If it's a board game and can be played in less than a few hours, I'll probably be willing to try it. Today's case in point: Quinto (the vintage 3M version).
Quinto is basically number-Scrabble. Each player takes five tiles (which each depict a number from 0-9). The number five starts in the middle of the board. Players take turns placing numbers in a row or column, but must use a previously placed number in their new string of numbers. When placing a new row, the numbers in that row must all add up to a multiple of 5 (hence "Quinto"). There are a couple of minor extra rules. First, no row can consist of more than five numbers. Second, if you place all five of your tiles in a single turn, it must be able to score in at least two directions (such as when you add an "S" to a word in Scrabble and then create a new word going the other direction). Players get points equal to the sum of the numbers in each of the scoring rows and columns. Play continues in this fashion until no more tiles can be played - at which point players lose points for any unused tiles and whoever has the most points is the winner!
The first thing that I like about Quinto is the rule that you cannot have more than five tiles in a single scoring group (row or column). Whereas this seemed like a completely arbitrary rule that played off of the title when I first read the instructions, it really is crucial to the game. If it weren't for this rule, players would simply continue playing off of the same row repeatedly until the row stretched the length of the board. Therefore, if you scored 75 on your turn, I would easily be able to add 10 to what you had placed and score 85. This rule prevents these kinds of situations, and causes the players to actually play the pieces in more of a crossword fashion.
The second thing that I like about Quinto is that it is math based instead of number based. Whereas I do not have a poor vocabulary, word games help me to realize that my vocabulary is not exhaustive. In Quinto, however, all of the players are on an (approximately) even playing field. Assuming that everyone can add in multiples of 5, anyone can play the game and there is no advantage going into the game based on previously acquired knowledge. I wish that there were a way of leveling the playing field like this in Scrabble.
There are some cons to Quinto, however. Though I really enjoy math (I have a degree in it), I still find the game to be fairly boring. There simply isn't anything engaging in it. If I were working with young children on how to count by fives (or how to add in general), the game would be an incredibly useful teaching tool. However, as a game to play for fun, there are a lot of other games that I think are much more engaging. Here's really the best gauge I can come up with for you to determine whether this game is for you: ask yourself, "How many times can I look at an 8 and a 7 and go 'oh! I can make 15!'?" If the answer is not "I could do that all day!" but is closer to "twice," then this probably isn't the game for you, either.
Secondly, the game isn't even really very creative. Whereas Quinto is a really old game by modern standards (it was first published in 1964 from what I can tell), it really is just a derivative of Scrabble, which came out in the 1940's. Worse yet, I'm not really a major fan of Scrabble - which leads back to the first con, which is that Quinto is boring.
Overall, I give Quinto a 6.0/10. This game's mechanics work; they're just not fun. I am able to have fun joking around and laughing in games, and I'm able to have fun deeply strategizing in games - Quinto doesn't fall into either of these categories. If you're looking for a game to help teach children how to add, Quinto would be a good fit. For anything else, I'd recommend looking elsewhere.
If you like math intensive games like Quinto, you might also want to check out Power Grid, Lost Cities, and Atlanteon.