About half of the maid cafes allow you to play a board or video game against one of the maids for 3 minutes for about 500 yen. The games can include the Pirate in a Barrel, seeing who can take out the most red beans from a bowl using chopsticks, and the Chomping Alligator game (pull a tooth from the alligator's mouth until it snaps shut). Winning the game may get you a free maid photo.
And, there are a lot of bars that offer games. But, there are a few maid cafe/bars that are specifically designed for one kind of game like darts or mahjong. Most have a cover charge (usually 500 yen for 1 hour) and none offer cash prizes. If you win anything, it's either an ashtray or a maid photo. (At Akiba Guild, it's the right to *buy* an ashtray.)
I've been to Akiba Guild, which is a fun place to lose $10-$20 at roulette, and Mermaid, which wasn't as much fun. I don't play mahjong so I have no idea when I'd go to MSN or Tempane. I'll eventually get to PSX, after I've gone to the other regular maid cafes. (PSX charges a cover, and I don't like going to places with a cover charge.)
Akiba Guild (Vegas-style gambling games)
Little MSN (Mahjong)
Little PSX (Darts Bar)
Cafe Mermaid (Darts Bar)