This header plots the critical line of the Riemann Zeta Function.  A complete understanding wins a $1,000,000 prize.
. . .
Main   Links   Orders   Post   Next Page   Next + 10

My game Chaos Tiles is related to Dominoes.  A friend mentioned that he really liked my Domino game Ups and Downs, and I promised to post it, somewhere.  This isn't one of the typical domino games. This game makes an interesting puzzle, too.  Note, in the sample game below, I accidentally used two 7-9 pieces.  Thanks to Chris Lusby-Taylor for pointing this out.

Ups and Downs

Equipment: a set of 55 double-9 dominoes.  Smaller or larger sets may be used.
Setup: Distribute the dominoes randomly to all players.  Three players is ideal with the double-9 set.  Keep the extra tiles hidden.  At the start of the game, the play is going Up.  Each player keeps their hand of tiles secret from the other players.  Whoever has the lowest double starts the game.  Each player should arrange their tiles with the higher number on top.
Winning:  Get rid of all your dominoes.  Score a number of points equal to the number of unplayed dominoes.
Special Pieces:  Dominoes with exactly nine pips (for the double-9 set) can reverse the direction of play in the next trick.  If an odd number of ninepip dominoes is played during a trick, the direction of play changes for the nuxt trick.  Doubles may be played as either one or two pieces, at the player's discretion.
Up:  When going UP, the other number must be higher or equal to the played number (Valid play: 3-7, 3-3, 3-9).  The next play must be the same size with a higher played number (Valid next play: 4-4, 4-7).  Tiles should be sorted by the lower number.
Down: When going DOWN, the other number must be lower or equal to the played number (Valid play: 9-4, 9-9, 9-1).  The next play must be the same size with a lower played number (Valid next play: 7-3, 7-1, 7-0).  Tiles should be sorted by the higher number.
Play:  Play starts going Up.  Whether UP or DOWN, the first player of a trick plays a set of dominos containing a played number on one side. The size of the set is equal to the number of dominoes played (doubles may count as one or two dominoes).  The next player must play a set of the exact same size, or pass.  Sets continue to be played until everyone passes, ending the trick.  A player may play multiple times in the same trick. The last person to lay down a set of the given size leads the next trick.
Sample Game:
Red: 0-0 0-1 0-3 0-5 | 1-2 1-8 1-9 | 2-6 | 3-4 3-6 | 4-4 4-5 4-7 | 5-8 | 6-7 6-9 | 7-9 | 9-9.
Blue: 0-6 0-9 | 1-3 1-4 1-5 1-6 | 2-3 2-4 2-8 | 3-5 3-8 3-9 | 4-9 | 5-6 5-9 | 7-7 7-9 | 8-8.
Green: 0-2 0-4 0-7 0-8 | 1-1 1-7 | 2-2 2-5 2-7 2-9 | 3-3 3-7 | 4-6 4-8 | 5-5 5-7 | 6-8 | 8-9.
First Trick (up): Red starts the game (lowest double).  Red plays four zeroes (0-0 0-1 0-3 0-5).  This could be five zeroes, but it is played as four.  All further sets played in this trick must have a size of four.  Blue plays four ones (1-3 1-4 1-5 1-6).  Green plays four twos (2-2 2-5 2-7 2-9). Red plays four fours (4-4 4-5 4-7).  All players pass after that, ending the trick.  Since an even number of ninepips was played (2-7 and 4-5), the direction of play does not change.  Red played the last set, and starts the next trick.
Second Trick (up):  Red starts with three ones (1-2 1-8 1-9).  Blue plays three twos (2-3 2-4 2-8). Green plays three fives (5-5 5-7). Red passes. Blue plays three sevens (7-7 7-9).  All players pass.  An odd number of ninepips (1-8) was played, so the direction of play changes.  Blue played the last set, and starts the next trick.
Blue: 9-5 9-4 9-3 9-0, 8-8 8-3, 6-5 6-0, 5-3.
Green: 9-8, 8-6 8-4 8-0, 7-3 7-1 7-0, 6-4, 4-0, 3-3, 2-0, 1-1.
Red: 9-9 9-7 9-6, 8-5, 7-6, 6-3 6-2, 4-3.
Third Trick (down): Blue starts with four nines (9-5 9-4 9-3 9-0).  All players pass.  Play changes direction due to the ninepip (9-0).
Blue: 0-6, 3-5 3-8, 5-6, 8-8.
Green: 0-2 0-4 0-7 0-8, 1-11-7, 3-3 3-7, 4-6 4-8, 6-8, 8-9.
Red: 2-6, 3-4 3-6, 5-8, 6-7 6-9, 7-9, 9-9.
Fourth Trick (up):  Blue starts with two threes (3-5 3-8).  Green plays two fours (4-6 4-8). Red plays two sixes (6-7 6-9). Blue plays two eights (8-8). Green passes.  Red plays two nines (9-9).  All players pass.  No ninepips were played.
Fifth trick (up):  Red starts with two threes (3-4 3-6).  All players pass.  A ninepip was played (3-6), so the direction of play changes.
Red: 9-7, 8-5, 6-2. Blue: 6-5 6-0. Green: 9-8, 8-6 8-0, 7-3 7-1 7-0, 4-0, 3-3, 2-0, 1-1.
Sixth Trick (down):  Red starts with one six (6-2).  Blue passes.  Green plays one four (4-0). Red passes. Blue passes. Green plays one three (3-3).  Red passes.  Blue passes.  Green plays one two (2-0). Green sees a way to win the game at this point.  All players pass.  Green could play again, but that would be a losing play. No ninepips were played.
Green: 9-8, 8-6 8-0, 7-3 7-1 7-0, 1-1. Red: 9-7, 8-5. Blue: 6-5 6-0.
Seventh Trick (down):  Green plays three sevens (7-3 7-1 7-0).  All players pass.
Green: 9-8, 8-6 8-0, 1-1. Red: 9-7, 8-5. Blue: 6-5 6-0.
Eighth Trick (down):  Green plays one nine (9-8).  Red plays one eight (8-5).  Blue plays one six (6-5).  Green plays one one (1-1).  All players pass.
Ninth trick (down):  Green plays two eights (8-6 8-0), and wins.  He scores two points for the two unplayed tiles.

