## Thursday, April 1, 2010

### We Have a Winner!

At long last, Mario finally gets some help.  We have a Fermi contest winner!

How many times has our lovable Italian, shall we say, left the platform?

According to Wikipedia, over 210 million Mario games have been sold, but this doesn’t include the number games that have been downloaded, purchased at yard sales, or resold on E-bay.  To account for these extra players, I’ll assume 400 million people have owned Mario games.  One usually gets bored with a game after a few months at which point the amount of game play decreases.  If you average an hour per day for the first few months, then you’ll have about 100 total hours of game play in this time.  Occasionally, nostalgia kicks in and you start playing again.  I’ll assume 100 hours of nostalgia play giving a total of 200 hours per player.   Some players are so good they never die, but most Mario players, or rather their Mario avatars, die fairly regularly especially when starting out.  A reasonable estimate is one Mario death per minute.  I say “reasonable” because even terrible players don’t die every 6 seconds, and even fairly good players usually can’t last 10 minutes without accidentally falling into a bottomless pit.  Using these numbers, we can estimate the total number of Mario deaths:

# of deaths = (# of game owners) · (hours of play per owner) · (deaths per minute)
= (400 million game owners) · (200 hours per owner) · (0.5 deaths per minute)
= 4.8×1012 Mario deaths

Congratulations to our winner, Melgamoose!

A couple of observations about the contest
There really weren’t any bad entries.  There were 29 entries in total and the average answer was 8.35×1012 Mario deaths.  This makes me feel reasonably confident that my answer isn’t too far off since it’s within a factor of 2 of the mean.  Fermi estimates are only expected to be good to within an order-of-magnitude, so it’s interesting to look at the distribution of magnitudes:

The mean magnitude was 11.5 and the standard deviation was about 1.3, i.e. roughly an order of magnitude.  This tells me two things.  First—forgive the sucking up—I have a really smart readership.  Second, just about any of these answers could reasonably have won the contest.  So please enter our next contest which will be announced this weekend, because next time the winner could be you!

#### 2 comments:

1. This comment has been removed by the author.

2. I think your problem is wrong. In the paragraph you said someone might die once per minute and in the equation you put 0.5 deaths per minute.