|
#1
|
|||
|
|||
Very simple expectation problem
Gambling game, a man is paid $3 if he draws a J or Q, $5 if he draws K or A from ordinary deck. Any other card and he loses. How much should he pay to play if the game is fair? The only reason I ask is that I think a book has the answer wrong.
|
#2
|
|||
|
|||
Re: Very simple expectation problem
$1.23
|
#3
|
|||
|
|||
Re: Very simple expectation problem
Okay, that's what I thought, the book had $1.78, forgetting to take into account that you pay when you win I think.
|
#4
|
|||
|
|||
Re: Very simple expectation problem
the problem is posed as you are "paid 3 and paid 5" not you "win 3 and win 5", so unless the problem is worded poorly $1.23 is a better answer than $1.78.
Its like the old ploy of saying they are giving you 3 for 1, instead of 3 to 1 odds. In the latter the 3 is in addition to your stake, in the former it includes it. |
#5
|
|||
|
|||
Re: Very simple expectation problem
The book specifically says he is paid $3 or $5 if he wins, so according to the wording of the question, the answer needs to be $1.23. If they actually meant he WINS (i.e. profits) $3 or $5, then they worded it very very very poorly. I'll probably have to give credit for either answer.
|
#6
|
|||
|
|||
Re: Very simple expectation problem
Give them credit for either answer, or challenge them and require two different answers along with the circumstances that make each one correct.
|
#7
|
|||
|
|||
Re: Very simple expectation problem
$1.78 is what he should pay if he gets his money back when he wins, in addition to the money he wins.
EV = 8/52 * 5 + 8/52 * 3 - 36/52 * x = 0 x = 1.78 If he doesn't get his money back, then he should only pay $1.23. EV = 8/52 *(5-x) + 8/52 * (3-x) - 36/52 * x = 0 x = 1.23 |
#8
|
|||
|
|||
Re: Very simple expectation problem
I think it is only a semantic issue. "paid" could be the amount won, or the amount won + amount returned.
Still, it would be nice if the phrasing were not ambiguous. |
Thread Tools | |
Display Modes | |
|
|