Backgammon... is less luck dependent than Dominion if you play matches...
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Have you played Backgammon for more than a few games?
I have lose quite a few Dominion games because of bad luck, but I have never in my entire life lost a Backgammon match were I (after analysing the logs) could honestly say I have lost due to bad luck. In most games where someone claims he is losing because of bad luck he is actually losing because the other player effectively minimizes their number of possibly good rolls and duplicates their other very good rolls.
Backgammon has so little luck in it that in the last ~10 years even top-tier Backgammon players couldn't win 7-point matches against proper backgammon bots, simply because they (the bots) play far better than any human could ever dream of.
Sure, you can lose a singe game (or worse, a single doubled game) due to bad luck, but that does not really matter all that much in the "long" term of a match most of the time.
How many games are there that DON'T get better via doubling cube inclusion?
Actually, 1st turn might make dominion really one of them... that plus a little shuffle luck.... nah, doubling cubes are awesome!
Many card games and most (physical) sports. There are exceptions though. :>
Also, doesn't the doubling cube only matter if you're playing for money? (Or presumably points in a tournament. But wouldn't that seriously screw up the ranking?)
Why would it screw the ranking? You win or you lose a match, there is nothing inbetween in backgammon. It doesn't matter if you won a game without any doubles and lead 7:5 in the match or you won a gammon that was redoubled several times to a worth of 256 and lead 263:0 in the match, in both cases you have simply won the match.