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

Interesting

[Taral]

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?

Enhancing RISK

[AtariAmarok]

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).

Re:Enhancing RISK

[dschuetz]

We always player nuclear RISK

The only game of Risk I've ever won (I'm lousy at these sorts of games) was a Nuclear variety. Rolling three sixes would slag a country such that nobody could go in, ever again. Rolling three threes killed everyone, and you had to wait six turns before you could go back in. Rolling three ones was a neutron bomb -- kills *all* of your opponent's armies in the war zone, but none of yours, and you can move right in.

We'd slagged right down through Eurasia, as well as Alaska, so we had a full-out east-vs-west battle in the one remaining non-slagged country: The middle east. We threw some "normal" nukes, built up and moved armies on both sides for six turns, threw another normal nuke, built up some more, etc., etc., until someone (me, luckily) threw a neutron bomb, and marched through the rest of the countries with little effort (since, naturally, all my opponent's armies were clustered conveniently nearby).

The craziest game of Risk I ever watched was a three-board, multi-day marathon session. I'm not sure any of the players went to class for at least three days.

Confimation

[Henry V .009]

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.

No one calculated this?

[epine]

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.

RISK 2210 AD

[trevorrowe]

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.

Risk is Terrible

[Apreche]

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.

So true

[Schezar]

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.

Re:So true

[Omestes]

Ah, but we have Monopoly, the greatest board game ever (barring Chess, Go, and Pente of course). And if anybody cracks that Monopoly is based on randomness, I dare you to play me a game, I'm undefeated.

I'll agree that the "family" board games are all random chance, but those are for playing with your family, not being a ruthless cuthroat. Who expects Candyland to have strategy?

Also RISK isn't just all random chance, strategy does play a sizable role. I used to slaughter my ex-girlfreind (when not letting her win), (slaughter = more than 50%).

Also alot of time that people play boardgames they want random social fun, and not blatant competition. You don't want to play a game with a 500+ page rule book, that required an IQ of 150 to win or even comprehend. Sometimes even Scrable is too taxing, and Trivial Pursuit takes to long, so I reach for Monopoly, or RISK, or Stratego.