Morelli stats Morelli
7 replies. Last post: 2014-11-06
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Richard Moxham at 2014-11-01
An opponent commented in an email the other day that it was fun watching the understanding of theory take shape in the case of a game as young as Morelli.
Indeed. And one aspect of the theory which I’ve been watching with interest is the question of whether Black or White (or neither) has the advantage. Still early days, but I can report that of 229 games completed so far on LG, 109 (48%) were won by Black, 108 (47%) won by White, and 12 (5%) drawn. -
Richard Moxham at 2014-11-01
Hmm. 50 games ago White was leading – by almost 3 percentage points. And Black’s lead at the moment (remembering that 48% and 47% are rounded figures) is actually less than half of 1%.
I know pretty much nothing about stats from a strict mathematical point of view. Anybody able to shed light on what sort of lead, over what sort of sample, would constitute unassailable evidence of an advantage one way or the other? -
alihv at 2014-11-02
Nice one Carroll :)
Richard, you can read up on some theory here:
http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair
except the theory is useless because as players are developing skill, a bias may suddenly turn up as has happened with A Few Acres of Snow. -
Carroll at 2014-11-02
1/e^2 isusally a good sample size with a 95% confidence interval for a margin of error e.
Wolfram statistical applet http://www.wolframalpha.com/input/?i=sample+size+for+binomial+parameter gives a sample size of 38415 for a 0.5% margin of error.As alihv said you need some more hypothesis so that this binomial estimation is correct. -
Richard Moxham at 2014-11-06
Thanks very much, alihv and Carroll, for the pointers towards a beginner’s grasp of matters statistical. In the event, a quick glance in each case was enough to confirm what I already suspected: namely that the time and effort required to follow this stuff from my starting-point, let alone internalise it, is greater than I would be prepared to budget for the task. Too many other things to be getting on with.
So I’ll leave the formal evaluation to anyone who in due course is interested enough to undertake it. In the meantime, I’m happy, personally, to rest upon the strong hunch that Black/White outcomes will turn out pretty even. Black has a small arithmetical advantage in move options and also first bite at setting the strategic agenda; White gets to see Black’s choices before having to reply and also (the key balancer, in my view) has last move, all other things being equal, in a game where that can be more than usually important.
As for draws, I’d be surprised if the long-term pattern didn’t conform pretty closely to all numbers generated so far: i.e. somewhere round 5% at 9x9; considerably fewer at 11x11; and hardly any at 13x13 (the real game, as I lose no opportunity of reminding the populace). I’ll just add the footnote that Morelli has an anti-draw characteristic which, if not unique, is at least extremely rare amongst two-player games of pure skill in which draws are possible. This is the fact that, since possession of the Centre is not in itself the win condition (it’s possession at close of play that counts), an interim occupation is something which – particularly on the larger boards – an opponent will often not be unduly concerned to prevent. And whereas allowing such an occupation need not in any way compromise one’s chances of winning, it does definitively rule out the draw. An interesting factor to stack up alongside the pure probabilities...