Chess Bishops vs Human Bishops: Who Travels Farther?
In the comments of a Vote Chess game I am participating in, BlargDragon posted an interesting question:
"Also, has anyone ever wondered whether more physical distance has been travelled by chess bishops or human religious bishops? Like, if you add all of all their journeys together."
I posted a quick answer based on my own intuition, but the question kept bugging me, so I thought it would be worthwhile and fun to do some more research. As it turns out, my intuition was partially wrong!
Let's break this down, shall we?
Chess Bishops
It's pretty difficult to estimate how much physical distance has been traveled by chess bishops over-the-board, but we can give it a try.
First, we need to know how many OTB games are played. I wasn't able to find any good data about how many OTB games are played in the world, but I was able to find this poll of chess.com members. The results of the poll (after 4,440 votes) show that the chess.com members play an average of 2.5 OTB games per week. A lot of people play no OTB games at all, sticking with online games. But WGM Natalia Pogonina says she plays "About 60-100 standard time control games per year." So I think the estimate of 2.5 games per week is valid.
Chess.com has 11,737,499 members (according to the home page) as of this blog post. If we extrapolate our estimate to these members, we find that:
Chess.com members play over 29 million OTB games per week.
Now that we know this, we need to find out how far the bishops in these games travel.
Tournament standard chess boards have squares with a side length of 2.25 inches. But bishops move diagonally, so every square that a bishop moves is 3.19 inches (8.1 cm).
The Slow Chess League has an archive of 5,818 games played by its members. I downloaded this archive (a large .pgn file) and, using a Python script, counted all the bishop moves in all the games (including the number of squares moved).
It turns out in this representative sample of 5,818 games played by normal chess players, there were 63,415 total bishop moves (average 10.9 bishop moves per game), and the bishops moved a total of 117,873 squares (average 20.26 squares per game).
So now we know the number of OTB games played, the average number of squares moved by bishops per game, and the distance of each square move. Doing the math, we can work out:
(11,737,499 members) * (2.5 games/week/member) * (52 weeks/year) * (20.26 squares/game) * (8.1 cm/square) / (100,000 cm/km) =
2.5 million km per year that bishops move on chess board of OTB games played by chess.com members.
Wow, that's a lot more distance than I expected when I started researching this! 2.5 million km is far enough to go around the entire world over 60 times! Those chess bishops sure get a workout, don't they?
But this is still only part of the puzzle. What about the other part?
Human Bishops
For the sake of simplicity, I will only be considering human bishops of the Catholic Church, not any other religious institutions.
According to Wikipedia, "As of 2009 there were approximately 5,100 bishops total in the Latin and Eastern churches of the Catholic Church."
This table of data from the US Bureau of Transportation Statistics shows that the average travel distance of an American in 2009 is 36.1 miles/person/day, which works out to about 21,205 km per person year.
(By the way, according to this other table from the US BTS, the total distance traveled by Americans in 2009 is 7.8 quadrillion km. At least we know that people are traveling more than chess pieces.)
If we take our population of 5,100 Catholic bishops and assume they travel an average of 21,205 km/year (which is an overestimate, since most travel is via airplane, and most bishops probably don't fly too often), we can work out:
108 million km per year that human bishops travel.
That puts our chess bishop travel distance to shame, doesn't it? Not so fast! The chess bishops have one more trick up their sleeve.
Space Bishops
Yes, that's right. Space bishops.
On 31 May 2008, US astronaut Gregory Chamitoff brought a chess set on board the International Space Station. The picture above is from this article about the games he played against Ground Control centers around the world.
The International Space Station orbits the Earth at a speed of 7.66 km per second. It travels around the entire world in 92 minutes, or about 16 times per day. Can you imagine seeing 16 sunrises and sunsets every day?
Since we know the speed that these 4 bishops in this chess set were traveling around the world, we can work out that they traveled a combined total of 524 million km while they were on board the ISS. Since they were on board for 198 days (a little over half a year), that about:
1 billion km per year traveled by the 4 space bishops on board the International Space Station.
Conclusion
Chess bishops move pretty far.
Human bishops move even farther.
Space bishops are out of this world!
...
Also, I had too much free time today.
