vpFREE2 Forums

One For The Math Gurus/ NOT VP/ Updated

#1

In a message dated 11/3/2003 12:00:20 AM Eastern Standard Time,
Cardfather@Aol.com writes:

A casino is having a scratch card promotion.
You can get 1 card per day just for showing up.
You can get more cards by hitting various jackpots.
There are 12 spots on a card.
You have to scratch 4 spots ONLY to reveal 4 moneybags, to win
$100,000.00.
Every card has the 4 moneybag spots.
There are no other prizes on the card.
Can this promotion be beaten?
How many cards would it take?

I posted the above info a week ago & now I have the update. Here is all the
info from the back of the scratch card..

(I'm skipping the usual promotional bs.)

How to play. Section 1
Scratch off (4) money bag symbols:
Remove a maximum of any 4 of the 12 scratch off squares.
Removing more than 4 squares in whole or in part will void the card.

If you reveal 4 moneybag symbols, you win $100,000.00 cash, subject to
verification.
In the event of multiple grand prize winners, the $100,000.00 cash prize will
be split evenly between winning contestants. There are a total of
Twenty-five (25) potential grand prize winning game pieces that will be distributed for
this contest. Odds of obtaining a potential grand prize winning game piece is
1:2,000.
Odds of revealing the 4 (four) winning symbols on a potential winning game
piece are approximately 1:495.
Scratch is void and not eligible for any prize if more than 4 (four) are
revealed in any manner, in whole or in part, for any reason.
Any scratches or marks on any portion of the surface of a losing scratch off
card will result in the card being void and will not be eligible for any grand
prize award.
Scratch card received in a condition that contains any damage or marks to the
surface of a losing scratch off square may only be redeemed for a
replacement card, and is not eligible for a prize claim.

A maximum of 50,000 scratch of cards will be distributed.

Prizes: Available grand prize and odds of receiving a potential grand prize
winning card are as follows--$100,000.00 Cash- maximum of one prize available
(1:2000). In the event of multiple grand prize winners, the $100,000.00 cash
prize will be evenly split between winning contestants.

The rest of the card is the usual legal mumbo-jumbo.

Well.....This is quite a bit different from what I was told before this
started, & as I posted.
The advertising for this is quite misleading. The ads read that all you have
to do to win is scratch off 4 moneybag symbols. This obviously is wrong.
I'll bring it to their attention tomorrow.
Any thoughts on this?
CF

[Non-text portions of this message have been removed]

#2

Cardfather wrote:
< snip >

I posted the above info a week ago & now I have the update. Here is
all the info from the back of the scratch card..

< snip >

Any thoughts on this?

These details sound a whole lot more plausible :slight_smile:
Each scratch card as an EV of a little less than $.10.

···

------

The odds of being successful in scratching off the 4 moneybags when
you receive a card that has all of them is correctly stated at 1 in
495 tries.

With 1 in 2000 cards having the necessary 4 moneybags, your general
odds of hitting the prize when you receive a card is 1 in 990,000. So
we're basically talking a one-in-a-million shot here.

If the rules were that the first person to successfully scratch off
the 4 moneybags scored all the dough, we could stop here. The value
of the scratch card would be $100,000/990,000, or 10.1 cents.

However, it's the case that if one or more other people manage to
scratch off the 4 moneybags on one of the remaining 24 gamepieces,
then you split the money with them.

As stated above, each person receiving a "4 moneybag" gamepiece has a
1 in 495 shot at a win. With 24 other pieces available, there's a 24
in 495 chance that at least one other winning game piece will be
exposed in addition to your winning card, should you be so lucky.

Resorting to a bit of non-precision arithmetic, that means that
there's about a 5% likelihood you wouldn't won't be receiving the
entire $100K as a winner. In those cases where you share the money,
you'll evenly split it about 95% of the time, and the other 5% of the
time you'll receive less than half (due to multiple winners - more
than 2).

So, a winner will receive the full $100 grand 95% of the time and a
little less than $50 grand 5% of the time, for an average likely win
of around $97K.

Multiplying this adjusted value by the 1 in 990,000 chance of being a
winner, you get a revised scratch card value of 9.8 cents.

------

In answer to the question posed in your original post, CF (if I recall
correctly): You're better off scouting for spare change in the
machine trays than trying to beat this one.

- Harry

#3

I don't think that answer makes sense. The promotion has 50,000
cards that have an equal chance of winning, and the prize
pool is $100,000. That means the average card is worth $2,
assuming ONLY that at least one card wins. If any one card
has a 1/495 chance of sharing in the prize pool, then the
probability of ALL cards losing is (494/495)^50000 = 1.22x10-44.
So, the real value of a card is an infinitesimally small fraction
less than $2. If all cards are played, the most likely outcome
is 101 winners splitting the prize.

···

On Monday 10 November 2003 04:58 pm, Harry Porter wrote:

Cardfather wrote:
< snip >

> I posted the above info a week ago & now I have the update. Here is
> all the info from the back of the scratch card..

< snip >

> Any thoughts on this?

These details sound a whole lot more plausible :slight_smile:
Each scratch card as an EV of a little less than $.10.

#4

Steve: The 50,000 cards do not have an equal chance of winning, only 25 cards have any chance of winning. There will probably be no winners and there could theoretically be 25 winners sharing the pot.

Regards
A.P.

···

----- Original Message -----
  From: Steve Jacobs
  To: vpFREE@yahoogroups.com
  Sent: Tuesday, November 11, 2003 12:32 AM
  Subject: Re: [vpFREE] Re: One For The Math Gurus/ NOT VP/ Updated

  I don't think that answer makes sense. The promotion has 50,000
  cards that have an equal chance of winning, and the prize
  pool is $100,000. That means the average card is worth $2,
  assuming ONLY that at least one card wins. If any one card
  has a 1/495 chance of sharing in the prize pool, then the
  probability of ALL cards losing is (494/495)^50000 = 1.22x10-44.
  So, the real value of a card is an infinitesimally small fraction
  less than $2. If all cards are played, the most likely outcome
  is 101 winners splitting the prize.

[Non-text portions of this message have been removed]

#5

You're right, my apologies. I wasn't accounting for all of the new
information.

···

On Tuesday 11 November 2003 06:17 am, Albert Pearson wrote:

Steve: The 50,000 cards do not have an equal chance of winning, only 25
cards have any chance of winning. There will probably be no winners and
there could theoretically be 25 winners sharing the pot.