I often find new games by looking at other peoples' collections and seeing how their tastes align with mine. I feel compelled to write something in case other people are doing the same to me so here it is.
For two player games I like a decent amount of chance and/or hidden information to put a barrier on analysis and relieve the pressure to play perfectly. I despise Chess and other games of its ilk. Pretend I rate all combinatorial games as a one. I gravitate strongly towards wargames because they tend to have tighter designs than a lot of other two player games on the market but there are still a ton of stinkers. I would love to find a good two player CCG style game to delve into.
I'm much less tolerant of chance in 3+ player games if only because it is so often poorly implemented. I mostly prefer economic games with bidding, stock holding, incentive manipulation and emergent alliances. I shy away from area control games because they always seem to have a greater potential for king-making.
On the other hand I quite enjoy card games, as long as the chance elements are properly implemented. I like Mage Knight quite a lot, for instance. I like lighter multiplayer card games and trick takers. If I win a game due to dumb luck I'm likely to not play it again.
I pretty much hate dice and will tolerate them only as part of an otherwise great design, which usually happens to be a wargame. I prefer cards for chance. Dice are for RPGs.
Maybe it's a phase but I find my tolerance for any sort of engine building to be nonexistent at the moment. It feels like a bunch of faffing about with fiddly bits to accomplish very little. Minutiae goes in, VPs come out. Blech. Mostly these are efficiency, resource conversion, or logistics-oriented Euros and I just don't like those much.
I suffer from Psoriatic Arthritis and will therefore avoid the following types of games due to the pain or discomfort they will cause me: Miniatures, real-time/timed games involving manipulation of pieces, dexterity games, and wargames with large stacks of counters that need constant manipulation. Pretty much anything where I have to bend or reach frequently.
I prefer the alternate ratings descriptions:
10: Outstanding game. One of my all-time personal favorites.
9: Excellent game. Always a pleasure to play. Shines under most circumstances.
8: Very good game. Rarely disappoints me. High on my request/recommend list.
7: Good game. Usually willing to play. I might even request or recommend it.
6: OK game. Some fun or challenge at least. Enjoyable in the right circumstances.
5: Average game. I'm indifferent, but may be willing to play.
4: Below average game. I avoid playing and would need to be persuaded.
3: Poor game. Will strongly resist playing.
2: Very poor game. I refuse to play this.
1: Dead game. Seriously negative entertainment value. Black Hole of Fun.