5 ms·
Sprouts game
- nazgulnarsil 18y agoI really like the brussel sprout variation as the shape makes the rules more visually intuitive. i'm going to introduce this to my friends.
- abstractbill 18y ago... the players cannot affect the result by their play ... a game starting with an odd number of crosses will be a first player win, while a game starting with an even number will be a second player win regardless of the moves. That makes the brussel variation a lot less interesting I think.
- benjamincanfly 18y agoBy enumerating all possible moves, one can show that the first player can always win in normal-play games starting with n = 3, 4, or 5 spots. The second player wins when n = 0, 1, 2, or 6. Am I missing something, or is the outcome of every sprouts games predetermined?
- timm5 18y agoThats exactly what i said!! What is the big deal? Actually I did play someone with 6 dots and won... so i think there might be ways of changing the outcome, for example if you use a line to encircle other lines to cut off their access. Either way, I thought this was a strategy game and it seems closer to the "dots and boxes" pencil game, ie...
- timm5 18y agoclarification: i played someone as player 1, with 6 dots, and won.
- gjm11 18y agoBrussels Sprouts is completely determined: it doesn't matter how you play, the winner is a function only of the number of spots. Sprouts is not; one can play it well or badly, and it makes a difference.
- gjm11 18y agoDots-and-boxes is a game with real strategy to it, too. See "Winning Ways" or Berlekamp's book that's just about D+B.
- ars 18y agoJust because he can force a win, doesn't mean he will. So it's still fun for novices, or large numbers of initial spots.
- jacobolus 18y agoThis means the first player wins for n = {3, 4, 5} if both players play perfectly. Similarly, if both players play perfectly, tic tac toe and checkers games result in draws. Fortunately, humans can make mistakes, rendering the outcomes less certain. :-)
- avinashv 18y agoI've been playing this game over the summer on long train/plane journeys--it's brilliant. I incidentally stumbled across it on Wikipedia, too.
- Darmani 18y agoAt Canada/USA Mathcamp last summer, a few kids found the Nim reduction for Brussel Sprouts for their project. Shame I don't remember it, though.
- dfranke 18y agoHey, another mathcamper on news.yc. '02/'03 alum here.
- jacobolus 18y agoWinning Ways and On Numbers and Games are both excellent. Math is fun!
- Angostura 18y agoI remember playing this as a kid about 35 years ago. It was described in a book called The Indoor Games boo, published in the UK. The same book also introduced me to the rather fun 'Nine Mens Morris' - http://en.wikipedia.org/wiki/Nine_Men's_Morris http://en.wikipedia.org/wiki/Nine_Men's_Morris
- pwk 18y agoI played Nine Mens Morris with my grandmother when I was growing up (we called it "Mühle"). She never gave me an inch just because I was a kid, and I still remember with great vividness the first time I ever beat her. A few years ago I wrote a java applet that plays the game. It's buggy and unpolished, but usable. http://pi-guy.net/games/muehle/ http://pi-guy.net/games/muehle/
- bumbledraven 18y agoThe 7th annual tournament of the World Game Of Sprouts Association is coming up! http://www.geocities.com/chessdp/trny2008.htm http://www.geocities.com/chessdp/trny2008.htm This is your chance to battle four-time world champion Roman Khorkov for first place. http://www.geocities.com/chessdp/champions.htm http://www.geocities.com/chessdp/champions.htm