I think part of the answer is that you have to play the same games with different styles of game play (see below, speed games). We all succumb, at one time or another, to the min-max problem. Said another way, in many games, there actually is an optimal solution that can be calculated decisively at certain points (especially near the end). But calculating it in ones head can be a slow process for some.
The best solution (in my opinion) in those situations is to just work with the player. You'll all learn more about the game and be able to make the decision faster next time. They'll have the satisfaction of knowing they scored the best they could (or at least others agreed with them). In fact, if done right, everyone can have a maximum score. (Doing this gets much harder as the number of players increases -- consider it a group challenge. And, recall, it's just a game and it'd be silly for someone to win or lose because of a mere accident or true mistake.) (Some games are well suited towards this style of group play. Highly recommended with the significant other, too. ;) )
As for the type of game, mix in play of "speed games" where everyone has to take fast moves. Compare to a 2 minute speed chess game -- it's a completely different game when played that way.
This can balance full, thoughtful, strategy play with intense, and sometimes silly, action play.
If someone is the only one affected by the "rules of speed" they'll feel picked on or just won't have as much fun. Everyone, at some time or another, probably takes a long turn. Another solution is to just have a limited number of "long turns" -- this way, the slow thinker or optimizing player can plan for one turn (or so) a game and the rest of the group can go refill their drinks and snacks.
Finally, as others have said, unless it's chess, game familiarity will almost always speed everyone along. Give new players a chance. Play "open discussion" games. Open it up so the "slow" player can ask for advice and receive fair, honest answers. If it's a constant problem, the person is probably just unsure of their moves and boosting their confidence will go a long way.