I like to think of Sodoku as the Mathematician's Crossword puzzle. I was never, and probably never will be much good at crossword puzzles, but something clicked when I saw my first Sodoku puzzle. Now, this isn't a boardgame persay, but it is a puzzle, and puzzles can be games, so hence the article.
What triggered this post for me was an article that proved that it is impossible to solve a Sodoku puzzle with only 16 clues. Proof Now, the mathematics does get a tiny bit tricky, but I see it as more logic than math.
This brings up the idea of "solvable" games. That is, a game with limited options where the best move in any circumstance can be determined. Checkers is an example of a solvable game. Chess is to an extent, but there is not a complete solution as of this post (at least not one I know about). A simple to solve game such as Checkers still holds some appeal, at least until you see the solution, but partially solvable games are where the fun happens.
Think of your favorite game. If you look at the different things going on, there are probably some things that you always see as being the best thing to do. Other times, things are less defined. It's a tricky balance to maintain, but I hold that it is a necessary balance. A game with all luck will leave the victor less than satisfied and the losers complaining of bad dice rolls, or bad card draws, but a game with no luck tends to see the same person always winning, and dominant strategies emerge, which takes the fun out of the game.
Soduku has sharpened the logic of the people who solve the puzzles. The puzzle is full of deductive reasoning, and the more you can do that, the better you'll be at some boardgames. Sure it won't help you the next time you play Farkle, but it might help you when you play Liar's Dice.