From pirround@NOSPAMhotmail.com Wed Nov 10 18:15:36 CST 1999 Article: 281807 of sci.math Path: news.math.niu.edu!husk.cso.niu.edu!vixen.cso.uiuc.edu!howland.erols.net!sunqbc.risq.qc.ca!carnaval.risq.qc.ca.POSTED!not-for-mail From: "Malcolm Harper" Newsgroups: sci.math References: <38224055.3D57270F@crypt0.demon.co.uk> Subject: Re: Game Theory & Risk Lines: 43 Organization: McGill University X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Message-ID: Date: Fri, 05 Nov 1999 07:49:11 GMT NNTP-Posting-Host: 198.168.182.184 X-Complaints-To: abuse@mcgill.ca X-Trace: carnaval.risq.qc.ca 941788151 198.168.182.184 (Fri, 05 Nov 1999 02:49:11 EST) NNTP-Posting-Date: Fri, 05 Nov 1999 02:49:11 EST Xref: news.math.niu.edu sci.math:281807 Hugo van der Sanden wrote in message news:38224055.3D57270F@crypt0.demon.co.uk... > Chris Simmons wrote: > > Anyway. There's a point in the game where someone, say A attacks someone > > else who has to defend, say D. Now the rules are thus: A gets to throw > > three dice. Now D can choose to throw one or two dice in defence; D has a > > slight help in that if there's a draw on the dice, D wins. D's best score > > goes up against A's best score and should D choose to throw two dice, D's > > second best (worst) score goes up against A's best score. Then it's > > simply a matter of keeping track of how many you score each go. For > > example, say A threw 5,3,4. Then if D threw 6,2 in responce, the score > > for that round would be one each. In the actual game, each player has a > > finite number of troops, but as a good approximation we could presumably > > think of the game as not necessarily ending. > > > > So my question is this; what's the optimal stratergy for D to employ; > > obviously A can do nothing but roll dice, but D has choices [...] > > As mentioned by Eric Dew, A can choose to roll fewer dice, however it > never benefits him to do so - being allowed to roll 3 dice when his > opponent may only roll 2 is his only balance for D's advantages, that > D wins on tied scores and that D gets to choose how many dice to roll > _after_ seeing what scores A has rolled. This is not how I remember the rules, but I no longer have a game set for reference. I found Owen Lyne's Risk FAQ at www.maths.nott.ac.uk/personal/odl/riskfaq.html. Apparently there were different rules for different versions of the game. In the North American version the defender did not get to see the attacker's roll prior to deciding how many dice to roll (#2.6.2 in the FAQ). He also gives a breakdown of attacker/defender losses in #3.2 -- Malcolm