Need Some Help From Mathematicians or Statisticians

I'm trying to explain to somebody that the improbability of life evolving is
nowhere near as remote as some people make it out to be.

I'm taking the Perfect Bridge Hand - 13 spades - as an example as the
probability calculations are worked out quite well here:
http://tinyurl.com/ysygle
(Link to google books - 'Fifty Challenging Problems in Probability With
Solutions' by Frederick Mosteller)

The author calculates the odds at 1 in 160 billion; he goes on to point out
that if the estimated 10 million bridge players in the USA alone play an
average of 10 hands per day, then we can expect a Perfect Hand once every
four years on average.

That bit's fine but I want to go on and explain the impact of Natural
Selection.

I've taken the example that if I set out to deal thirteen cards and get
thirteen spades, I could expect it to take 80 billion deals on average (half
of 160 billion).
If we assume 0.5 second to deal a card and for simplicity's sake ignore the
time taken to lift and reshuffle the cards, then this would take just under
1 million years dealing non-stop (0.5secs x 13 x 80 billion).

This, however, ignores the point that if the first card is not a spade, then
I can scrap that deal and start the next one; three quarters of the deals
will therefore only take 0.5 seconds instead of 6.5, which by my
calculations reduces the total time from 1 million years to just under 300K
years.

Similarly, if the second card is not a spade, then that deal too can be
scrapped so slightly more than three quarters of the remaining deals
(allowing for the fact that there is one less spade in the undealt cards)
will only take one second, reducing the 300K years to about 100K years and
so on; the only deal that will actually take 6.5 seconds is the one with 13
spades.

Are any of you mathematicians or statisticians up to calculating what the
expected time actually is?

BTW, I realise the risk of suggesting a purposeful aspect to Natural
Selection with this example, I'll be emphasising that is not the case but it
does have a similar impact. I will also be going on to make the point that
these calculations are based on only one person dealing, if one thousand or
one million people were to do the exercise simultaneously, then one of them
would get the result in a very short time.

I would also be interested to know if there have been any computer
simulations of this or similar exercises.


.

Relevant Pages

  • Re: Detroit Appeal 4
    ... The play had proceeded as follows: ... The table director applied Law 57 ... the spade king. ... Neither North nor West saw East's cards. ...
    (rec.games.bridge)
  • Re: Who was more to blame?
    ... You need 8 quick tricks after the advertised spade lead. ... I would not bid 3C with this hand. ... First I said 10 cards in the minors, which is not the same 5-5. ... Partner can bid 5C over 4C with a singleton spade himself. ...
    (rec.games.bridge)
  • Detroit Appeal 4
    ... The play had proceeded as follows: ... The table director applied Law 57 ... the spade king. ... Neither North nor West saw East's cards. ...
    (rec.games.bridge)
  • Re: Who was more to blame?
    ... I would not bid 3C with this hand. ... First I said 10 cards in the minors, which is not the same 5-5. ... Partner can bid 5C over 4C with a singleton spade himself. ...
    (rec.games.bridge)
  • Re: Another hypothetical question
    ... ace of spades for my opening lead. ... he plays two cards together -- a small spade and the ... back in South's hand and the spade stands as played. ... If you did not see where the card came from his hand your inference is ...
    (rec.games.bridge)