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!"
So for equal battles, break-even is at 5 vs. 5, whereas one extra army always gets you 50%.
But there's no link to the actual paper. Anyone?
Taral
WARN_(accel)("msg null; should hang here to be win compatible\n");
-- WINE source code
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
If you have multiple boards, you can add to the fun by trying "multiple world" Risk. Either place them side by side (so the Alaska connects to the Kamchata of the other board, and vice versa), or play such that the boards are "stacked" (one Egypt can attack another).
Don't blame Durga. I voted for Centauri.
I thought the WPOR told Professor Falken that "the only way to win was not to play". Now we are learning that the way to win is to attack, attack, attack.
What if the defender has nuclear weapons?
http://www.geocities.com/justaguy93/Nuke.html
Bob.
I can confirm this. I recall one game with a friend years ago when we were both young teenagers. Early in the game we found that we were rather balanced as far as the map went. Since my friend had a triple set of armies, we simply built up our armies until we had used up all of the spare pieces. Both sides were perfectly balanced, but I attacked first.
It took a lot of dice rolling, but I wiped out his entire force in one turn suffering only 1/3 losses or thereabouts.
I was interested, so I did a calculation of the odds. Yeah, they're stacked for the attacker.
"Already, they're wrong...as an attacker, you have to have more armies than dice,"
Indeed! Chalk this one up with the chess article that refers in passing to pawns moving in an "L" pattern, or the video game history article that talks about Pac-Man breaking bigger asteroids into little asteroids.
Next, Science News will publish an article about "Improving the Odds in Clue" that will tell us about good ol Colonel Ketchup in the mud room with the mastadon-leg as the weapon.
Don't blame Durga. I voted for Centauri.
It was in 1988, shortly after an event involving a certain famous hockey player switching teams.
The guy who had Western US and Alberta moved one army down from Alberta into Western US as a troop transfer.
Someone commented "There goes Wayne Gretsky".
Don't blame Durga. I voted for Centauri.
Guess who must have played a lot of Risk and those frat parties.
So far, I've been really enjoying the Tolkien Risk that came out last year, but I've not really given it enough play yet. The new board is really interesting, as you can't do the same old strategies, and the heroes and fortresses make strategy pretty different too.
Best of all is the Fellowship movement, which keeps game length down and means that even in a four player game you're likely to all still be alive at the end.
Has anyone played this enough to get some more detailed opinions yet? Strategy-wise Rohan seems to be the new Australasia for us, for instance.
"I Know You Are But What Am I?"
The analysis of Risk is a trivial problem. I once wrote a small program to do exactly the same analysis for Axis und Alies, a vastly superior game IMHO. Sometimes I played A&A for 24 hours straight and then couldn't sleep because of a pivotal scenario developing, usually a land grab in Indonesia by one side or another before a fateful invasion of Tokyo by the Americans.
Then I would get up and it would take another 24 hour day, several pots of coffee, and two trips to the beer store to play it out.
Axis and Alies has more degrees of freedom than Risk. The person losing units has the choice about which units to sacrifice. Not all units can attack other units. Submarines can't attack airplanes. (They laughed at me the first time I played for thinking I could do this, no one told me I couldn't, they let me buy four subs to defend against a fighter plane outpost. Later I was reading about submarine technology in WWII and I discovered that submarines often carried surface to air mortar shells--not terribly effective though).
Because of the problem of the exact order in which each player chooses to remove their own casualties, the complete tree explodes exponentially. However, in practice, the order of removal is automatic 90% of the time, and the cases where the removal order is debated tends to come at the end of a close battle where you are more concerned about what is left behind when the roles reverse than who actually wins.
In my program, the attack and the defense both submit their roster in a predetermined removal order. You could try different removal orders, but you couldn't make the removal contingent on battle outcomes.
My program calculated the exact probability of every terminal outcome. You don't even need Markov models, that's just a view of what the final math represents. The actual algorithm is like a fertilizer spreader that tosses little chunks of probability from one bucket to another until all the probability is sorted into buckets representating terminal outcomes.
It worked out to perhaps three pages of code. Memory requirements go up roughly on the cube of the number of armies involved IIRC.
I learned an incredible amount about the strategy of A&A from this program. Moral of the story: you can never have too many grunts. The strategic problem with grunts is they move so slowly. I learned to invest in waves of grunts (esp. for Germany) at the beginning of the game, get the waves moving outward, and once the fronts were established, replenish a fixed supply of tanks as these were consumed in battle, and grunts grunts grunts with the leftovers.
For my money, A&A is the best game I've ever played at pressuring the strategists to set up confrontations with the potential to break symmetry and channeling the game down unpredictable paths, forcing everyone to adapt their goals. Except for the Eastern front, where the game was a little too close to being historically accurate. For a five person game, being stuck with Russia was a chore in the early going.
No one has calculated Risk in 50 years? Phffff.
More likely, no one interested in that kind of analysis considers Risk much worth the bother.
The Markov analysis of Monopoly I saw a few years ago in SciAm was far more interesting to me. Verdict: Never underestimate "go directly to jail" as a form of rent control.
I had to laugh when I saw the comment that "go directly to Australia" was a fundamental Risk strategy.
" and for my salvo in this war, though I can not comment of the syntax of the referring article, paws in chess can move in a "L" pattern"
You got me there! Please see this link for more "paws in chess". The move (more of an up-one over-one than a "L") is called "en passant" by the way.
I should have referred to castling bishops instead.
