The Ivory Tower

Firstly, this is a long technical blog post about the board game "The Game of Life," so if that sounds lame, feel free to stop reading. Second, I'm basing this on the 1992ish era version, not the most recent 2005 update with new salary rules, career abilities, and house sales.

So the other day I was thinking about the game of LIFE and how I always pick "college" because I assume you'd be a complete dumb ass to choose "career." You need to go to college to be the doctor who's the sweetest job on the board right? How likely can you get big bucks as an artist? They've got less spots than other jobs, don't they? Which is better....career or college? I decided to find out.

First of all I had to choose my criteria for "better." Obviously the one that led to the most money. In this game the most money is made in A) your salary, determined by your salary card B) your income, money you get from other players when they land on your career space, and C) LIFE tiles. Especially in this version where they are typically around 100 to 500 thousand dollars. I decided to tackle these in order.

Counting the spaces on the board I found 18 pay days for all players, and a 19th for "career" players. That was easy enough, and I know that the average salary is $60k so career players get $1.14 million dollars in salary every game of life.

College salaries proved more complicated, as each college grad gets three salary cards and then chooses their favorite. Okay, high-school probability class...nine choices of salaries means 48 possible 3-card combinations (3 nCr 9 in my TI-83). And surely players would choose the highest salary in each combination..but how many involved each salary. Well....if there was only 8 salary cards, taking out the 100k holy grail, we get 61 possible sets of 3. Logic tells us that 28 combinations out of the 84 contain the highest salary of a tenth of a million dollars. Using this method we get 26 for 90k and not 100k, 15 for 80k, 10 for 70k, 6 for 60k, 3 for 50k, and 1 for 40k. It's impossible to be stuck with 30k or 20k because you get three options no matter what.

Now, what to do with this data? Well to get the average I multiplied each salary with its probability of being chosen and added the sums. This gives the college player an average salary of $90,357. Multiplied by 18 paydays gets a lifetime wage of over 1.6 million.

This already placed college players at a half-million ahead of their career counterparts. However, I hadn't answered the question of which career card gave the player the best edge. I kept on crunching numbers, now trying to find the best careers.

Income from careers occurs when an opponent lands on one of your career spaces, then they must pay the given amount. To determine the average income I had to take the sum of cash these income spaces had per career, divide by the amount of spaces to determine average pay-out per career space, and finally multiply that by the likelihood of someone landing on one of your spaces. Cash-per-career space was simple arithmetic, but the likelihood of landing on a given space required some fudged statistics. On the game board there are 108 spaces all players must land on, plus or minus four depending on branching paths. I slopped on 2 spaces to average it out, getting 110 spaces. Average spin is 5.5 spaces...meaning a typical player lands on 20 spots on the 110 space board, or roughly 20% of the spaces. This gives any space a 1/5 shot at being hit, so I multiplied the per-space average by 20% times the number of spaces in that career. Finally, I multiplied all incomes by three, based a four-player game. This gives me the following ranking of careers by income:

Artist with $112,500, Travel Agent and Athlete with $96,000, Superstar with $80,500, Teacher with $84,000, Doctor with $77,100, Accountant with $75,000, Salesperson with $43,500, and finally Police Officer with $39,000.

Calculating for the teacher was different, because they are all dependant on other players' actions. There are two night school spaces, which are each $20,000. I decided that there would be a 50/50 chance of someone wanting to use them, so I factored them in at half their value. Then the other spaces were paid on a per-child basis (college, summer school, day care). For these I needed to determine the average amount of children per player.

There are 8 spaces on the board awarding children to players, on average 1.2 children apiece. Given that out of any 8 spaces, a player is likely to land on 1.6 of them...which gets about 2 children per player. So, all the teacher spaces dependent on child count were assumed to be at the 2-child value.

Another special case was the police officer who only gets on space, but gets five grand for every time someone spins a "10" Given the 20 turns each game has, assuming 4 players, provides 60 spins a game by opponents. So in a typical game the police officer can expect for about $30,000 from "speeding." This is what puts them at the bottom of the economic bracket.

Finally the accountant only collects when taxes are paid, so these were calculated in a similar manner as the teacher, the odds of landing on the space multiplied by the average taxes played by a player.

Surprisingly the college degree required jobs (teacher, doctor, and accountant) are in the lower half of the salaries. But, when you take the odds of being able to choose the best jobs, college ends up on top again, earning an average income of about $376,821 which outdoes the average of a career player, just short of $80,000.

This puts the total gap about 800 grand now. This puts them clearly ahead, regardless of the $50,000 debt. Plus college players get four more chances at LIFE tiles, which are extremely valuable in this version.

So, hypothesis proven! Maybe next time I'll put this kinda effort into something less obvious.