## The odds in the game risk

In risk, the attacking party rolls 3 die and the top two numbers of the 3 die rolled get put up against 2 die rolled by the defender. If the die are equal then the defender wins. For example if the offender rolls 5 5 2 and the defender rolls 4 3, then 2 defender men die. If the offender rolls 5 5 2 and the defender rolls 5 4 then they trade kills because when die are equal the defender wins.
If offender rolls 5 5 2 and the defender rolls 6 6 the defender wins. Who has the advantage? Attacking or defending? What is the comparative advantage?

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 Recognitions: Homework Help Science Advisor Here's one way to approach it. Break it into four cases from defender's perspective: ++ win on both +- win on high dice, lose on low -+ etc. -- Case ++: For each defender roll, count attacker possibilities: 6+6: 63 6+5: 53+3.1.52 (attacker rolls no 6s or one 6) 6+4: 43+3.2.42 (attacker rolls no 5s nor 6s, or just one such) : 6+1: 13+3.5.12 (attacker rolls nothing above 1 or just one such) (remember to count all above except 6+6 twice) 5+5: 53 etc. Summing, we get sum for r = 1 to 6 for each of: r3, 2r3(6-r), 6r2(6-r) = -2r4+7r3+36r2 Sum the series to r and plug in r=6. Similarly, for case +-: 6+5: 13+3.12.5 6+4: 23+3.22.4 etc.

## The odds in the game risk

 Quote by haruspex Here's one way to approach it. Break it into four cases from defender's perspective: ++ win on both +- win on high dice, lose on low -+ etc. -- Case ++: For each defender roll, count attacker possibilities: 6+6: 63 6+5: 53+3.1.52 (attacker rolls no 6s or one 6) 6+4: 43+3.2.42 (attacker rolls no 5s nor 6s, or just one such) : 6+1: 13+3.5.12 (attacker rolls nothing above 1 or just one such) (remember to count all above except 6+6 twice) 5+5: 53 etc. Summing, we get sum for r = 1 to 6 for each of: r3, 2r3(6-r), 6r2(6-r) = -2r4+7r3+36r2 Sum the series to r and plug in r=6. Similarly, for case +-: 6+5: 13+3.12.5 6+4: 23+3.22.4 etc.
Thanks man. I'm a little confused by what for example 3.1.5^2 means but thanks for the help

 Analyzed here: http://datagenetics.com/blog/november22011/index.html