Help My Game - RISK

calebb writes "RISK is a classic board game that's been around since 1959. This week, Science News posted an article titled 'Improving the Odds in RISK.' They mention that '...the chances of winning a battle are considerably more favorable for the attacker than was originally suspected.' Amazing! Risk is over 40 years old & nobody ever calculated the odds of winning a 5 vs. 5 battle!"

Comments

Wrong

[(trb001)]

An attacker with three or more attacking armies rolls three dice, one with two armies rolls two dice, and one with only one army rolls one die. A defender with two or more armies rolls two dice, and one with one army rolls one die.

Already, they're wrong...as an attacker, you have to have more armies than dice, i.e. you have to have 4 armies to roll 3 dice. The article already lost my confidence, every true Risk player knows this.

--trb

Diplomacy

[ggambett]

Doesn't anyone play Diplomacy? It's much more interesting. No dice involved, no randomness at all.

Re:Interesting

[Saige]

While IANAMathmatician, I would believe that the defender rolling only 1 die would actually be detrimental to their defense as opposed to rolling two.

By only rolling one die, whatever the result is on that die, it is guaranteed to be matched against the highest roll on the attacker's dice - and if they're rolling three dice to your one die, then that essentially gives them three chances to beat your roll. For example, if you roll a 5, then they have to get a 6 on one die to beat you - the odds of that are 91/216, or 42%

By rolling two defense dice, you decrease their chances of beating you, since they now have to win two matchups with the same three dice - they don't get three whole dice to beat each single die of yours. If you were to roll 2 fives, for example, they still have the 42% chance of winning one die roll, but what about the second? With your second five, they only have two chances to beat it with a six. The odds of that? 11/36, or 31% - a 11% improvement in the odds for you.

(For comparison, if you had a third defense die, the chances of a third five being beaten are only 16%, much better odds than the first and the second)

If you roll only one die at a time, the attacker gets the benefits - they get to focus more resources per defender, without any worries of greater loss.

Risk Probability Calculator

[puusism]

I made a small web application to calculate battle odds for the board game Risk, because there were questions in our game group whether to attack or defend in certain situations. I thought I would share the address, if anyone is interested to see how various battle situations could turn up. The calculator is in the following web address:

http://db.cs.helsinki.fi/t/ipuustin/webrisk/webris k.jsp

Use of the program should be pretty straightforward: user chooses the number of attackers and defenders, checks the rules version and presses the button. The result diagram shows horizontally all possible end-states (the remaining forces in the winner's army) and vertically their probabilities.

The algorithm is exact, meaning that the result is not an approximation and thus does not vary in several battles with the same parameters. The program works in time O(n*m), where n is the number of attackers and m is the number of defenders. The program is made with Java.

All comments are welcome!