I have a question about a popular dice 'slot' game in Belgium. A couple different casinos seem to be calling it "Mystery Box". I'll do my best to describe the rules...
The game board is made up of 4 3x3 grids.
The player gets 12 throws of 3 10-sided dice and chooses one grid to place each throw in. Each throw is place in the leftmost available position of the chosen grid.
Face probability
1 1/6
2 1/9
3 1/6
4 1/9
5 1/9
6 1/9
black 1/18
blue 1/18
green 1/18
red 1/18
After placing a throw, the player may throw and place again until all grids have been filled.
Once each grid is filled, points are awarded for 3 of a kind on any of the winline in that grid. Points per winline are earned according to the paytable of the game. Once all 12 combinations have been placed, the amount of points is totalled. Prizes are earned according to total points achieved.
I've been trying to write a program to compute the optimal strategy to this game (it certainly doesn't seem to be a pen & paper job), but I'm not making much progress. It seems to a tough problem.