Randomness of games

New use for my spreadsheets! Consider this: if the outcome of a game is random, the win percentage should depend on the amount of players. In a completely random two-player game it should be 50% after enough games.

Well. My spreadsheet enters the picture here. I can count the average number of players in each game. Divide one with that number and you'll get the expected win percentage if the game were totally random or all players of equal skill. Then we can count the difference between the expected and the actual win percentage.

Let's see the most interesting results, now. There are few zeros, but with statistically irrelevant amount of games.

Mythos. 14 games with 2.21 players with a difference of -2.30%. This is because of limited sample and the circumstances. There's a definitive skill element in Mythos.

Battle Line. 44 games, difference of +6.82%. Lost Cities. 95 games, difference of +8.95%. Here we are closer to the point. I've played my share of newbies, against better opponents my win percentages would be closer to 50%. Or then I'm just a bit above average player. I'd like to disagree, though.

King Lui. 14 games, difference of +8.37%. Not much. I'm quite sure the difference won't grow much from that - King Lui definitely feels like it's pretty much random. Or to phrase it better: players reach the max skill level possible pretty fast. Coloretto. 23 games, difference of +10.10%. I'd say Coloretto is more skillful of the two, but still has a big dose of luck in it.

Puerto Rico. 39 games, difference of +18.69%. I'd say that's statistically significant and another piece of evidence that I'm good in that game. Or at least better than my opponents... Same goes with Carcassonne. 63 games, difference of +21.87%. El Grande. 13 games, difference of +30.63%. Ricochet Robot. 13 games, difference of +55.13%. Sunda to Sahul. 16 games, difference of +56.13%.

I guess I should give a well-rounded picture, so here's some big negatives: Villa Paletti. 11 games, difference of -26.19%. But in Villa Paletti one should really count no-loss percentage, not win percentage... Go. 43 games, difference of -20.93%. Mamma Mia!. 9 games, difference of -10.61%. TransAmerica. 6 games, difference of -27.27% (see, that's why I hate TA and claim it's a total luckfest with no skill needed whatsoever!)

But what about this: 6 Nimmt!. 22 games, difference of +15.00%. I would've expected 6 Nimmt! to be more random! Also Fluxx has 15 games and a difference of +10.00%.

Anyway, this is something rather interesting. It'll get even more interesting with more data. I wonder what's the limit of statistical insignificance and significance... Less than 10 games doesn't mean much, really, at least. But as always, stats like these should be taken with a grain of salt and only for purposes of entertainment!