If I flip a fair coin 100 times, 50 heads and 50 tails as the actual outcome is not likely[*]. The possible outcomes form a Gaussian curve and a 1 SD wide swath holds lots of different possibilities.Cornfed wrote: ↑Mon Jun 29, 2020 12:28 amI think the proverbial 'sample size' answer just kind of begs the question.Dann Corbit wrote: ↑Sun Jun 28, 2020 2:16 amIn less than 1000 games practically any outcome is possible amongst approximate equals.

I guess that they are very close to equal, but SF had some fortunate outcomes.

And if SF is stronger, it is not by an enormous margain, as evidenced by the draw count.

What does "fortunate" mean? Did LZ0 stay out late partying the night before?

[*] OK, it is the most likely SINGLE outcome, but the probability is enormously close to 49/51 and 51/49 and 48/52 and 52/48, etc, with the probability tailing off gradually.After 71 games SF leads 37.5 vs 33.5 (and game 72 looks like it will end in the Fish's favor as well...). A 4 to 5 pt lead at this point is actually reasonably significant. That said, there are more games to be played and Game 72 has LCZero defending the Latvian Counter Gambit...which is bad. Has SF yet to defend it? I don't know. The Devil is in the details.

EDIT: It has, the game before and SF lost...just as LCZero looks to at the moment.

To convince yourself, get a PRNG that generates random numbers between zero and one and run it one hundred times for 1000 cycles and record the different outcomes (numbers above and below one half) that actually occur. You will see some 50/50 outcomes, but you will also see some off a bit and a few that are way off. Remember, now that the "opponents" of "above a half" and "below a half" have exactly the same strength.

For another really funny outcome, see how many numbers are exactly one half with your generator. If it is an 8 byte floating point number and the values are uniformly distributed I would guess zero results of exactly one half for an individual value will show up in all 100,000 emitted elements. Of course, I would insist on testing for equality using == rather than the more usual definition because 1/2 is a special number that can be represented exactly and that is the odd outcome I refer to.