Oct 7, 2015

How likely is it that Chase the Ace will last until the final card?

It was an absolute pleasure to work the weekend of the final Chase the Ace in Inverness, Cape Breton. I stayed at CBC for a full extra hour just to watch the excitement. It was fabulous entertainment. As we watched, we talked about the odd chance that turned a small town fundraiser into a $1.7-million jackpot. As our friend and colleague Blair Sanderson put it on Twitter:
How unlikely was the fundraiser at Inverness? How improbable was it that it could grow so big, and last so long?

I went home determined to think this through. What are the chances that the game of Chase the Ace would go almost all the way to the end? Here's what I came up with (with a big thank you to the boy, a mathematician at MSVU, and two statisticians from SMU for verifying this is correct).

I thought about the probability of drawing the ace from a deck of 52 cards. The probability is 1 in 52. The same probability applies to every other card in the deck. So I imagined there are 52 simultaneous games of Chase the Ace running. In one of those games the ace will be drawn first, and in one of those games it will be drawn last. In all the other games the ace will be drawn somewhere in the middle.

Or, you could think about it this way.

So it's a 1 in 52 chance - or, if you want to express it another way, a 1.9 per cent chance - that the ace will be the final card drawn.

That's not very high, but depending on how you look at it, it's not very low either.

So knowing this, I wondered: could the magic at Inverness happen again? The answer is a definite yes. And if you look at it statistically, it's not only possible, but it's almost becoming likely.

Consider this: the Chase the Ace phenomenon is spreading throughout the Maritimes, fuelled partly by the success story in Inverness. The phenomenon only arrived here two years ago. CBC Radio reported on Oct. 6 that 25 games of Chase the Ace have been registered on P.E.I. in recent days.

25 games! Roughly halfway to 52, in just a few days - and there's no reason to think they'll stop there. If the fundraisers prove successful, people will try to replicate that success again and again. And as the frequency of games goes up, so will the number of games that progress all the way to 52 draws, or close to it.

What happened in Inverness will happen again - you can bet on it.

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