David Spence: How many aces equal a full deck?

[Don Schlesinger]

> One other thought: as the number of tracked cards
> increases, the ln2 approximation becomes less
> accurate, as the median approaches the mean.

> Consider the degenerate case: what's the median number
> of cards dealt from a single deck by the time you see
> all 52 cards? Certainly, the median=mean=52, and ln2 x
> 52 is a horrible estimate. I think the estimate works
> best when you're looking for a single result (e.g. a
> single ace of clubs, a single 28 in roulette, a single
> 3 on a die, etc.).

Well, that question isn't interesting, but if you had, say, 6 decks, and you asked the same question, the answer would be somewhat different.

> So I'm still leaning towards the median solution for
> this problem, but with an accurate calculation of it.

I know where to go to get the right answer. :-)

Don

[David Spence]

> I know where to go to get the right answer. :-)

I'm not surprised :-)

David

[Don Schlesinger]

Mike Shackleford did an Excel study and got 40 cards for both the mean and the median!

So, while not perfect, and surely not the equivalent of counting all the cards, the iPhone methodology isn't so bad after all.

Don

[David Spence]

> Mike Shackleford did an Excel study and got 40 cards
> for both the mean and the median!

But I think this is for an infinite pack; the median is certainly not 40 for a single deck, and may not be so for small numbers of decks either.

Thanks for finding out this result.

David

[Don Schlesinger]

> But I think this is for an infinite pack; the median
> is certainly not 40 for a single deck, and may not be
> so for small numbers of decks either.

It's supposed to be for 6-deck. We don't care about SD, and infinite deck has no practical application.

Don