Tonight we have hot pot dinner at Jason’s place to celebrate the Santa Clause Festival, the politically correct name for Christmas. As usual, I brough some board games to the party. Some of us played Monoploy and some of us played Risk. Somehow Jackson like to change to official rule of Risk, and claimed it will speed up the game. Instead of getting at most one card per turn, a player can get one cards each territory he conquer. There are two consequences of this house rule, first we run out of card fast, and it really tips the balance of the game. It makes the strong player even stronger when he trade in his cards for armies and start a battle tour. This rule ensure him in a big army in every following turn. It is almost impossible for the weaker players to catch up once someone has cashed in an big army. Poor Doug being the last player to start, he got wiped out early in the game because of this rule. In short, Jason’s rule makes the game less fun.
I did some research on the mathematics of risk after I came home. As I suspected, there is a slight advantage to the attacker. The probability of winning a battle favours the attacker if both side has equal number of units, if it is more than 5 units. The odd expected lost for the 0.9 of the attacker to 1.1 of defender. It is interesting to know that the defender has better odd to have even number of troops in the all his territories. Deploying 2 and 4 troops in two territories has better odd than deploying 3 and 3. In the Risk FAQ, I came across a house rule on rolling the dice. The defender can choose to roll 1 or 2 dice after he saw the roll of the attacker. This rule give an advantage to the defender by minimizing his lost if they attacker got 2 high numbers. The expected lost ratio is closer to 1:1 in this rule. The only drawback is the game takes longer to play.
To speed up the game and make it more fun, we should play the official rule, and use the mission card next time. Instead of have to conquer the world to win, the player first conquer two contintents or number of territories stated in the mission cards wins the game. It will force the players to fight over the same contintent.