Don't blame Durga. I voted for Centauri.
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'
How about if the number of attacks per turn is theoretically unlimited, but for each additional attack you make per turn, you must remove 1 army from the attacking country?
For instance, if I were to attack three countries in a particular turn, the first attack would be carried out as normal; for the second attack, I'd have to remove one army from the attacking country before the attack can begin; and for the third attack, I'd have to remove two armies from the attacker.
This rule, or something like it, would allow the number of attacks per turn to be left to the player's discretion, but would also discourage people from making "too many" attacks per turn.
I can't believe Risk has been around for about 50 years and I've never heard of it. The study that they conducted seems like it would make sense though.
I liked risk, but it was to much of the same. Castle risk tried to fix this, but IMHO Risk 2210 AD takes the cake.
I don't know how many of you have played this game, its a refreshing approach to risk.
New Features include:
-New pieces, mech-like units.
-5 new units (generals) that add attacking and defense bonuses (namely they roll 8-sided)
-No more changing in cards for the 'next big bonus'. Extra units awarded for how many territories you control, plus complete continent bonuses. Very well balanced, the bonus scales, so it remains very fair.
-Territories are chosen round robin style at the beginning of the game, so you wont get shafted with bad luck.
-Sea colonies and moon colonies to expand into, these are vaccant at game start.
-general cards (strategy cards that enchance generals' powers).
-Random territories nuked at the beginning of the game (significantly alters the map every game, new choke points, battle strategies, etc).
-Energy is gained through combat and territories that allows you to hire generals, purchase general cards, and more.
-Turn order is bid for each round, with a 5 round limit (faster games). Energy is used for bidding, so strategies exist around the saving of energy for turn order (imaging going last one round and then first the next!)
-more, more more, and much more!
No, I don't work for Hasbro(current game owner?), but I do really like this game. There are options for playing classic risk too. I have found a few copies at WoTC, but have heard rumors that they are out of print know, don't know. Expect a 30+ price tag, there are a lot of pieces.
The game of risk is not that terrible, but it does suck in comparison to real board games. If you've ever played the likes of Puerto Rico or El Grande you will realize the lack of strategy in risk. American board games are too much based on luck. Sure, you can calculate the odds and make better decisions, but european board games have almost no luck involved in deciding the winner.
After a game of risk the winner can not safely say they are strategically superior to the losers. In a game of Puerto Rico there is no doubt who is a better person.
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American board games are generally garbage. I was always amazed my how my friends could enjoy a game like LIFE, where the outcome is 100% random, or Trouble, where the outcome is also 100% random (yea, you can make decisions, but there is always an obvious "best" decision, so unless you're a complete moron the game is random). Why even play the games, when you could just flip a coin and declare a winner?
Axis and Allies was a decent game, except that it's unbalanced. All players being of equal competance, the Allies WILL win. Period. If they don't, then the Axis made a fatal and/or stupid decision early on. It's not a game of strategy or skill, it's just a game of avoiding obvious errors until America lands in Normandy.
Puerto Rico, El Grande, Settlers of Catan, Entdecker, Tikal, Mexica, Java, Carcassone... Those are real games. Tactics and strategy, deterministic outcomes, and real competition. You're comparing brain power instead of comparing dice rolls.
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Doesn't anyone play Diplomacy? It's much more interesting. No dice involved, no randomness at all.
My website
I just did this with the chances in a 3 dice versus 2 dice, to see who would win. I then ran it like 1,000,000 times. It came something like this(I can't remember exactly except that attackers had the advantage):
Defender lose two men: 35%
Tie: 33%
Attacker loses two men: 31%
It was a simple perl script, but interesting.
... have they done any calculations on the accuracy of the Kramer Theory of Risk, namely that "the Ukraine is weak!"
You rode the short bus to school, didn't you?
I wrote a C++ program in college to calculate the odds. I am sure I am was not alone in doing this since I wrote the algorithm in about 5 minutes, and the program in about 20.
From what I can gather, from speaking with my parents, American Board games used to be social things. Social events are better where there is a level playing field, luck does this. The fun for my friends and I as far as board games go also comes mostly from the social interaction, and almost not at all from the game.
Photos.
Looks like you can buy a copy on ebay for about US$10.
-B
Ash and Hickory, straight-grained and true, make excellent bludgeons, dandy for the cudgeling of vegetarians.
Speaking of Settlers of Catan, check out the gnome version: gnocatan. Major improvements (incl GTK/GNOME 2 move) are slated for RSN, and the next release should be great.
I believe it was the WOPR.
At
http://www.daimi.au.dk/~sandmann/risk.cc
you can find C++ source that simulates battles between up 30 attackers and up to 30 defenders. Then it prints out LaTeX source code for a nice table that lists
a) the probability that the attacker wins
b) _given_ that the attacker won, how many
armies would survive
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
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'
Absolutely correct. Grab a calculator if you don't believe him. The author of this article definitely factored this in. He even linked to the RISK FAQ in the article.
The AI's that it ships with have been released under the GPL along with an AI SDK, so you can write your own if you want.
A Multiplayer Strategy Game for Mac OS X, Windows, and Linux
"the chances of winning a battle are considerably more favorable for the attacker than was originally suspected."
Somebody's obviously never used my dice before!
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tight little vagina pounded into a wet sloppy mess by The Living Incarnation of Pure Evil? You know where to find me ...
tight little vagina pounded into a wet sloppy mess by The Living Incarnation of Pure Evil? You know where to find me .....