How likely is it for you to sit next to your brother-in-law at a Bulls game?
(Author's note: Since the original research for this question was carried out, circumstances have made it somewhat less likely that you'll sit next to anyone at a Chicago Bulls basketball game. For the purposes of this column, we will delude ourselves that it is still the era of the inevitable SRO.)
Next comes a probability based conundrum suggested by a real life event. As most of you have heard by now (over and over and over again), mrlucky invited Ed Maroney to a Bulls game recently, and upon arriving, we discovered that we were seated directly next to said colleagueís brother-in-law. Golly, we burbled, what are the odds of THAT happening? Having determined that mrlucky can indeed ask himself questions, I set out to analyze this event.
I began by framing the circumstances as exactly as possible: What are the odds of you finding yourself seated next to your brother-in-law at any one Bullís home game in any one season?
After tossing this issue to the zanies in the Usenet Newsgroup Alt.Fan.Cecil-Adams, I got exactly no help at all, except for one chump who said that probability wasnít involved. He suggested that the less you like your brother-in-law, the more likely that heíll show up next to you. Ahhh.
Of course, there are two separate, independent random events here; (A) going to the same Bulls game and (B) sitting next to each other.
(A) is pretty simple to figure out. It ends up being 1 in 41, or about a 2.4% probability that you two will be at the same game, assuming you and b-i-l attend one game per year. (If your brother-in-law is Bob Carr or Yamus, of course, you will inevitably be at the same game.)
(B) is also pretty straightforward. The probability that you will sit in a seat is 1 in 1 (forget standing room). Call your seat seat n. As there are 21,500 seats in the United Center, the probability that b-i-lís seat will be seat n+1 or n-1 is 2 in 21,499, or 1 in 10,749.5. (Iím not including Standing Room, which brings Bulls crowds up over 23,000.)
Thus, the probability that you will sit next to your brother-in-law at a Bulls home game in any one season is 1 in 440,750. As a comparison, the odds of drawing a royal flush are 1 in 650,000; a straight flush, only 1 in 65,000.
The problem here is the situation I have analyzed is dry, simplistic and unreal. In fact, it would be just as cool to have your second cousin sitting in front of you, or your great uncle just behind you and to the left. Letís try and figure out some more realistic odds.
I will arbitrarily postulate that the typical family has about five members who would go to a Bulls home game in any one season. Applying some basic proba-math, we discover that the odds of two people in a group of five going to the same Bulls home game are 22 %, or nearly 1 in 4. (P = 1- (41*40*...(41-5+1))/415).
Now that we have included any contiguous seat, there are 8 in 21,499, or 1 in 2687.4 chances that you will be within hitting distance of each other.
In this situation, the odds of this freakiní miracle occuring are 1 in 12008.
This is considerably more likely than dry statistical example # 1, but in a game of poker youíll draw 4 of a kind 1 in 4000 times, so you may yet evade the old b-i-l.
We still havenít filtered out all the unrealities of our random experiment, i.e., no cheap seats included, desirability of certain games, inclusion of playoff games and Cecil knows what else, but I figger itís gonna stay pretty unlikely that Ed will participate in another coincidental family reunion any time soon. Or draw a full house, for that matter, and thatís only 700 to 1.
Hey, the next time you buy a Lotto ticket, think about two things. Number one, youíre 80 times more likely to sit next to a specific individual at a Bulls game than win the lottery. Number two, everyone at Swell has met a Lotto winner (Iíll reserve her name out of common courtesy). In other words, math, shmath, it might as well be you!