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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!"
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
The author is not counting the 'army that has to stay behind' as an attacking army - So, to roll three dice you need 4 armies, but only three of them are 'attacking'
Auction my friend auction.
Yes, the games is tipped to the Allies.
You simply auction off the Axis, whoever bids the lowest get the Axis the that much extra money.
Also, Russia can't attack first turn.
Game is much more even when this happens.
Doesn't anyone play Diplomacy? It's much more interesting. No dice involved, no randomness at all.
My website
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.
"You know your god is man-made when he hates all the same people you do."
If you don't have a major continent to yourself, the isolationist strategy will never win you the game. Europe and Asia have too many open borders to hold defensively without expanding. By the time you succeed at holding either one in a six-player game, you are probably already strong enough that you can expect to win the game. Australia has only one border, but rewards you with so few armies that it's just a matter of time before somebody (whoever eventually conquers asia) decided to wipe you out. South America is worse. No more armies that Australia, but with two border states to defend. Africa has three border states to guard, and whoever is playing in South America has to go through you to get to most of the rest of the world.
North America is the sweetest plum. Put up a massive force on the panama canal, and then leave South America alone. They will decide fighting you is not worth it and go attack Africa. Then split the rest of your force between holding your two northern borders, and collect 5 bonus armies per turn while picking off easy, strategically unimportant countries in Europe and Asia to get your cards. Once you are strong enough to devour South America with lots of armies left over, do so, and you will then be collecting 7 bonus armies, again with only three borders to hold. The game is pretty much over at that point. Just about the only way for the other 5 players to beat that strategy is if somebody "takes one for the team" and badly weakens themselves to make sure that the person taking North America does not succeed at holding it. Whoever steps up to do so will not win, either, so there is little incentive to do so, unless you really hate that guy. Otherwise, somebody holding Europe early in the game (which requires real ineptitude on the part of the other players) can rival North American power. I have seen the game won many times by a "Europe and Africa" empire... but most of the time, victory eventually goes to North America.
This is one of the reasons why my circle of friends eventually stopped playing Risk and moved on to other games, like Diplomacy.
Information wants to be anthropomorphized.
Your analysis is correct if the defender rolls first, but that never happens in Risk. The throws are either simultanious, or attacker first, depending on which set of rules you got in your set. I the attacker rols first it can be better for the defender to only roll 1 die.
Consider what happens if the attacker rolls first and gets 2 or 3 sixes. The defender then only has a 1 in 6 chance of matching the 2nd 6 and therfore successfully defending with his second die.
He is better off not throwing it this time, since the attacker is likely to throw less than 2 sixes next time, which would give him better odds.
A pizza of radius z and thickness a has a volume of pi z z a
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:
s k.jsp
http://db.cs.helsinki.fi/t/ipuustin/webrisk/webri
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!
- Ismo