A first for 'Jeopardy!': What is a three-way tie for first place? ~ NanoThoughts 1.0

Sunday, March 25, 2007

A first for 'Jeopardy!': What is a three-way tie for first place?

Let's disregard the fact that three way ties HAVE happened before on Jeopardy! (Think, everybody bets the farm and misses FJ, and they all go home losers.) This was simply the first three way tie of winners.

This quote caught my eye:
AP article

The show contacted a mathematician who calculated the odds of such a three-way tie happening - one in 25 million.

Hmmmm. I wonder how he came up with those odds? A frequentist maximum likelihood approach would go something like this: Observed ties for first place / Total Number of Episodes.
1 / 4000 or so? The ML odds would then be 1 in 4000.

1 in 25 million ? Then (1-1/25000000)^4000 gives 99.98% chance it won't happen after 4000 independent trials.

Jeopardy is clearly non-random and the people aren't dice thrown in the air. Ties happen a lot and it's definitely not a 1 in 25 million chance.

We could devise models of average contestant behavior, look at frequency of two way ties, etc. but that would be way beyond the scope of this blog post.


Jeremy said...

By my calculations, the chances of this happening are 1 in 4:

P1 != P2 != P3
P1 = P2 != P3
P1 != P2 = P3
P1 = P2 = P3

Jeez, I don't know where they come up with this 1 in 25 million crap.

Rog said...

What about the wrap around,
P1 = P3 != P2
Looks like the odds are 1 in 5!

Jeremy said...

See? This is why I'm not on Jeopardy. The only reason, too.