a Scratchcard

[jkkkk]

So you get sent a scratchcard, but instead of throwing it away you decide to humour yourself and take a look at what its offering, its called Derrens Box

It reads:

"Hello there!

We are offering one lucky person the chance to win $10,000! We have sent 10,000 tickets to different members of your surrounding area, one for each dollar!

Below is Derrens Box, it has been proven that his box is 99% accurate in telling someone if they have won the jackpot of $10,000!

If you decide to take a shot at our jackpot, you can call this number and enter your name and unique ticket code into our draw! (xxx xxxx xxx)

It will cost you $200 to enter."

You reach into your pocket and find a coin and scratch out the box beneath and read; CONGRATULATIONS YOU ARE A WINNER!

You smirk but then consider for a second, what your EV would be if the card were telling the complete truth.

What would it be?

[Kerth]

So if the box says that you've won, it means that you've won 99% of the time? If that's the case, then the EV is 0.99 * $10000 - $200 = $9700

It makes no sense though.

[jkkkk]

Incorrect

[PhantomGoose]

[ QUOTE ]
It makes no sense though.

[/ QUOTE ]
It doesn't. Here's why:

[ QUOTE ]
his box is 99% accurate in telling someone if they have won the jackpot

[/ QUOTE ]
[ QUOTE ]
what your EV would be if the card were telling the complete truth

[/ QUOTE ]

This box and these quotes are all part of the card. If the card were telling the complete truth then wouldn't that require Derren's Box to also be 100% accurate, not 99%? It contradicts itself.

Now if we want to get all nitty and start claiming that Derren's Box is not part of the card, or that there are other prizes besides the 10k prize, or something goofy like that there are all kinds of answers to this.

Taken literally, the box could be 99% accurate for 10k prizes but 2% accurate at predicting $1,000 prizes.

[rakemeplz]

Aha I figured it out I think...the ev is less than you might think.

[rakemeplz]

'This box and these quotes are all part of the card. If the card were telling the complete truth then wouldn't that require Derren's Box to also be 100% accurate, not 99%? It contradicts itself.'

Hmmm, are accuracy and truthfullness are the same thing? Anyways, this contradiction has nothing to do with the solution.

It would be interesting if the solution were somehow less than 9700 and the card were somehow truthful.

[jkkkk]

Derrens Box is 99% accurate as stated and the answer is not 9700.

[Mclane665]

I'll take a shot is it $9702 ?

[kalur]

[ QUOTE ]
Below is Derrens Box, it has been proven that his box is 99% accurate in telling someone if they have won the jackpot of $10,000!

[/ QUOTE ]

The EV of the proposal depends on the interpretation of this sentence. People reading this sentence for the first time would assume, as the posts above show, that the sentence means something like "If the box says that you have won, there is 99% probability that you have actually have won." This interpretation is naive, obviously.

There is more sound and possibly negative interpretation in terms of EV. Namely: "The box makes a mistake in 1 out of 100 times when telling whether you have won." This means that the accuracy depends also on cases when the box says that "you have not won".

Worst case scenario and probably the most realistic one would allow the card maker to create 101 cards that say that you have won and 9899 cards saying that you have not won the jackpot. If only 1 of the 101 one gets the jackpot then all other 100 are wrong -- accuracy is then 9900/10000=99% (1-jackpot card is correct and 9899- 'you lose' cards are correct).

Thus the EV is = 10000/101 - 200 =~ -100

[jkkkk]

Correct. [img]/images/graemlins/smile.gif[/img]