21 Jun 2003 Bram   » (Master)

Lost Mail

Due to technical difficulties, I lost some mail from last week.

Apache and BitTorrent

There's some interesting discussion as to whether Apache will come with the BitTorrent mimetype already configured.

New Puzzle

I came up with a new puzzle.

Snail Racing

I saw a very cute board game in a store the other day. It features a racetrack which six different colored snails move along. There is a single six-sided die to roll. All snails start at the beginning line, and a snail to move forwards is repeatedly selected by die roll. The game ends when a snail crosses the finish line.

It's clearly meant for very young children, and the box says that players try to guess which snail will win in the end, and it's a family game with no winners and losers. Natuarally, I immediately noticed that it would make a great prop for a cutthroat gambling game.

Snail racing, a game for two players.

Both players start by putting a fixed ante into the pool. Before each die roll, both players write down an amount of money. The amounts they wrote down are then revealed, and they each put the amount they wrote down into the pool. The player who wrote down the larger number (determined by coin toss in the case of a tie) gets to put a single token on a snail of their choosing. A snail is then advanced by die roll, and play continues with another round of writing down numbers. When a snail wins, all the money in the pot is divided among the two players proportionately to how many tokens each of them had on that snail.

Hexagonal Game Rules

There was an error in my analysis of game winning positions given in my last entry. Before explaining what the error was and why I've made a slight rules change, I'd like to recap the rules, since they're now considerably more understandable.

Game is played on a hexagonal board with hexagonal cells. Players alternate placing pieces of their color. At the beginning, one player puts down the first piece and the other player decides which color they want to play.

A player wins whenever they make any of the following configurations:

  1. A single group which touches four or more edges

  2. Two separate groups, one of which touches three adjacent edges and one of which touches three edges not all adjacent, and which share exactly one edge between them.

  3. Two groups each of which span three edges and a third group which spans two non-adjacent edges not connected by either of the other two. The third group may touch more edges as well.

These rules are straightforward, and force there to be no draws. They also make winning require clear board domination, resulting in a game with much long-term positional play.

The error in my last post was that one of the winning configurations was a superset of another. To see where the difficulty comes from, compare the three following positions (see my last entry for notation):

  1. ((1, 3, 5)) ((1, 2, 3), (3, 4, 5), (5, 6, 1))

  2. ((1, 3, 5), (1, 2, 3)) ((1, 3), (3, 4, 5), (5, 6, 1))

  3. ((1, 2, 3, 5)) ((3, 4, 5), (5, 6, 1))

In each of these positions player A is strictly better than in the previous one. In each case where there are two completed positions which are individually ambiguous as to who should win and in which player A is strictly better in one, I wanted player A should win in the former, and lose in the latter. This criterion can't be satisfied due to position #2 above. I decided to make position #2 a win for player B, mostly because that makes the rules much more succinct.

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