 standard deviations from the mean, and so on.
For a single tailed test where the null hypothesis is "The coin does not favour heads", what result do we need to reject the null hypothesis with 99.99% confidence? The answer is a score of 559 or greater.
So if you do get a score of 559 you can reject the null hypothesis and confidently state that the coin favours heads. But repeat this infinitely and the expectation is that for every 10,000 times you reject the hypothesis, you will reject one fair coin (a type II error).
For 99.9% confidence you would get it wrong once in a 1000 times.
For 99% confidence you would err once in 100 times.
For 95% confidence you would err once in 20 times.
The question is, what level of confidence is sufficient? And what is most acceptable; rejecting fair coins, or not rejecting unfair coins?
Applied to game modding, there is no doubt that statistical inference is a very useful tool. In cases of extreme deviation where the probability of a type II error is statistically implausible, it can satisfy, in its own right, the burden of overwhelming evidence beyond reasonable doubt.
However, it is much more commonly used in conjunction with other direct or circumstantial evidence.
15 Mar 08
Originally posted by Dragon FireI'm tired of hearing people being accused of being engines without any formal action.
It is and if the stats are correct it does not seem to prove a great deal.
There also do not seem to be any "engine" moves in the samples given as far as I can tell.
I'm glad to hear that you went over the games. I'm at a funeral and haven't the time.
Why didn't you run?
15 Mar 08
Originally posted by Richardt HansenWoh now......Calm down with the high level Maths.
Actually Kepler the theorem I am using is "The law of Large" numbers. We know that:
P(heads) = P(tails) = ½.
Let X_i be the outcome of the i'th toss. Now the menalue of X_i is:
E(X_i) = ½*1 + ½*(-1) = 0
(X_1,X_2,......X_N) is idenpendent and identical distributed with meanvalue 0.
and hence we know that:
1/N \Sum_{n=1}^{N} X_i -> E(X_ ...[text shortened]... " number - off course for the Law of large numbers to apply we need much more repetitions.
This is a true heavyweight battle of the the mathematicians....who will come out on top. 🙂
By the way anyone want to talk about Bronsted Plots in the elucidation of Organic Reaction Mechanisms and Transition State Structures? 🙄
15 Mar 08
3 edits
Originally posted by najdorfslayerYou do know a Bronsted plot is just a particular example of a fairly simple mathematical equation don't you?
Woh now......Calm down with the high level Maths.
This is a true heavyweight battle of the the mathematicians....who will come out on top. 🙂
By the way anyone want to talk about Bronsted Plots in the elucidation of Organic Reaction Mechanisms and Transition State Structures? 🙄
So are issues of probability ... the point of the above posts is to say that maths has a lot of things it can do, helping to discover the truth in many misunderstood scenarios ... and also some it cannot (see gate's point that "However, it is much more commonly used in conjunction with other direct or circumstantial evidence." ).
Bronsted's plots are just Bronsted plots and not much more ... i do hope you enjoy them 😉
15 Mar 08
Originally posted by murrow😀
No
But what Richard is questioning is; how does one construct the trials? Flipping a coin is a simple trial with a 50-50 outcome. The probability that a player will match an engine is a far more complex problem, and the trials are not necessarily uniform.
I'm not going to go into how these problems have been addressed, but the long and short of it is that no statistical outcome should ever be accepted without question. Inherent bias in the samples, unsuitable control data, incorrect assumptions in the models, can all lead to skewed outcomes.
15 Mar 08
Originally posted by GatecrasherSure. What I don't agree with in Richard's post is this:
😀
But what Richard is questioning is; how does one construct the trials? Flipping a coin is a simple trial with a 50-50 outcome. The probability that a player will match an engine is a far more complex problem, and the trials are not necessarily uniform.
I'm not going to go into how these problems have been addressed, but the long and short of i ...[text shortened]... unsuitable control data, incorrect assumptions in the models, can all lead to skewed outcomes.
"We can get p-values, but what conclusions can be drawn from this ? Well it all depends on which games is analyzed (the game sample) - surely some games will have a higher matchup rate due to the opponent, the tourny, the nature of the game, ...... So to me this information is useless."
15 Mar 08
1 edit
Originally posted by najdorfslayerIt would be better than the constant cheating accusation codswallop. I think in stead of a game mod team we should have a Cheat Finder General. Sort of like a Witch Finder General but with a nicer hat.
Woh now......Calm down with the high level Maths.
This is a true heavyweight battle of the the mathematicians....who will come out on top. 🙂
By the way anyone want to talk about Bronsted Plots in the elucidation of Organic Reaction Mechanisms and Transition State Structures? 🙄