Or my continuing series of learning more from poor examples of play than good examples, that is "Happy families are all alike, every unhappy family is unhappy in its own way." So the game last Sunday was billed at a political intrigue/combat game. The other choices were investigative/combat, horror, and then a "whatever folks want" type game.
So lets talk about what various types of games mean? Or at least if I use the phrase "Political" game to describe what I'm looking for, what I mean. Now, I'm not discussing something in the style of Rob Donoghue's Adventure Triad - that's more how the play is styled, than what it is about, what tropes can be expected, or if the DM is feeling cruel, intentionally thwarted.
None of these are styles are in isolation to each other, in fact, my favorite style games combine investigation, political intrigue, and combat; puzzles and exploration are not games I particularly enjoy playing, so tend not to show up often in my games.
Combat. When I say this is going to be a "Combat heavy" style game, that means dice are going to hit the table frequently. Or perhaps not - this is going to be a game that rewards the character's combat abilities, and the player's tactical abilities. Ideally, there will be chances to ambush and be ambushed, as well as more set-piece combat; hopefully with interesting terrain that changes up the usual strategies and provides new ones. Some games (particularly D&D 4th edition) can be extremely oriented towards location tactical combat; whereas some (like Exalted 2nd Edition) are oriented not so much where you are spatially, but "when" you are - that when you choose to attack, and how you choose to attack, is as important as where you are attacking from.
The key to a combat game is making the combat interesting and challenging - whether intrinsically from the combat itself, or what the combat means.
Investigation. Investigation games center around finding things out and piecing them together. Depending on the game system, this can be as simple as rolling investigation when at a scene and getting information, or be far more detailed out (Gumshoe, apparently, though I've never played and it does not seem to be a system that I'd enjoy intrinsically for itself). However, the key to investigation is the need to get facts, and then piece them together. Sometimes the act of looking for facts brings to light the facts as the "bad guys" get nervous and try to take out the investigator - I call this "poking the bear". In narrative, this seems to be about every paranormal detective story written - bumble around, bumble around, get attacked, survive being attacked, use who attacked you as the clue to get you the way in and piece together the facts. Mage, in both the Awakening and Ascension makes it really hard to do a "hide the facts from the players" routine, so almost the entire focus needs to be on making it interesting to piece the facts together and figuring out what to do with those facts.
The key to an investigation game is the idea of finding out facts and piecing them together. (Note: This is about as close as I get to a puzzle in my games.)
Political Intrigue. Political intrigue is about people who want something, and are prevented from doing so through overwhelming force (otherwise the superior organization would just kill those that stood in its way). It requires at least two factions, with the players forming a third faction. My preference, solidified after long discussions with someone I consider a master LARP writer, is to have at least three factions, maybe more. The shorter you want the game to go, the fewer factions you should have -- so in your standard Con game? Two factions. Long running LARP that you want to last a while, at least three, preferably five or six, with natural allies and enemies within each. That way there are numerous people to play off each other and band together. If there are only two, then as soon as one has enough force to just kill off the other side, they will do so.
And that's the key to a political intrigue game, binding various groups together in a common goal, and thwarting others who are doing the same.
Exploration/Environment. Exploration games are interesting in that they are really hard to do well in an open environment in a table top game. Why? Because most of exploration in popular media comes from the visual aspects, or covered with a montage and the challenges are the interesting part for the viewers. So Exploration may be deemed more about conflicts with the environment, from food and shelter to "how are we going to get across this chasm."
Puzzles. Puzzle games involve a lot of "engaging the player, not the character" type games. Translation/code breaking, piece together these items in the right order, that sort of thing. You can see a lot of these in video games with the visual elements engaged. As a rule, I hate them. I get bored with them. I'm going to end talking about them now. (No, this doesn't have ANYTHING to do with the fact that I'm horrible at them. No not at all. /sarcasm)