There is a kind of tetris game. I need to fill an area (4 column and 6 row) with the pieces below. The pieces has no rotation and reflection.
1 2 3 4 5 6
## # # ## ## #
# ## # ## ##
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When the game starts, you will have a random piece which you may use that piece or you can throw it. After that, you will get another piece randomly (all six pieces have the same probability) and so on. The point is to complete the whole area by using maximum 10 pieces. You use the piece or throw it both count.
The question is how to play this game perfectly. I mean, how can I decide a piece to throw or keep and where to place it. Every move will change the probability of completing the puzzle up to 10 move and, I need to keep that probability higher. What would the best strategy be? Thanks for help.