I was looking for a review game for logarithms, no calculator. I found a game not related to math that had kids roll one die and try to roll a 6. When they did, they started writing numbers 1-50. Meanwhile, the next person in the group of four kids rolls the die and tries to get a 6. When they do, they take the pencil from the other person and they start writing their numbers 1-50. And, so on. I thought I would try it with logs. I can't get the word doc to upload correctly to google docs and show the equations, so I just took a picture. It is so small, sorry. I had the kids folded it in half and cover it with scrap paper so they weren't trying to figure out the problems when it was not their turn. Then, they moved the paper down, one question at at time.
You could do it with any subject that is pretty quick to answer. The kids really got into it. I gave them each their worksheet, one die, and only one pencil is allowed. This is KEY because only the person that rolls a 6 can start working with the pencil. When the next student rolls a 6, they kindly take the pencil and start working. The dice started hitting the floor, pencils were thrown, hair was pulled, but all in a fun competitive way. They really liked it. It was an easy thing to prepare.