“Excuse me, but don’t I know you?”

“Funny seeing you here!”

“What are the chances?”

Chance encounters, or seeing you someone you know out of context, can take anyone by surprise. But if you’re commuting from New York City to Washington, D.C. on the Amtrak Acela Express – as 14,000 businesspeople do every day – it turns out that a chance encounter is actually more expected than you think.

But exactly how likely? We did the math: It’s 12.29 percent likely, which is almost equivalent to one in eight people.

As digital networking through sites like LinkedIn continues to be a valuable part of business relations and success, it’s good to remember the thrill and value of a quality face-to-face run-in.

So the next time you’re on the Acela, keep your eyes peeled – a new business opportunity, or at least an old friend, may be just a few seats away.

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The Fine Print (aka the math that helped us arrive at this conclusion):

  • Assumptions:
    • You live/work in or near NYC and take the Amtrak Acela Express when traveling on business to Washington, DC.
    • Amtrak Acela is 100 percent business travelers (consisting of only business and first class cars).
  • People have an average of 930 LinkedIn connections, but according to Dunbar’s number you can only maintain 150 relationships.
  • If you regularly travel to DC for business, it’s reasonable that a portion we’ll assume 20 percent of your relationships are related to DC/work and those people also take the Acela. (20 percent of 150 equals 30 people).
  • The Acela train that travels the Northeast Corridor has five passenger cars and one café car. Each passenger car holds 62 people.
  • The earliest NYC Acela trains leave at 6 a.m. daily (getting you to DC in plenty of time for a full work day) and can hold up to 310 passengers – or 309 total (saving one seat for yourself!).
  • There were 3.5M riders on Acela in FY2014. There are 52 weeks in a year and 11 widely recognized federal holidays. That leaves 249 days a year (260 minus 11) for commuting and an average of (3.5M / 249) = 14,000 Acela riders on a weekday.
  • The probability that nobody you know is on the train is (13,970/14,000 * 13,969/13,999 * … * 13,910/13,940) = 87.71 percent
  • The probability that at least one person you know is on the train is 1 – 87.71% = 12.29 percent. Voila!