Puzzle:  Who has the best starting hand, above?  Who goofed up in the play?  What are the right strategies for this game?

Here is an excellent write-up by Joseph DeVincentis:

The Domino Ups & Downs game is very interesting.  It is a bit like Great Dalmuti, and has the pyramidal structure (few high pieces and lots of low pieces) which separates that game from the classic games it was based on, but the reversal feature takes advantage of the dual nature of dominoes that cards do not have.  I've played forty-two, which similarly uses the dual nature of dominoes in what is otherwise a standard trick-taking card game.

I think red had the best starting hand, due to having both of the strongest pieces (double-0 and double-9), and that great set of (upward) 4s.  He also has 3 of the ninepips, so has a good deal of control over when the direction reverses.

Red goofed up.  His hand is dreadfully weak after leading the 6-2, so much so that he cannot hope to ever win another trick, and thus never have a chance of playing the 9-7.  He should lead the 9-7 at this trick, or perhaps alter his play earlier to avoid reaching the weak 9-7 8-5 6-2 hand at all.  Most likely, he should play the 3-6 singly, retaining the 3-4 which becomes a relatively strong piece after the reversal, at the expense of perhaps losing control.  Then, he should play the 7-9 if given the opportunity (if blue and green don't jump right to the 8-8 or 8-9). Possibly, red should hold back on his 9-9 so he can play it to win the trick when he throws the 3-6, and have control when the play starts its final downward journey, but I think he has to play it to ensure blue doesn't go out. (Indeed, with the actual hands, if red holds back the 9-9, blue will go out before red has a chance to play the 3-6 and top it with the 9-9.)

It also seems unwise of red to throw all those 0s on the first play, because they are so powerful for downward play.  Better is 0-3 0-5, or 1-2 1-8 1-9, or 1-8 1-9, or 0-1 0-3 0-5.  This may be the real reason he got into such a predicament to begin with.

The "monster" strategy of leading your biggest set and avoiding breaking up sets is often not correct for this game, because a single piece may be part of an upward set and a downward set, or may be part of a large, low upward set but a single strong downward piece, and you have to consider both possibilities for a piece before deciding to play it.  The doubles are all strong pieces, but even without the ability to play the piece as a pair, the pieces with close-together numbers are either strong in one direction (0-1, 7-8) or of moderate strength in either direction (4-5).  Pieces with far-apart numbers (e.g., 0-8) are weak for both directions unless part of a large set.  1-8 1-9 and 1-2 1-8 1-9 are probably Red's best two opening plays.