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Saturday, August 31, 2013

The Statistics of Monopoly with Respect to Cornish Game Hen Provisioning: Part 2 "Probability is a bitch"

In part one we figured out the average likelihood of a guest ending up on any particular square. So what's the problem with that?

The problem can be summed up in one, easy to remember, phrase: "YOLO".

YOLO

So we did 100,000 simulations, that seems like it should be enough right? Maybe we should do one million to be more accurate? Nope, that's not the problem. The problem is that we're not throwing one million dinner parties. Or even 100,000. We're only throwing one dinner party. And frankly, anything could happen.

Just because the expected value over the long run says that we'll need 5.44x the cornish game hens, this doesn't mean that the actually dinner party won't have 30 guests just haphazardly roll 12's on their first roll, throwing our expectations into turmoil.

So what is a Culinary Experience creator to do?

It turns out that Monte Carlo works really well here too. Since we recorded all 100,000 simulations, we can ask the question "How many game hens do I need to buy in order to have enough in 95% of simulations." Obviously we can change the percentage we use here too. The average, is actually just saying, "How many game hens do I need to buy in order to have enough in 50% of simulations." Which is pretty much like saying "How can I run out of game hens HALF OF THE TIME!"

Gimme Code:

Get an array of the pretty names for the squares.


SQUARES is something like:
What we really want is to put all the Baltic Avenues together. Put all the B&O Railroads together. You know, kinda 'zip' each of these arrays together.


Now zipped is:


Then we process the results:


And:

These results have the average in column one. The 95th percentile in column two and the max observed in column three. So what's the result? Well, say we run 4 moves. The average on chance was 5.44x. But if we want to provision enough food with 95% certainty that there will be enough, we're going to need 9x. And out of 100,000 simulations, one simulation had 15x the number of cornish game hens on Chance. That sure doesn't make it easy to plan the menu.


PS

But what if we want to play by the monopoly rules? Well, then we just change our move function and run things again. This time you can see the super high prevalence of Jail and a bit of a secondary bump ~7 squares after Jail.




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