I recently published a word game for Windows Phone and I am really happy to have some players. The game is entirely offline and at the end of a game, the player's score is published to a server. I'm collecting the scores to build a leaderboard. Right now, I don't believe that the leaderboard I offer to my users is appropriate. I essentially accumulate the score of all the games of a user for a given day and that becomes their score. So if Player 1 plays 3 games and gets 100, 150 and 200 points, its score for the day is 450 points.

I would like to get your ideas and opinion. How do I keep my game challenging and engaging with a good leaderboard? Should I continue accumulating the score for a day? Should I just keep the best score?

Thanks!