Randomizer Theory

Thread in 'Research & Development' started by colour_thief, 12 Jan 2007.

  1. "Drought" is a bit fuzzy (e.g., Should we use the properties of 7 Bag as an indicator and consider the minimum condition for an I-piece drought to be >12 pieces before seeing that piece dealt? Should we consider anything beyond the expected value of 1/7?), but "sequence" I think we can get a better handle on.

    The length of the game before reaching the more-or-less unsustainable Level 29 is 230~290 lines depending on starting level. At 2.5 pieces per line, that makes the bare minimum piece count 575~725. If we allow for some play into Level 29+, you could start seeing piece counts around 750~850, but we have not seen much more than that. "A sequence" long enough to constitute an entire game for a human at current standards of play is certainly less than 1000, so we can use that as a very generous upper-bound.
     
  2. Droughts are always a bit context sensitive, aren't they? I don't know what metric they use at the NES tournaments, but certainly anything longer than 12 pieces starts to feel like a proper drought. We may as well throw down a (somewhat) arbitrary marker there. When I have time to go back thru this whole thread, I can probably work out the solution myself, but I was hoping someone already knew the answer, even if it's just intuitively from a deeper well of experience.
     
  3. zid

    zid

    Why arbitrarily rebase them onto an offset from 12?

    Just the number of pieces since you last saw that piece is a perfectly acceptable metric. It'll probably be about 7, 12 is slightly unusual, more is painful.

    It's more like an "x hours since coffee pot was changed" sign than a metric you want to keep as low as possible, so maybe it's just the word 'drought' that needs fixing.
     
  4. Because the question I'm asking is "How many droughts will I have in an average maxout run of NES Tetris?"

    That's a question whose answer has direct implications for stacking strategy.
     
  5. In NES Tetris, the sum of the probability of droughts size 1 through 12 is slightly less than 86%. So if you consider 1000 pieces, your expected I-drought count is roughly (1 - 0.86) * (1000 / 7) = 20. Or put differently, once every 50 pieces.
     
    JBroms, GyRo and Kitaru like this.

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