An interesting new Reversi variant Reversi forum
7 replies. Last post: 2009-08-17Reply to this topic Return to forum
geoff at 2009-07-17
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.
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).
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.
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.
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.
wccanard at 2009-07-17
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).
geoff at 2009-07-18
Thanks for the info, wccanard
I'm curious as to the previous history. I spent a few hours researching Reversi variants on the web and couldnt find any mention of this one. I know an old variant could make it onto the web, but then again, it seems somewhat unlikely that it would have ever been considered pre-computer because it's reasonably unwieldy to track a big reaction OTB.
As to the player 2 advantage, so far at wifight the games have been split evenly between the players (albeit amongst a bunch of non-expert players). Just as in normal reversi, player 2 does not always get to play the last move, e.g.
geoff at 2009-07-18
that should be “I know an old variant could miss out on making it onto the web…”
geoff at 2009-08-16
can you recall more details about your previous experience with the “chain reaction” variant?
wccanard at 2009-08-17
I cannot, I'm afraid. I remember reading about it on the web somewhere years and years ago where it was disregarded as being “unplayable” but can't remember the context and perhaps it was not even a good authority who said it. I've just failed to find it using google though. Because I can't back up my comments about the game with hard evidence I should probably retract them. My comments about the final outcome of flipping being independent of order still stand, at least…
geoff at 2009-08-17
Thanks for trying, my hours of web hunting also failed to unearth anything. I contacted Christiaan Freeling, who hadnt come across it before, but did make the interesting comment that computers tend to be better than humans at these chain reaction games. And that therefore it wouldn't be hard to program a superstrong AI version. Finished games on the wifight site are still split evenly between players 1 and 2, but sample size is small (30 games).