thanks, boomslang .. that is one nice piece of work
as they say, a picture is worth a thousand words or in this case 42,000 moves .. i tried to say it before as simply and completely as i could only to be summarily shot down .. it appears your graph and comments support my perception (certainly not unique) perhaps even establishing a proof of concept .. so, pardon me while i repeat myself
the better player minimizes his error rate
in so doing he optimizes his 'luck' potential
yielding the impression the better player is luckier
than less skilled opponents
in answer to an earlier question, yes, 'luck' potential
is simply another way of saying equity change, but change on a subsequent turn
.. when a bot optimizes for equity on the current move, part of that optimization must directly include the careful analysis of the opponents next possible rolls and moves as well as the bot's next turn where equity based "luck" is calculated .. this look ahead analysis seeks an optimal position in subsequent moves .. this appears to effectively optimize the equity based "luck" calculation for the better player .. i think that may be what we are seeing in boomslang
by definition, the less skilled player will make decisions that yield suboptimal equity gain, thus the "luck" calculation of the less skilled player will be impacted negatively or be suboptimal .. this impact is directly seen in equity changes from move to move .. since the "luck" calculation is a calculation of equity change based on the roll, the concept that optimal versus suboptimal play may impact "luck" calculation seems almost transparent to me .. obviously, it is neither transparent of trivial
most importantly, i am not saying the better player is luckier .. i am saying that the "luck" calculation is NOT a perfect reflection of pure luck which theoretically would be the same for both players regardless of skill .. however, since the "luck" calculation is an equity based calculation only approximating
the impact of pure luck, it is biased toward equity not probability .. since the better player optimizes equity, is it any surprise we see results biased toward the better player?
all i am saying is "the nature of backgammon", as boomslang
says, and the nature of the "luck" calculation yield "the impression the better player is luckier
" .. boomslang
's graph number 4 seems to directly support this .. indeed it appears to may be more than an impression, but it is a slippery slope as we have seen to attempt to equate pure theoretical luck with "luck" calculations .. i think all of us who play bots significantly more powerful than we are have repeated first hand experience that bots just seem too damn lucky - don't we? i would contend that this perception is merely a reflection f what boomslang
's experiment has shown
, would you consider conducting another experiment to test another aspect of of this theory?
i believe that the more moves (or games) analyzed the more the calculated "luck" differential will diverge between a better player and a less skilled player probably up to some limit .. while 42,000 moves may be a large enough sample to have reached such a limit, it may not be .. so, if it isn't too time consuming, how would that last graph look after say 100,000 moves or more? any idea where that limit may be or if there is a limit at all?
finally, has anyone yet directly addressed diane
's original question and really
defined how the "luck" calculation really
works? now that we seem to have established that it works differently than we expected, it seems a good time to revisit that original question