Correcting for the first-player advantage in Risk

http://www.stat.columbia.edu/~cook/movabletype/archives/2009/08/correcting_for.html

by cwan • 17 years ago

15 22 17 years ago

stat.columbia.edu

petemack• 17 years ago

This was actually addressed in the newer version of the game, Risk 2008 Revised edition, states in the rules:

Player 3 receives an additional card Player 4 receives an additional card Player 5 receives two additional cards

In the games we play, this usually neutralizes the first players advantage.

Novash3• 17 years ago

Wonder if they will do anything similar with the War game. The last players certainly also suffer an unfair advantage there.

msluyter2• 17 years ago

Most modern eurogames make this sort of correction. Caylus, for example, gives the the second and subsequent players extra money.

pavel_lishin• 17 years ago

There's money in Risk?

msluyter2• 17 years ago

No, I just meant to point out that a lot of modern games make up for the first player advantage (in cases where there is one) in various ways.

fizx• 17 years ago

What if you auctioned first move? I'll take first move, but give each other player a 2 army advantage. Then, proceed with a 2nd move auction.

mshafrir• 17 years ago

Good idea - this is often done in the game Puerto Rico.

fugue88• 17 years ago

We adjusted by changing the order to count, attack, place (cf attack, count, place, as I remember). If the 1st player goes on a major offensive their first turn, they end up spreading themselves thin, so this balanced things out a lot.

gthank• 17 years ago

Not having played Risk in ages, I have a few questions:

* Is there a statistically significant first-mover advantage?

* How big is it?

* What is its mechanism?

icefox2• 17 years ago

You might be able to find the answers this over on board game geek http://www.boardgamegeek.com/boardgame/181

hristov• 17 years ago

Well you should check out the stats of the national risk league or any of the multiple professional risk league sin Europe.

mcantor2• 17 years ago

Remember when you were a new coder, and sometimes you'd see an off-by-one error that for the life of you, you couldn't track down? And after a long enough time searching, you just gave up and added or subtracted one from the variable? I don't mean to badmouth these suggestions, because I have none that are better, but they all feel like that to me. Voo-doo fixes.

Just a thought.

edw5192• 17 years ago

And after a long enough time searching, you just gave up and added or subtracted one from the variable?

Don't pull that trick in my shop. Isolate your bug and fix it. Whatever is causing it is probably causing other bugs that will affect other people, including the poor sucker who has to clean up your mess.

Novash3• 17 years ago

He refers to the known floating point rounding error. You should not expect a 'new coder', as he put it, to trully understand floating point rounding errors because to understand it, you need to already be a coder with some experience.

mcantor2• 17 years ago

Sorry--I should have been more specific. When I said "new coder," I really meant "new coder." I started programming when I was 9- or 10 years old, and thus worked without the onus of keeping my code clean for its future maintainers. As a victim of my own folly, however, I learned to avoid voodoo fixes by the time I was 14. :-)

gaius• 17 years ago

That is remarkably content-free. Where's the maths?

icefox2• 17 years ago

Or really any real content. The author didn't even try out his own example to see if it would work. And honestly how horrible the old Risk rules is really old. There are both new rules and much more enjoyable games these days.

iterationx• 17 years ago

Novice players will overextend themselves and in this case the first player might have an advantage, otherwise I don't see it.

jonshea• 17 years ago

I played risk online at warfish.net for a while until I felt like I had maxed out the strategy to within the noise level. It isn’t obvious to me that there is a first mover advantage. In our games the initial territories were randomly distributed, and I always felt that whoever got the “most closely clustered” territories had a tremendous advantage.

The best advice I’ve ever heard for competitive Risk is “play the other players, not the continents”. You want to try to create situations such that you are the least desirable player to attack. In general, this means turtling. Occupy a few territories that are close to each other with about 5 armies on each, and put as many armies as you can on one territory that is adjacent to enemies. Don’t take a whole continent because people will try to crack it so you don’t get the bonus armies. Try to get your armies off of continents that it looks like people will fight for. Try to get a card every turn, and hold them as long as you can.

You stop turtling when and only when you can eliminate a player in one move and get a bunch of cards from them. You will usually do this by trading in a set of cards, putting all of the armies on your big territory, and marching it all over the place. You will almost always succeed if you have about 0.75n + 1.0t armies to push with, where n is the number of armies you will need to kill, and t is the number of new territories you will need to occupy.

(Corollary, if you’re weak then try to use all your cards so that you’re not a valuable target.)

Eliminating a player who has 5 cards almost assures that you will win the game.

After a player or two has been eliminated the game will transition to one where the players try to hold continents to collect bonus armies. If the players are fairly competent then the winner will mostly be decided by how lucky people are with collecting cards. The yield from trading in a set of cards starts to dwarf the armies collected from holding territories. Almost as important, the new armies can be place freely.

I have never seen Asia successfully held for even a single turn.

(Regarding the first alleged first-mover advantage: obviously it can’t be disadvantageous to move first. If it were, then the first player would take no action so as to avoid the disadvantage. By induction, if it was disadvantageous to go first then the game would never advance past the initial state.)

lionhearted• 17 years ago

Good comment. I liked to consolidate my troops in an area that gave me access to lots of places - like Western Africa or the Middle East. Then, you strike at wherever people leave alone. Getting that flexibility instead of getting locked into plans is key.

Correcting for the first-player advantage in Risk

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