Latest stats Morelli
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Richard Moxham at 2015-01-21
Taking together Monthly Cups, User Tournaments and Rating Games (I’ve made an executive decision to ignore Infinity, the harvesting of whose data is slightly more laborious), Little Golem’s 400th game of Yellow (9x9) Morelli has just been completed – which seems a good excuse to update a few statistics. For present purposes the larger board sizes have also been set aside, partly because the number of completed games generated by them is still relatively low, and partly because any overall tendencies in outcome seem likely to be usefully amplified by the tighter format. The 400 results break down as follows: Wins for Black (first player): 187 (46.75%);Wins for White (second player): 193 (48.25%);Draws: 20 (5%). Elimination of the drawn games gives: Wins for Black (first player): 187 (49.2%);Wins for White (second player): 193 (50.8%). The most remarkable feature of these figures is the consistent proportion of drawn games across an ever-increasing sample. The very first attempt at quantifying 9x9's drawishness – conducted some time before the implementation of Morelli on this site – revealed precisely 5 draws out of 100 games examined, and in the course of several statistical visits over the intervening period the needle has barely wavered from that figure. It was interesting to read purgency’s comment in a recent Forum thread that “with perfect play Morelli-Size 9 probably results in a first player win in almost all starting positions”. Though obviously the set-up is indeed a factor to be taken into account (as I have pointed out elsewhere, Size 9 has over 8,000 of them), my own generalised guess would have been the reverse. Since victory at Morelli is determined by the state of affairs obtaining after the final move, and since (all other things being equal) the final move will be made by White rather than Black, it seems to me that a prima facie case exists for second-player advantage. But of course purgency’s intuition, or at least the underlying basis for it, could be correct too. Against the advantage of having the final say, in other words, we may need to set the countervailing benefit of tactical initiative which in two-player abstracts generally accompanies the right to move first. If this and my previous assumption are both justified, then perhaps Morelli possesses – built into its very DNA, as it were – a form of natural balance unusual in games of its genre. Be all that as it may, these latest statistics testify to quite a fine equilibrium between Black and White. Previous sets of figures have oscillated marginally between the two, with White coming out just ahead overall. It will, of course, be a long time before anything approaching certainty emerges as to the true picture, but in the meantime these are outcomes for which I think most designers would be happy to settle.