h*****g
发帖数: 21 | 1 There are infinite cards numbered 1-5. You construct a deck. Someone guesses
a value and draws a card. If they guessed correctly, they get the value.
What composition of the deck minimizes their expected value？
题目没看懂， 一个deck是5张还是不限张数还是infinite的全部。5张的话是随便取五
张还是要一到五俱全？
要是把题目改为： here are five cards numbered 1-5. You construct a deck.
Someone guesses a value and draws a card. If they guessed correctly, they
get the value. What composition of the deck minimizes their expected value？
就简单了。 |
K*V
发帖数: 192 | 2 no matter how many numbers of cards in a deck, the answer is always the same.
only have 1 in your deck
guesses
【在 h*****g 的大作中提到】
: There are infinite cards numbered 1-5. You construct a deck. Someone guesses
: a value and draws a card. If they guessed correctly, they get the value.
: What composition of the deck minimizes their expected value？
: 题目没看懂， 一个deck是5张还是不限张数还是infinite的全部。5张的话是随便取五
: 张还是要一到五俱全？
: 要是把题目改为： here are five cards numbered 1-5. You construct a deck.
: Someone guesses a value and draws a card. If they guessed correctly, they
: get the value. What composition of the deck minimizes their expected value？
: 就简单了。
|
C**V
发帖数: 2198 | 3 a different question: what if you have to tell the other person the deck
composition before he starts guessing?
same.
【在 K*V 的大作中提到】
: no matter how many numbers of cards in a deck, the answer is always the same.
: only have 1 in your deck
:
: guesses
|
C**V
发帖数: 2198 | 4 a different question:
what if you have to tell the other person the deck composition before he
starts guessing?
same.
【在 K*V 的大作中提到】
: no matter how many numbers of cards in a deck, the answer is always the same.
: only have 1 in your deck
:
: guesses
|
s*********y
发帖数: 284 | 5 The probability of number k (k=1-5) should be proportional to 1/k.
So 1/k/(1+1/2+1/3+1/4+1/5) for number k. |
h*****g
发帖数: 21 | 6 Yeap, That's exactly the condition that simplify the question. with the
composition known, and assuming that the counterparty is allowed to see the
card after he/she guessed , we can play with the sequence to find the
minimum using the conditional probability.
【在 C**V 的大作中提到】
: a different question:
: what if you have to tell the other person the deck composition before he
: starts guessing?
:
: same.
|
k*****n
发帖数: 117 | 7 This condition is guaranteed if you see this is a "game" with both you and
player are rational and have complete information, which are
infinite number of cards for 1 - 5
his objective: maximize his expected gain
your objective: minimize his expected gain
the
【在 h*****g 的大作中提到】
: Yeap, That's exactly the condition that simplify the question. with the
: composition known, and assuming that the counterparty is allowed to see the
: card after he/she guessed , we can play with the sequence to find the
: minimum using the conditional probability.
|
