Re: high-school presentation, suggestions?

Johanne Fairchild <jfairchild@tudado.org> writes:
<snip>

So I decided to make a simulation.  I wrote the code and ran the game.
What I found surprised me.  On the computer, after the two players's
cards were face up on the table, the player who won the table would take
the cards all in the order they were placed.  The fact that this order
was not changed seemed to have made the game very likely to repeat on
forever.  Using a sample of 1000 game runs, the probability that a game
would end was 0.128, about 13%.  So the probability of a never-ending
game seems to be about 87%.
>
I then decided to run the game such that the player who won would
shuffle the cards before putting them back at the end of his stack of
cards.  Doing the simulation this way results in the game ending nearly
always---99% probability.  Now, I'm saying 99% because I simply did not
find a single game run that went on forever.  (But I don't think the
probability is 100%.  But the statatistic /is/ 100%.)
>
I asked myself---why does the shuffling make the game likely to end?  I
don't know.

In your sample set of two real-world games, both games ended. Based on
your initial simulation, there's about a 1.6% chance that in two games,
both would end -- lucky, I guess?

As a child, I played War plenty of times, and while I'm sure we gave up
on some games, I believe most of them ended. I certainly don't remember
giving up on 9/10ths of them as unwinnable.

This would lead me to believe that your initial simulation was
flawed.

First, I'd want to know how you determined that a game was "unending" --
since by definition such a game could continue indefinitely, you must
have selected a number at which you'd "give up" on the game. How did you
pick that number?

Secondly, I'm a bit confused by your assertion that collecting the cards
unshuffled would make the game "very likely to repeat".

I'd hesitate to use this example for your presentation because many of
the students in your audience will have played War, and they will
probably balk at your initial simulation's results the same way I did
("9 out of 10 games of War will never end? That doesn't sound
right"). Also, although you got different results due to shuffling, you
don't have any idea *why*, which is unsatisfying. So the moral of your
story is that, using the computer, you were able to get two answers
which don't actually make any sense.

john