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?
Thanks to all who help.
CF
"Play every day, you never know when you're walking around lucky"
Cardfather wrote:
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?
The more typical question asked is "What is the EV of a card" (or
value on average, recognizing that the actual is either $0 or $100K)
On this count, something seems a bit off in these details. It's just
not that rare to have a 4 moneybag hit under these circumstances.
On the first scratch your odds are 4/12.
On the second, if you hit on the first, it's 3/11.
Likewise, hit on the first two, and the third is 2/10.
When you're just one moneybag away from the jackpot, the of completing
a win with a fourth moneybag is 1/9.
Multiply these together and you get the odds of scratching 4 moneybags
out of 4 scratches, given four moneybags hidden under 12 spot --
1/495. That makes each of these cards worth just under $200.
If, indeed, every scratch card is a potential winner and the details
are as you specify, then someone's going to taken to the cleaners
while this promo lasts.
By the way, for what it's worth, if there were 24 spots rather than
12, the value of the card drops to a little under $5.
- Harry