The Tao of Gaming

A few days ago, I ran my experiment asking the age old question: "How many games have I played this year?"

I not only asked for a number, I asked for a 95% confidence interval range. I got the idea from a remarkable document by N.N. Taleb called "The Scandal of Prediction". Taleb, I gather, is a stockbroker/money manager (I'm not exactly sure) who became interested in questions of knowledge and self-deception. He'd find out an obscure (but knowable) factoid. Here's how he explains it:

Let us examine what I earlier called epistemic arrogance, literally, our hubris concerning the limits to our knowledge. Episteme is a Greek word that refers to knowledge; I learned from the great medical profession that giving a learned-sounding name, preferably Latin or Greek, makes people automatically take you more seriously. This naming is, furthermore, necessary for ideas of some abstraction. True, we tend to gain in knowledge, but such knowledge is under the threat of greater increases in confidence canceling its effect. Now, it is trivially easy to measure how much of this excess confidence there is in the human race. You even can do it at the dinner table of the next extended family gathering, if it is sufficiently large. Take room full of people. Randomly pick a number. It could be anything: the proportion of psychopathic stockbrokers in Western Ukraine, the sales of this book during the months with “r” in them, the average IQ score of business book editors (or business writers), the number of lovers of Catherine II of Russia, etc. Ask the members of the audience to each independently estimate a range set in such a way that they believe that they have 98% chance of being right, and less than 2% chance of being wrong. In other words, whatever they are guessing has about 2% chance to fall outside their range. For example:

“I am 98% confident that the population of Rajastan is between 15 and 23 million”.

...

Note that the subjects (your victims) are free to set the range as wide as they want: You are not trying to gauge their knowledge but what accuracy they have in their minds about such knowledge.

I just used 95% instead of 98% because I figured I wouldn't get that many respondents (I should have guessed a range!) and because it's the standard confidence interval used in scientific papers. Let's look at the results (when this experiment was performed scientifically] --

The researchers who picked it up were actually looking for something quite different, and more boring: how humans figure out probabilities in their decision making under uncertainty (something that had the learned name “calibrate). They came out befuddled. The 2% error rate turned out to be close to 45% in the population being tested! It is also quite telling that their first sample was constituted of Harvard Business School students ...

The entire article is worth reading, and I plan on buying his book "Fooled by Randomness."

Depending on how you count (including solitaire games of Battlestations, but nothing via computer), I've played 72 different titles so far this year. In fact, if you just took my games played for last year and pro-rated (by 3/4) to adjust for the fact that we are just into October, you'd be almost dead on. I knew the # of different games I played last year, but even I underestimated the number of games I've played this year (I thought the number was around 55), but I did have the correct answer inside my confidence interval.

Now I'm clearly the expert (I was there when all these games were played). But I couldn't remember all of the games. I just figured I had played less games than last year (because of the move and all). However, I've played several games that I never would have played at all because of exposure to new gaming groups. A fact that didn't cross my mind until looking at the titles.

Anyway, about half of the people missed the confidence interval. Given the number of respondents, the answer 50% is close enough to 45%...

One of Taleb's points is that, from an epistimological standpoint, something you don't know is effectively random. I'm terrible at estimating things, but good at calculating. Many of the European games we play have simple enough randomness (a single die roll, or card/tile draw) that most players with any mathematical background can explicitly model the outcome. Many other games have entire sub-systems where I've been constantly surprised by outcomes. I'm thinking, in particular, of Titan. Here you have to model a range of outcomes for a single battle (the sub-game). I'm pretty good at estimating that (I have played several hundred games of Titan, although I'm suddenly wary of being more exact than that). But now that I think about it, shocking outlier results of battles seemed to occur fairly often.

Anyway, Taleb's work is interesting to chew over, mainly from an investing point of view, but also for anyone who deals with complicated games of chance.

Lou wins some GG if he wants it. To be fair, he actually saw me play a large chunk of those games (and has known me for almost a decade).

Update: I found out about Taleb via Colby Cosh.

