deal or no deal

[Bengt Richter]

On Thu, 22 Dec 2005 09:29:49 -0500, rbt <rbt at athop1.ath.vt.edu> wrote:

>The house almost always wins or are my assumptions wrong...
>
>import random
>
>amounts = [.01, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750,
>            1000, 5000, 10000, 25000, 50000, 75000, 100000, 200000,
>            300000, 400000, 500000, 750000, 1000000]
>
>results = []
>
>count = 0
>while count < 10:
>     count = count + 1
>     pick = random.choice(amounts)
>     if pick < 100000:
>         results.append("NBC won... Your briefcase contains $%s" %pick)
>     else:
>         results.append("You won... Your briefcase contains $%s" %pick)
>
>results.sort()
>print "Here are 10 random picks: "
>for result in results:
>     print result

I don't know what you are doing, but 10 is a small sample to draw confident
conclusions from. E.g., try counting how many times pick<100000 out of
a larger number, e.g.,

(BTW, the expression x<y has the value True or False, and True and False are
int subclass instances with int values 1 and 0 respectively, so the sum below
is adding 1 whenever random.choice(amounts)<100000 and 0 otherwise)

 >>> import random
 >>> amounts = [.01, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750,
 ...             1000, 5000, 10000, 25000, 50000, 75000, 100000, 200000,
 ...             300000, 400000, 500000, 750000, 1000000]
 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000))
 736
 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000))
 734
 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000))
 730
 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000))
 721
 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000))
 753

What should the sum be?

 >>> amounts.index(100000)
 19
is the number of numbers < 100000 in amounts

 >>> len(amounts)
 26
is the total number of numbers

So if you choose with uniform probability, you'd expect
 >>> 19./26
 0.73076923076923073

to be the fraction satisfying pick<100000

With a larger sample, the fraction should show better, e.g.,

 >>> sum(random.choice(amounts)<100000 for _ in xrange(1000000))
 730983

Does that help?

Regards,
Bengt Richter