The Tao of Gaming

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.

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.