This is the story of my lockdown during a global pandemic. [Cue post-apocalypse 🎼]
Amid a global pandemic, schools and workplaces shut down, and families had to huddle together at home. There was no escape. Everyone was getting on each others' nerves. Running out of options, we played Monopoly Junior, which my daughter recently learned how to play. As we went over several games, we found the beginner winning every game. Was it beginner's luck? I seethed with rage. Intuitively, I knew the odds were against me. I wasn't terrible at Monopoly. I had to prove it with science.
How would I prove it with science? This sounds ridiculous at first, but you'd do it by playing 5 million Monopoly Junior games. Yes, once you play enough games, suddenly your anecdotal observations become INSIGHT. (Senior lawyers might also call it experience, but I am pretty sure that they never experienced 5 million cases.)
This is the story of how I tried different ways to play 5 million Monopoly JR games.
What is Monopoly Junior?
Most people know what the board game called Monopoly is. You start with a bunch of money, and the goal is to bankrupt everyone else. To bankrupt everyone else, you go round the board and purchase properties, build hotels and take everyone else's money through rent-seeking behaviour (the literal kind). It's a game for eight and up. Mainly because you have to count with hundreds and thousands, and you would need the stamina to last an entire night to crush your opposition.
If you are, like my daughter, five years old, Monopoly JR is available. Many complicated features in Monopoly (for example, counting past 30, auctions and building houses and hotels) are removed for young players to join the game. You also get a smaller board and less money. Unless you receive the right chance card, you don't have a choice once you roll the dice. You buy, or you pay rent on the space you land on.
As it's a pretty deterministic game, it's not fun for adults. On the other hand, the game spares you the ignominy of mano-a-mano battles with your kids by ending the game once anyone becomes bankrupt. Count the cash, and the winner is the richest. It ends much quicker.
Determining the Approach, Realising the Scale
There is a pretty straightforward way to write this program. Write the rules of the game in code and then play it five million times. No sweat!
However, if you wanted to prove my hypothesis that players who go first are more likely to win, you would need to do more:
- We need data. At the minimum, you would want to know who won in the end. This way, you can find out the odds you'd win if you were the one who goes first (like my daughter) or the last player (like me).
- As I explored the data more, interesting questions began to pop up. For example, given any position in the game, what are the odds of winning? What kind of events cause the chances of winning to be altered significantly?
- The data needs to be stored in a manner that allows me to process and analyse efficiently. CSV?
- It'd be nice if the program would finish as quickly as possible. I'm excited to do some analysis, and waiting for days can be burdensome and expensive! (I'm running this on a DigitalOcean Droplet.)
The last point becomes very troublesome once you realise the scale of the project. Here's an illustration: you can run many games (20,000 is a large enough sample, maybe) to get the odds of a player winning a game. Imagine you decide to do this after every turn for each game. If the average game had, say, 100 turns (a random but plausible number), you'd be playing 20,000 X 100 = 2 million additional games already! Oh, let's say you also want to play three-player and four-player games too...
It looks like I have got my work cut out for me!
Route One: Always the best way?
I decided to go for the most obvious way to program the game. In hindsight, what seemed obvious isn't obvious at all. Having started programming using object-orientated languages (like Java), I decided to create classes for all my data.