Need to Improve Your Calculation Skills? Then Calculate!
Sunday, September 5, 2010 at 6:31PM In his new book Studying Chess Made Easy, Andy Soltis offers advice on a wide array of chess topics, including improving calculation skills, and one of his suggestions is to play checkers. The point is that checkers is a very tactical game, and so the skills of looking ahead and working through complicated variations will be of general use to your chess "muscles". It makes sense, and maybe we can extend the idea.
For example...I'm in the middle of watching the slightly insane movie (or "film", if you must) "Last Year at Marienbad", and in it they play a simple but not quite trivial game I learned when I was about 11 from my old chess friend Jeff Gallegos. (I wonder if he learned the game from someone who watched this movie, or from someone who learned it from someone who watched the movie, etc.) Here's how to play:
Arrange a set of objects (cards, matchsticks, coins, small vertical lines on a sheet of paper - whatever) in four rows. The top row will have 1 object, the next 3, the next 5 and the last one 7. Players take turns removing at least one object per move. You can remove as many or as few objects as you like on a turn, with two conditions: you must remove at least one, and you can only remove objects from one row on a given move. The player to remove the last object loses.
Let's look at a sample game. We start with this setup:
I
III
IIIII
IIIIIII
(Normally it would be set up in a pyramid shape, but let's not worry about graphics here.)
Suppose the first player removed one from the second row. Then we'd have this:
I
II
IIIII
IIIIIII
Let's suppose player two is impatient and removes the entire bottom row, and player one in turn wreaks havoc with the third row. Then we have this simple situation:
I
II
Player two to move can force a win by eliminating the entire second row.
I
Player one must eliminate the last object, and thus loses.
In the movie the same player wins all the time, regardless of whether he goes first or not, but this does not reflect some sort of grandmasterly skill on his part. It's not too difficult to work out for yourself who should win - always - and why this is the case. It's a fun game until you do work it out, and might have some of that checkers-like value if you try to work it out mentally rather than solving it by pure trial and error.
Reader Comments (6)
The current issue of Chess Life had a very good article on chess and game theory. In my opinion it was the most interesting article (that doesn't aim to improve your chess) they have ever had. It discussed games like this and how to solve them using [DM: snip!]. This game is clearly solvable using that method, but I won't get into that since that would defeat the purpose of the exercise for the readers. I just wanted to say that if anyone finds problems like this interesting, and is looking for more games like it (with solutions), they should make sure to check out the Chess Life article. It's in the September issue and is called "Chess and Game Theory - Chess Players are Unwitting Game Theorists" by FM Mike Klein.
oh - memories... i used to play this game in highschool during boring classes with my best friend
It soon became very simple to win though... it's enough to know 3-4 patterns that always win (for instance: [DM: Snip! Readers, please don't post solutions or major hints: those who want either can easily find them online. I want readers to have the chance to solve the game for themselves without any hints.]) and then you don't really need to calculate a thing - you just strive for one of the above patterns.
So, because we mastered the game, we decided to extend it by allowing a "capture" to happen in the middle of a row (essentially cutting a row in 2 parts!)... It's not that hard to master even that variation, but it is entertaining for a while - try it!
Anyway, for those wanting to see the game online (against simple or flawless AI), i once made a java applet for it - it's at http://andyhot.gr/old/Java/baloon/index.html.
Hope it brings some minutes of fun to all :)
[DM: Excellent: thanks for letting us know! I like your variant idea too. It's a nice way of adding a little complexity to the game and forcing us to use schematic thinking - that's another very important chess skill, especially in endgames.]
on the topic of games in movies...
This is chess in Doctor Who a cool UK sci fi series from the BBC
http://www.youtube.com/watch?v=WSoC1VUdavE
Im enjoying the new series of these ... I bet other chess players will like it too.
Martin Gardner discussed this game (called Nim) in very old editions of Scientific American. The book collections of his columns were some of my favourite books as a teenager.
The game is called Nim, and unfortunately the winning strategy (adding in binary without carry) can be done without any chess-like calculation at all. The game is analyzed in full in "Winning Ways" by Conway, Berlekamp, and Guy.
I would suggest Dodgem, Chomp, Sprouts, and Hex as simple abstract mathematical games without simple winning strategies.
Slightly off-topic but "Last Year in Marienbad" is a rip-snorter of a film. Who can forget those gardens?