14 replies. Last post: 2007-09-28Reply to this topic Return to forum
I thought it better beginning a new thread for discussion and listing extreme situations of dvonn as we were sidestepping a bit from FatPhil's bot.
So as far as I know (in no reasonable order):
A) Longest possible game: 140 moves (passes counted as moves, white's double move counted as one move)
B) Shortest possible game: 52 moves (same count as above)
C) Highest possible stack: 49 rings
D) Largest possible kill: 46 rings
E) Most possible choises for a move: 111
F) Largest possible amount of singletons left in the end of the game: 7
A and E might possibly maybe be too small, but others probably hold. Please continue the list, add real game extremities &c.
I have been spending some time to give DVONN a nice page on Wikipedia. I have put up this nice list there as some trivia on the game ;-)
(Should I have made any errors, please feel free to improve / correct)
The close-up image doesn't show a legal position, does it?
It indeed is not. I already mentioned that on the discussion page. (Thereafter the person who put it up there changed the text with it to showing the board and the pieces instead of showing the game in play). I (or someone else who feels like doing this) should find / make a different picture to put up there.
What is the largest number of possble choices for a game-ending move, such that every possible move is a game-ending one. I have no idea what value this might be.
I don't think it's particularly high, but am prepared to be amazed.
I can think of 5…
7 is also possible for sure.
G) The longest chain of stacks only connecting to 2 neighbours (and 1 in the end). Theoretically you can go really far. In an actual game - not with newbies - I got to 6: http://www.littlegolem.net/jsp/game/game.jsp?gid=771669&nmove=80
Looks quite fun :-)
G) Like yours, this is ephemeral, but of length 10: #772325/82
To Fatphil's: 11 is possible and I'd bet that more is not.
To Schaapmans's: This is more of a real game challenge than theoretical, but for the sake of completeness, the maximum seems to be 31.
…or 30. Not as trivial as I thought. Must get back to 31.
nah. 30 it is.
The move after the one I refered to, it became 11!
However, ephemeral ones don't interest me so much. Ones that have ossified are more interesting IMHO.
@FatPhil: well, in my counting yours is only 3. I did not specify it well. A 'free' chain should contain no Dvonns, since that's another anchor, won't contribute to a free chain. Mine has 6 without a Dvonn.
@Paavo: yes, it's more fun for a game situation. Theoretically you can come really far. However, a chain with no Dvonns probably won't reach 30 or 31, that will be 28.