4 ms·

from their description > Yes, you will get a lot of S pieces. But it doesn't give you solely S pieces - if that were the case, then it would be possible to mak

by dmoy 6y ago

from their description > Yes, you will get a lot of S pieces. But it doesn't give you solely S pieces - if that were the case, then it would be possible to make lines forever, which is much too easy.

moomin 6y ago
This is actually wrong. Some friends of mine proved that if you drop only S and Z pieces in an irrational ratio, the player is doomed irrespective of the dimensions of the board.
- temporalparts 6y ago
  This is interesting! Can you link the proof?
  - moomin 6y ago
    I can’t, but it was published in Eureka (Cambridge Maths Society/Archimedean journal) somewhere between 1988 and 1993 I think. I don’t know how to get old copies but they were all typeset in TeX. The same people also proved (earlier) that with 3-ominos its a win for the player. Incidentally, if you’re into cool maths that isn’t part of any major research line, Eureka is a great read.
    - chriskanan 6y ago
      Proof: https://harddrop.com/wiki/A_deadly_piece_sequence https://harddrop.com/wiki/A_deadly_piece_sequence Paper: https://www.semanticscholar.org/paper/How-to-lose-at-tetris-Burgiel/11c12871bfa138fa8bb93a4e5dbcca36c5d214fa?p2df https://www.semanticscholar.org/paper/How-to-lose-at-tetris-...
    - gjm11 6y ago
      The proof that Tetris is a win for the computer was published in Eureka 51 (1992) by Richard Tucker. (Someone else has posted a link to another paper proving this, but it's from 1997; Richard got there first.) The proof that Tris is a win for the player was published in Eureka 51 (1991) by Adam Chalcraft. Richard and Adam definitely know one another and I would be unsurprised to learn that they talked to one another about this stuff, but the actual writeups in Eureka were by different people. (Quite possibly a substantial amount of the thinking was done collectively at meetings of the "Puzzles and Games Ring", a sort of sub-organization of the Archimedeans (the student mathematical society at the University of Cambridge, which publishes Eureka).
      - moomin 5y ago
        waves Might have known you’d have the exact details.
- amptorn 6y ago
  No. It's right. If only S pieces are provided, you can make lines for ever. If S and Z pieces are provided, you can't.

by dmoy 6y ago

from their description > Yes, you will get a lot of S pieces. But it doesn't give you solely S pieces - if that were the case, then it would be possible to make lines forever, which is much too easy.

moomin 6y ago

This is actually wrong. Some friends of mine proved that if you drop only S and Z pieces in an irrational ratio, the player is doomed irrespective of the dimensions of the board.

temporalparts 6y ago
This is interesting! Can you link the proof?
- moomin 6y ago
  I can’t, but it was published in Eureka (Cambridge Maths Society/Archimedean journal) somewhere between 1988 and 1993 I think. I don’t know how to get old copies but they were all typeset in TeX. The same people also proved (earlier) that with 3-ominos its a win for the player. Incidentally, if you’re into cool maths that isn’t part of any major research line, Eureka is a great read.
  - chriskanan 6y ago
    Proof: https://harddrop.com/wiki/A_deadly_piece_sequence https://harddrop.com/wiki/A_deadly_piece_sequence Paper: https://www.semanticscholar.org/paper/How-to-lose-at-tetris-Burgiel/11c12871bfa138fa8bb93a4e5dbcca36c5d214fa?p2df https://www.semanticscholar.org/paper/How-to-lose-at-tetris-...
  - gjm11 6y ago
    The proof that Tetris is a win for the computer was published in Eureka 51 (1992) by Richard Tucker. (Someone else has posted a link to another paper proving this, but it's from 1997; Richard got there first.) The proof that Tris is a win for the player was published in Eureka 51 (1991) by Adam Chalcraft. Richard and Adam definitely know one another and I would be unsurprised to learn that they talked to one another about this stuff, but the actual writeups in Eureka were by different people. (Quite possibly a substantial amount of the thinking was done collectively at meetings of the "Puzzles and Games Ring", a sort of sub-organization of the Archimedeans (the student mathematical society at the University of Cambridge, which publishes Eureka).
    - moomin 5y ago
      waves Might have known you’d have the exact details.
amptorn 6y ago
No. It's right. If only S pieces are provided, you can make lines for ever. If S and Z pieces are provided, you can't.