Update: Finished the book (hey, it was written for MBAs, so it used lots of small words). I'm not sure that the book is better than the essay, especially since that essay was free. But it was amusing.

Notes from around the web...

Via Alfred's Best of the Gaming Blogosphere I stumbled across Rick's comment that 2005 is a bad year. But not linked was a masterpiece I wish I wrote — "Analysis Paralysis: When you're not smart or decisive enough" [Note to self, add Rick to blogroll.]

And you thought my comments regarding Taj Mahal were inflammatory. But I basically agree. Most games become painful as players agonize over moves.

Greg Costikyan has started a (computer) game company. See his announcement. I don't particularly buy computer games these days, but who knows? I may spring a few bucks if something looks interesting (and they promise wargames).

I'm seeing people hype Caylus as this year's Puerto Rico. As we know, building up too much expectations leads to disappointment, but the rules do look good. According to Rio Grande, this will be released in October. Duly noted.

I've some data from my last experiment, but I could still use some more.

Update: I was just wondering which games (if any) will pop up on BSW within a few days of Essen?

Mahalanobis references a few papers on Evolutionary Game Theory. You know you care.

Ok, a question for all of you readers. Since you are reading this, you may consider yourselves an expert on me (at least, my gaming habits). Or you may not. So, here's the question:

How many different games do you think I've played this year? Give your two answers: a best guess and a 95% confidence interval. Either put them in the comments or email them to me. In order to encourage correct answers, winner gets some geekgold (if they want it).

I'd say that you are on your honor not to just scurry to BGG to look up the answer — answer now!

Reasons for this weird experiment later.

Update: Just to clarify, this year means Jan 1st 2005 through today, Sept 28th. And remember, different games (titles).

Update: Remember to include a confidence interval range.

As I noted in a previous post, a Puerto Rice league with cash prizes is forming.

I was thinking about CCG tournaments earlier today, and one reason is that I play more Shadowfist than any other game. In fact, we just finished a 13-week league. In general, CCG companies run better tournaments than board game companies, and it's easy to see why:

Collectable card game tournaments make money by selling more cards. Free tournaments encourage players to escalate their purchases. More cards bought means more money for the company. So Z-Man games provided quite lovely prize support for our proving ground league, which was free. [The prizes included original sketches for some of the card artwork, signed cards, promotional cards, etc.]

Rio Grande has no such incentive. While they'd like to introduce new players, a league is of little to no value (beyond advertising). After all, if I play 4 hours of Puerto Rico each week, some of that time may come from new games! And my chances of winning don't correspond to how much I buy.

Of course, the board game league charges an entry fee. They have to get money, of course, to pay for valuable prizes. [Presumably they aren't associated with Rio Grande]. This is no different than the United States Chess Federation, or American Contract Bridge League, which promote the game, but charge entry fees in their tournament as a large chunk of their income.

Some boardgamers look down at CCGs; for tournaments, the CCG companies look good by comparison. I don't think this applies to convention tournaments, which are usually for nothing more than prestige and bragging rights. And early picks at the prize table!

On a more pragmatic note, I wonder who the target audience this league is going after. The games will be handicapped, which just strikes me as ludicrous. People will be gaming at least two systems, I wager. [The entire affair strikes me as doomed, and my nose detects a whiff of scandal already.]

I realize that one comparison, both in general and specifically, is to the Magic Pro Tour. Too bad I don't know anything about it. No doubt the comments will inform me (and I'm thinking of a few of you in particular).

At slashdot, you can post a question for Sid Meier.

Tom Vasel asks which games to use while teaching. I have no real opinions, except to wonder if this is during class or after class? Few games would qualify "during class," I hope. There are several games that you could analyze during class (especially if you were teaching probability). [Language skills let in a large class of games, which I'm discounting].

You know, years ago the fact that there was a super chess tournament to decide the world champion (or challenger, depending on how you look at it) would have been great news. [Via Colby Cosh]

I agree that A Game of Thrones is in the Diplomacy family. But then again, I dislike Diplomacy but like AGoT, so maybe I'm just not familiar enough with the family.

Update: I see a Puerto Rico league with cash prizes is opening up.