2000 Games of Pandemic

[ralphmelton]

I have been an enthusiastic fan of the board game Pandemic since I first played it in 2008. I like it because it involves cooperation and careful planning, which makes it a good way to talk to people through a game. For several years, I’ve been playing a lunchtime game once a week with friends. In 2013, Z-Man Games came out with a version of

Comments

[eub]

I am impressed with your enterprise, sir. And with the designers' intuition and playtesting. If I were judging your science fair project I would add credit for your digging into "games won" versus "hard games" (though I don't know if it fits the Official Scientific Method Rubric

[eub]

Oh hm, for the boredom problem, you could generate matched pairs. Pick three random roles xyz, play two games, xyzA and xyzB. That should control the 'other' roles between your A and B conditions, but give more variety. The games in the pair don't have to be played back-to-back, either.

[ralphmelton]

I can do some estimating. Let me take one example: In 4P5E, the overall success ratio is 84.1% +/- 3.0% after 578 games and the worst-performing Role is the Troubleshooter at 77.1% +/- 6.2% after 179 games. Let's assume those percentages don't change as I keep playing. How many games would it take to have a statistically significant difference at p < .05? (I recognize this is not exactly the question you asked

[eub]

sqrt(N) is the expected "distance from home" of an N-step +/-1 random walk, so that sounds like the right asymptotic...

Off on a side track, I'm puzzled about whether the whole "noise added by the other three slots" thing I was on about is a real thing. The argument against is, isn't "given Role A, do we win?" *some* Bernoulli process? So what if it's done by random choice of other roles and then depending on those -- it still boils down to success some P% of the time.

Let's see, concretely, it would be whether the confidence interval on e.g. the success is what you'd get for a p=0.841 binomial, or whether it's actually a wider CI? If success is a plain old binomial distribution and we've got 486 / 578 = 84.1%, I get the 95% interval is +/- 3.0%. Is that calculation the same way you got your +/- 3.0% too?

I think the "argument against" is right. But I'd have to expand an example to convince myself. And I still don't get what's wrong with the intuition for there being a real effect because of summing non-IID Bernoullis.