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Let's compare the 2 models for the Likelihood Ratio Test with the following example: n = 72772.; w = 12970.; l = 12790.; d = 47012.; H0 is w=l Trinomial distribution with draw probability MLE taken from the sample (ignoring the constant coefficients): pw = w/n; pd = d/n; L1 = pw^w*pd^d*(1 - pw - pd)...

Another problem with the model might be that the sample size is 2N while the actual games are N. However, the terms that decrease the P value: (draws + 2*wins) and (draws + 2*losses) also increase proportionally. Overall, granularity is increased 2 times which hopefully results in better precision i...

Isn't this where we started 20 years ago, and then people moved to trinomial because a binomial representation of a trinomial process didn't give satisfactory results? I am not aware of such old discussions. Looking at posts here in Talkchess, the oldest posts of 2007-2008 already talk about trinom...

In light of the above comment I have to correct the derivation for multinomial (including trinomial) distribution. Let X be a random variable following multinomial distribution. Then, P(X=x;n,p)=n! * Product from k=1 to K of pk^xk / xk! is the multinomial distribution. xi is the number of successes ...

You are right that the method using Langrange multiplier includes all the dependencies between the probabilities and this leads to the canonical formulas for the maximal likelihoods.

But my proposal still stands because it avoids estimating (or guessing) the draw probability.

In statistical tests for chess results (SPRT, Elo and LOS calculations, etc.), most people naturally choose trinomial distribution (wins, draws, losses) or some normal approximation to it. Trinomial distribution has two population parameters (probabilities): win probability and draw probability. For...

I see that you have applied the necessary changes in Winboard and UCI2WB. I will try them too.

Quick test: The book made as you explained and with legality test on works in FICS! Also with 2 machines after pasting the FEN.
Thanks a lot! It's all I need for now.

Thanks for the very detailed explanation. I will certainly try that and report for progress and problems.
I was always wondering why winboard insists to play fairy when I set it to suicide.

I was able to access FICS from the package with the following variants.bat file including playing normally suicide (book refuses to trigger): start winboard -zp -ics -icshost freechess.org /icsport=5000 /icshelper=timeseal.exe /icslogon ics-fishtest.ini /zippyGameStart="say This is a strong engine. ...