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**Dominion General Discussion / Re: Best/Worst Openings discussion**

« **on:**June 13, 2011, 12:07:48 pm »

On the technical side, I have some trouble understanding what the ratings mean and how they are calculated. For one thing, if I open the same thing with say, LV 5 with my opponent, but I am at LV 40 and he is LV 0, now we become LV 45 and LV 5, which persumably would have a different win rate I think. (Or does the win rate depend only on the difference of the level of the players? If so it seems a rather strong assumption for the levels to follow a normal distribution.) Even for asymmetric openings, it seems very impossible for every kind of player match up to shift for the same amount for the different openings. It would be easier for me to understand if there is just an explanation of how it is calculated.

TrueSkill makes the normal distribution assumption. So holding variance constant, if you add a fixed level to both you and your opponents skills, the model says there is no difference. The hard part is to understand TrueSkill. http://www.moserware.com/2010/03/computing-your-skill.html .

The openings data also makes the assumption that you and your opening form a team and that you add your skills together with equal weight on the player skill and opening skill. I'd guess the player matters much more than the opening, but optimizing this for the right criteria for multiplayer games is hard, http://stats.stackexchange.com/questions/10067/maximum-of-two-or-more-gaussian-distributions-with-known-and-possibly-different). Likewise the opponents team does the same thing, then you model a little noise from the outcome of the game, and then your combined normal distributions fight.