Outcomes in Risk
It is possible that no one but me cares, but I have been wondering about this for a long time, so I finally worked out the answer:
In a game of Risk, if the attacker is rolling 3 dice and the defender is rolling 2 dice, the average number of wins for the attacker is 1.079. So on average, the defender will lose very slightly more armies than the attacker.
However, the standard deviation is 0.8112, so many battles will go much better or much worse than this.
The raw numbers are: on 5 6-sided dice, there are 7776 possible outcomes. Of those, the attacker wins twice on 2890 rolls, wins once on 2611 rolls, and wins zero times on 2275 rolls.
(Edited to correct numbers.)
In a game of Risk, if the attacker is rolling 3 dice and the defender is rolling 2 dice, the average number of wins for the attacker is 1.079. So on average, the defender will lose very slightly more armies than the attacker.
However, the standard deviation is 0.8112, so many battles will go much better or much worse than this.
The raw numbers are: on 5 6-sided dice, there are 7776 possible outcomes. Of those, the attacker wins twice on 2890 rolls, wins once on 2611 rolls, and wins zero times on 2275 rolls.
(Edited to correct numbers.)