## Tuesday, February 7, 2012

### Combinatorializing Games: How do points actually work?

We've talked recently about combinatorializing connection games, but what about point-based games. Here's a general definition of a point-based game:

Players make moves and earn points during the game. This continues until there are no possible moves. When all moves have been made, the player with the most points wins.

What makes this not-quite-combinatorial is that it is not necessarily the case that the last player to move is the one who wins the game.

Flume is an example of such a game. Players score "a point" for each piece they play, and at the end the player with the most of their pieces on the board wins. Since there are an odd number of spaces, there will be no tie.

What happens, then, if you add two games of Flume together? What if you add a game of Flume to a game of Hex?

The way I've always envisioned these games working is as follows. Let's say the game ends with the left and right players each with their point totals (called left-points and right-points, respectively). Then a new game immediately starts with value: left-points - right-points, the winner of which wins the whole thing.

Thus, if you play a game of Flume and at the end the left player (Blue) played 9 disks while the right player (Red) played 16, then the result is game of value: -7, which the right player should win.

Is this how the "combinatorialization" is usually conceived? Is there another good way to handle this?

EDIT: Fixed a typo in the title. (Feb. 10, 2012)

1. A general theory for these types of games has already been developed.

I did my PhD thesis on those types of games. You can read it at.

www.combinatorialgametheory.com

2. I recommend it!

3. Fraser,

I'm not able to load that website. (It says the page is not found.) Do you have a link to that theory, or to your thesis?

I had the page working for a moment---it looks like you've got a nice blog started!---but no longer.

Urban, which part do you recommend? :)

4. Hi Kyle, yeah there was a problem with tumblr, I've moved it over to wordpress.

Try it again, it should be working now.

http://combinatorialgametheory.com/papers-and-preprints/

5. Hey Kyle, sorry I'm still having issues with my website at the moment. You can read my thesis at the link below, it has everything in it. Cheers.

If you have any questions just email me at fraseridstewart [at] gmail [dot] com

Cheers,

Fraser

6. Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing. the-guitarworkshop.com

7. Awesome blog. I enjoyed reading your articles. This is truly a great read for me. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work! แทงบาคาร่าออนไลน์

8. I was very pleased to find this site.I wanted to thank you for this great read!! I definitely enjoying every little bit of it and I have you bookmarked to check out new stuff you post. คาสิโน

9. I have to search sites with relevant information on given topic and provide them to teacher our opinion and the article. systeme alarme quebec

10. I have bookmarked your website because this site contains valuable information in it. I am really happy with articles quality and presentation. Thanks a lot for keeping great stuff. I am very much thankful for this site. 먹튀검증사이트

11. I found Hubwit as a transparent s ite, a social hub which is a conglomerate of Buyers and Sellers who are ready to offer online digital consultancy at decent cost. Zerp

12. http://www.365playpal.com/2015/05/discover-o-minimalist-game-app-review.html?showComment=1639643015988#c3616888272277234195

13. I feel really happy to have seen your webpage and look forward to so many more entertaining times reading here. Thanks once more for all the details. ซีรี่ย์ฝรั่ง

14. Excellent Blog! I would like to thank for the efforts you have made in writing this post. I am hoping the same best work from you in the future as well. I wanted to thank you for this websites! Thanks for sharing. Great websites! slot 2021

15. I am always searching online for articles that can help me. There is obviously a lot to know about this. I think you made some good points in Features also. Keep working, great job ! ซีรี่ย์ฝรั่ง

16. Very informative post ! There is a lot of information here that can help any business get started with a successful social networking campaign ! ซีรี่ย์ฝรั่ง

17. Interesting post. I Have Been wondering about this issue, so thanks for posting. Pretty cool post.It 's really very nice and Useful post.Thanks Download Opera

18. The automatic electric guns were introduced by a Japanese company first in 2005. As the name suggests, these airsoft sniper rifles require no manual force because it functions automatically. The AEGs are powered through batteries and motors. different kinds of airsoft sniper rifles

19. Get your favourite apps from www.apkdig.com