Reversi Chain Reaction (reacción en cadena)

En el foro de Littlegolem una persona publicó el siguiente mensaje (está completo pero comento cada párrafo):
http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=40&topic=102

Reversi enthusiasts may be interested in "Reversi Chain Reaction" - a new form of Reversi that I have introduced on the the gaming site, wifight (mostly Palm-based, but also Windows). It was coded up by site developer, Brennan.

Nos habla de su sitio "wifight" (http://wifight.com/) y cuenta que ha introducido una variante del reversi a la que llama "Reversi Chain Reaction".

It's a simple and logical extension of normal Reversi, so natural in fact that I was surprised to find it does not seem to have been tried before. The only difference is that discs that are flipped as per a normal Reversi move can cause further flips as part of that move, if they now trap one or more of the opponent's discs, and so on. Thus a normal Reversi move can set off a powerful "chain reaction" of flips that spreads across the existing array of discs. These reactions can be especially dramatic later in the game. The record so far for a change in "status" in a single turn is 83 (e.g. from having 21 discs less than the opponent to having 52 more).

Explica las reglas: además de voltear las fichas flanqueadas por la ficha recién colocada y las ya colocadas, también sirven como fichas pivote las fichas que se vayan volteando. El autor se extraña que nadie lo haya intentado antes. Como anécdota, dice que el máximo cambio de fichas (en las partidas jugadas en el sitio) ha sido de 83.

I'm no Reversi expert so I have no idea how it compares with the original for advanced play. Likewise we have no advanced players on wifight who can assess it from an expert's point of view. However, it has been very popular since it was introduced, in fact twice as much as the original. It is definitely exciting! It seems to require quite different strategy to normal Reversi, with the edges and corners assuming even greater importance than is usual. There can be quite prolonged battles over the diagonals, with a near-complete diagonal sometimes reversing color many times in alternate moves.

Comenta que la estrategia parece diferir notablemente en esta variante y que tiene más jugadores en su sitio practicando esta variante que el propio reversi.

It would be great if a couple of Little Golem Reversi experts could try it out and share their thoughts on it.

Using the link below you can also follow what I think has been my most exciting game to date, with lots of wild and crazy swings, especially from turn 40 or so onwards.

http://wifight.com/games/reversi-rcr/52ee052132549942b8d8c0314d80f64a

Nos da un enlace a una partida del sitio, lo que resulta de agradecer porque así no hay que registrarse / instalar cosas para ver una de estas partidas.

Aquí un movimiento para aclarar las reglas (en los primeros movimientos no se parecía notar la diferencia en las reglas):

Como se puede apreciar arriba, no se voltean todas las fichas flanqueadas: vemos que del movimiento anterior hay dos blancas flanqueadas por fichas negras que no se han volteado. Sólo se voltean las que están entre:
- ficha recién colocada - cualquier otra ficha
- fichas volteadas - fichas ya colocadas o fichas volteadas o ficha recién colocada

Por lo tanto, no se voltean las que están entre:
- fichas ya colocada - fichas ya colocadas

Y el de arriba es el resultado del movimiento.

El mensaje continúa:

Maybe some of LG's mathematicians might also be able to explain something that (surprisingly to me anyway) makes the game possible in the first place: that the final outcome of a chain reaction is independent of the sequence of flipping. In a complicated reaction, in addition to the primary sequence of flipping (i.e. flipping as per a normal Reversi move), there may be secondary, tertiary, etc sequences of flipping. Extensive testing on a physical Reversi board showed that it it does not matter if one completes each order of sequence in turn, or whether one "mixes and matches" them as it were. It is a bit like coloring in an outline drawing - you can start and finish anywhere you want - the picture will still get filled in. In playing the game, predicting the final outcome on a board with many discs might seem tricky at first but it quickly becomes intuitive.

cheers

geoff

Cuenta que no importa el orden de volteo y que al final resulta intuitivo ver cómo queda el tablero.

Asimismo puede ser interesante la contestación de otro jugador:

This is an old game---if I remember correctly it's sort of unplayable in practice because the player who makes the last move has such an advantage.

You're right in that the final outcome of a chain reaction is independent of the choice of flipping though: somehow the crucial part of the argument is that if there's a long row of whites with blacks at both ends, so the whites are going to get flipped, and then if a white in the middle of the long row gets flipped for another reason, then you're still going to flip all of the long row of whites because it's now in two lines both with blacks at each end. So now you can check that flipping in any order at all is equivalent to, at each iteration, flipping *all* lines that can be flipped at once, something which is well-defined (i.e. at first iteration, flip all the sandwiched lines, and then at the second one flip all the lines that are now sandwiched, and so on).

Dice que el último en jugar tiene demasiada ventaja. Asimismo, profundiza en lo de que el resultado es independiente del orden de volteo.

A mí me parecen muchas fichas a voltear.