I am currently programming a Tetris game and I want to add a custom Polyomino to the game with a maximum size of 3x3. I want this Polyomino to be the most disruptive figure, which means it to be not useful for the player in the highest amount of cases, with which I mean that it will not be helpful to fill up one row and that it will make it harder to fill up rows in consecutive turns.
Now I have to consider not only the possible states at the bottom, but also what states the custom Polyomino will leave the bottom in.
I was thinking of the 3x3 Block with a hole in the middle, since you have to have 3 empty fields in a sequence in order to place it beneficially, which reduces the amount of possible beneficial bottom states, which I consider to be 3 in a row with all combinations of occupied fields, to 1 in 7 and would lead to creating a state where the row, that will be occupied by the middle of the block will always be blocked until the row on the top is resolved.
But is there a way to calculate if the 3x3 Block with the hole in the middle is really the most undesirable Polyomino in most combinations of states? Do I have to consider something else?
Edit:
With the bottom states I mean that of course there will always be many places to drop the Polyomino, but looking at the bottom as a sequence of 3 fields in a row, you get the 7 cases:
- not a single field is occupied
- only the left field is occupied
- only the middle field is occupied
- only the right field is occupied
- the left and the middle field are occupied
- the left and the right fields are occupied
- the middle and the right fields are occupied
Now what I mean with beneficially is that placing the block can
- help filling up the current row
- not create a row that is harder or impossible to fill up until a row above is resolved (unreachable holes)
While the T-shaped block is beneficial in all situations, the stair-shaped block can never be beneficial in situation 1 and either situation 2 and 5 or situation 4 and 7. This is because the T-shape can be rotated always to either fill up the sequence of 3 fields or it can at least be placed in a way, that the player does not get any unreachable holes in the board. The stair-shaped Tetromino on the other hand will always place an unreachable hole in e.g. situation 1.
I have not considered that the likelihood of the 6 situations may vary from player to player, since they are playing after a certain strategy, they might get into certain situations way more often than in others. But all players are different and no one is ever going to play the same sequence of Polyominos (when not manipulating it to be so). I think we can assume that players will run nonetheless into all 6 situations and that the variety of strategies will make all 6 situations equally likely.