TGM randomizer

Most games in Arika's Tetris The Grand Master series randomize the order of tetrominoes using an algorithm that makes successive identical tetrominoes less common. It involves keeping a history of the four most recent tetrominoes and trying to choose a random tetromino not in the history. It "rolls the dice" a given number of times and takes the first tetromino that doesn't match any in the history. TGM1 uses 4 tries; subsequent games using the TGM randomizer use 6 tries.

The history is not a unique list. If the randomizer fails to generate a unique tetromino, which happens about 3.5 percent of the time in a 6-try system, then two or more of one tetromino may occupy elements of the history.

A few additional behaviors exist in the beginning of the game.

• The game never deals an S, Z or O as the first piece.
• The state of the history is initialized to a fixed state:
  • In TGM1, the history begins filled with 4 Z pieces.
  • In TGM2, the history begins with a Z,S,Z,S sequence.

Tetris The Grand Master Ace does not use the TGM randomizer; it uses TTC's Random Generator algorithm instead.
(But TGM-ACE also never deals an S, Z or O as the first piece.)

Pseudocode

The finite-tries variation used in TGM works as follows:

Function tgmRandomize(history as list of 4 pieces by reference, numTries as integer by value) as piece:

For try = 1 to numTries:

candidatePiece = random element of set {I, J, L, O, S, T, Z}

If candidatePiece is not in history:

Exit loop

Move all tetrominoes in history back by one position

Put candidatePiece at front of history

Return candidatePiece

As numTries increases without bound, the algorithm's behavior approaches the following:

Function tgmRandomizeInf(history as list of 4 pieces by reference) as piece:

candidatePiece = random element of set {I, J, L, O, S, T, Z} minus those pieces that are in history

Move all tetrominoes in history back by one position

Put candidatePiece at front of history

Return candidatePiece

References

• colour_thief's description of the TGM randomizer