Conference rusure::math

    Yucko.  I've had the same problem with Uncle Dave spreading his keno
    number picks over the entire card because "winning numbers tend to be
    spread out".
    
    Try this:  "Sure, there are twice as many single-digit B's, but picking
    the CORRECT single digit number is TWICE AS HARD as picking the correct 
    double digit number under those circumstances".
    
    Or make up your own set of 75 symbols, not numbers, and ask them how
    they would select "bingo cards" to play with your new symbols.  Point
    out that the balls don't know their numbers...
    
    Ultimately, though, there's nothing more difficult than trying to convince
    somebody that their moneymaking system is wrong, especially if it's
    making them money at the time.
    
      John

    1)  Take a standard deck of 52 playing cards (no jokers).
    
    2)  Remove and discard the clubs.
    
    3)  Pull out the 3 remaining Aces (Spade, Heart, Diamond) and place
    	them face up on the table.
    
    4)  Say:  	"Mom, Dad, lets try an experiment.  I have invented a game 
    		that is something like an very simplified form of Bingo.
    		In this game, instead of bingo cards, we each get one of
    		these playing cards (point to Aces).  Then one of us
    		shuffles the rest of these cards and turns up one of them.
    		To win all you have to do is hold the Ace of the same suit
    		as the one turned up."
    
    5)  Demonstrate the game:  Give one of the Aces each to your mother,
    	father, and yourself.  Shuffle the deck and turn up one card.
    	Say:  	"See you (or 'I') win because your Ace matches the card that
    		I have turned up."
    
    6)  Say:	"Now notice that there are no clubs in the deck (fan the 
    		cards.  This means that there are twice as many red cards
    		as black ones.  If your book is right then it must be
    		better to have a red Ace than a black one.  Since I don't
    		agree with the book I'll take the black Ace (take the
    		Ace of spades) and you may each have one of the red Aces."
    
    7)  Say:	"Now lets play a few games as an experiment and see who
    		will win the most.  To make it go faster, I'll just play
    		all the cards out one at a time instead of reshuffling
    		after each game."
    
    8)  Now shuffle the deck and turn the cards over one at a time.  As 
    	each card comes up place it beside the matching Ace and
    	say:	"You (or I) win this one..."
    	Continue until all the cards are gone.
    
    9)	Say:	"Now lets count them up and see who one the most."
    
    10) Count them up and say:
    		"Well, isn't that a coincidence.  We each one 12 times.
    		I wonder how that could have happened?"
    
    --  Barry

Play this "thought experiment" with them.  Suppose two otherwise equal cards
have B-1,2,3,4,5 and B-11,12,13,14,15.  The first is better by the book.
Suppose you wave a magic wand, and all the 11s become 1 and all the 1s
become 11s -- on the balls and on the cards.  The first card must still be
better, by the book; after all, all you did was 'rename' some numbers --
you might just as easily changed the 1s and 11s to FOOs and BARs.

Wave the wand four more times (for 2/12, 3/13,4/14, 5/15), and consider
that the book will still claim that the first card is better, and can
now claim that the second is better.

The book's not far from wrong, though.  The cards are equally likely to win.


[ This suggestion is the same as one that was previously suggested ]


An alternative way of explaining this is to consider labelling the balls
with two numbers -- black (as usual), and blue.  The bingo cards are played
either entirely with the black numbers, or entirely with the blue numbers.

	I disagree:  I find the arguments in .0 very convincing :-)

	The mother of a friend of mine is a keen occasional gambler, and 
believes that some people have infallible systems, but she doesn't try these
systems out herself.   I guess she thinks that they wouldn't work for her!

	However, she assures me that she once came across two adjacent
fruit machines which were in sync, at exactly the same point in their
cycle, so if bell-foo-brickbat appears on one, the the next roll
bell-foo-brickbat will appear on the other.   She said that these were the
standard casino machine where you can choose your stake from 1 to 5 each
roll.

	If what she says is true, and I don't know much about gambling,
then she could basically have emptied those two machines over a period
of time.   However she didn't think to do it.

Andrew.

    RE: .2, .3, .4
    
    Thanks. I'll give these a try. Wish me "luck."
    
    /Dwayne
    

    re:      <<< Note 1115.1 by VMSDEV::HALLYB "The Smart Money was on Goliath" >>>
    
>    Ultimately, though, there's nothing more difficult than trying to convince
>    somebody that their moneymaking system is wrong, especially if it's
>    making them money at the time.
    
    I agree with John.  Why do we both know that?  :-)
    
    My father-in-law tells the story of when he argued with somebody about
    the odds of throwing three straight sixes with one die.  The other guy
    insisted that the odds were less than one in ten of throwing a six,
    provided you had just thrown two sixes in a row *with that very same
    die*.  My father-in-law offered to bet, so he put a dollar down on the
    table and the other guy put down a ten, and he started rolling the die.
    When he finally got two sixes, the next roll was a four, the other guy 
    shouted "SEE!", picked up the ten and the dollar and walked out.