Going into the match it was almost a coin toss for
who is going to win. Its only 10 games! So, I tossed a coin
10 times and had heads 7 times. Is that statistically unlikely?
No! It is not with only 10 tosses.
So, lets look at ratinglists using 4 procs or more and long TC and
have a large number of games. In a quick search, I found CCRL
has a 4 proc 40/40 list. Not very long TC but best I could find.
The rating difference between the two is 66 points (3117 to 3051).
That puts the match odds at 59.14% in favor of Rybka for a long running
match. The thing to remember is that the probability of draws ( P(D))
has a considerable influence on a small match such as 10 games.
In a 100 game match, Rybka should gain 59% of the points. This
could happen by any combination between two extremes.
First, Rybka could win 59 games and Zappa could get 41 wins.
Second, Rybka could win 18 games and draw 82 games.
There are two key statistical points here.
- 1) Each outcome is equally likely.
2) Statistics can not and do not specify the order of individual game results.
important. So, a 10 game match could result in all draws, All wins
for either side, an even number of wins for either side or a score
of 5.5 to 4.5 with several permutations.
Even better yet, the individual game odds are not equal to the
match odds of 59%! This is due to the effect of draws.
The max wins Rybka should get, at 59% match odds, is 59 of 100.
The min wins Rybka should get is 18 of 100 - Zappa could gain its 41 pts
by 82 draws. If we average the two we get the probability of Rybka
winning a specific game (not match).
Thus, P(Rybka wins a specific game) is 38.5% - P(Draw) is large.
More practically speaking, the oddities of two of the games and
some tests I've run indicate there might be a bug in Rybka's
parallel search. (I said "might" be a bug.) If that is so, it could be
exaggerated by using an 8 proc machine.