m*******r
发帖数: 4468 | 1 three cards, one is a joker, i choose one card, and the dealer pionts me
one of the remaining two card is not a joker and offers me a chance to
swap. to maximise my chance of getting the joker, should i swap or not?
why? |
c********r
发帖数: 133 | 2 Of course, you should swap.
there is 1/3 chance that your current holding is Joke, in this case, you
lose if you swap,
there is 2/3 chance that your current holding is NOT joke, in this case,
you win if you swap,
so you should swap.
【在 m*******r 的大作中提到】
: three cards, one is a joker, i choose one card, and the dealer pionts me
: one of the remaining two card is not a joker and offers me a chance to
: swap. to maximise my chance of getting the joker, should i swap or not?
: why?
|
x*******1
发帖数: 28835 | 3 the same for swaping and not swaping.
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
x*******1
发帖数: 28835 | 4
It should be 1/2 becasue there is one card not joke in dealer hand.
in this case, you
you still have 1/2 chance to get card from dealer's hand by swaping.
1/2 vs 1/2 no meaning.
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
s***s
发帖数: 4329 | 5 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
yes yes yes yes yes yes yes yes yes yes yes yes yes |
m*******r
发帖数: 4468 | 6 given i know which one is a not a joker for sure, the probablity of my
card being a joker is 50%, is that right ?
this is what i think.
initially, i pick 1 out of three, my chance of getting a joker is 33%.
the second chance, i know one is not a joker. if i pick, my chance is
50%. if i dont make the pick, i will be staying with the decision i have
made when I only had 33% of chance. I would increase my chance to 50%
by picking it again.
you
case,
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
g*****a
发帖数: 1457 | 7 都是些什么智商阿，这个问题都想不清楚当初怎么出国的 |
c********r
发帖数: 133 | 8 你这个土人，再想想。这样吧，我们来玩真钱好不好？就这个游戏？一个joke算100美
元？
你说这个game我和你机会相同，我说一直玩下去我会赢，
【在 x*******1 的大作中提到】
:
: It should be 1/2 becasue there is one card not joke in dealer hand.
: in this case, you
: you still have 1/2 chance to get card from dealer's hand by swaping.
: 1/2 vs 1/2 no meaning.
|
m*******r
发帖数: 4468 | 9 this game dealer always win!!! your best chance is 50%
【在 c********r 的大作中提到】
: 你这个土人，再想想。这样吧，我们来玩真钱好不好？就这个游戏？一个joke算100美
: 元？
: 你说这个game我和你机会相同，我说一直玩下去我会赢，
|
g*****a
发帖数: 1457 | 10 there is 3/2 chance that your current holding is not joke, if you swap, you
only have half change to get the correct one so the chance is still 1/3
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
|
|
c********r
发帖数: 133 | 11 If swap all the time the expected return
is -1/3+2/3=1/3, not 1/2
【在 m*******r 的大作中提到】
: this game dealer always win!!! your best chance is 50%
|
m*******r
发帖数: 4468 | 12 we should have more questions like this so we know who is niuren who is
frog.
you
【在 g*****a 的大作中提到】
: there is 3/2 chance that your current holding is not joke, if you swap, you
: only have half change to get the correct one so the chance is still 1/3
|
g*****a
发帖数: 1457 | 13 my assumption is dealer also randomnly points |
c********r
发帖数: 133 | 14 Faint,
if you current holding is not a joke, between the 2 cards left, the dealer
already told you which one was not a joke, so the one left is always joke,
of course you need to swap your holding with that card!
you
【在 g*****a 的大作中提到】
: there is 3/2 chance that your current holding is not joke, if you swap, you
: only have half change to get the correct one so the chance is still 1/3
|
c********r
发帖数: 133 | 15 统计不及格，语文也不及格。
【在 g*****a 的大作中提到】
: my assumption is dealer also randomnly points
|
m*******r
发帖数: 4468 | 16 elaborate. is this from the players view or dealer's view?
【在 c********r 的大作中提到】
: If swap all the time the expected return
: is -1/3+2/3=1/3, not 1/2
|
x*******1
发帖数: 28835 | 17 only one chance to swap. I think mine is correct. 1/3 does not make sense.
【在 m*******r 的大作中提到】
: elaborate. is this from the players view or dealer's view?
|
c********r
发帖数: 133 | 18 From the player's view, if the player always chooses to swap, on average,
the return will be 1/3.
【在 m*******r 的大作中提到】
: elaborate. is this from the players view or dealer's view?
|
x*******1
发帖数: 28835 | 19 only one chance to swap.
【在 c********r 的大作中提到】
: From the player's view, if the player always chooses to swap, on average,
: the return will be 1/3.
|
g*****a
发帖数: 1457 | 20 语文也不及格 mayge
统计不及格 used to get 100 at college
【在 c********r 的大作中提到】
: 统计不及格，语文也不及格。
|
|
|
s*******e
发帖数: 432 | 21 1. strategy one: do not the swap, you win when the first card is a joker, so
the probability is 1/3.
2. strategy two: do the swap, you win when the first card is not a joker(
since the dealer will point out which one is not joker and you get the joker
if the first card is not a joker). So the probability is 1-1/3=2/3
You swap. Basically, if you do not swap you are not using the information
given by the dealer while you do swap you use this information. |
c********r
发帖数: 133 | 22 hehe, very classic problem.
joker, so
joker(
joker
information
【在 s*******e 的大作中提到】
: 1. strategy one: do not the swap, you win when the first card is a joker, so
: the probability is 1/3.
: 2. strategy two: do the swap, you win when the first card is not a joker(
: since the dealer will point out which one is not joker and you get the joker
: if the first card is not a joker). So the probability is 1-1/3=2/3
: You swap. Basically, if you do not swap you are not using the information
: given by the dealer while you do swap you use this information.
|
x*******1
发帖数: 28835 | 23 dealer has told u one of two remaining cards is not joker? is it a condition
? Is my english too bad?
so
joker
【在 s*******e 的大作中提到】
: 1. strategy one: do not the swap, you win when the first card is a joker, so
: the probability is 1/3.
: 2. strategy two: do the swap, you win when the first card is not a joker(
: since the dealer will point out which one is not joker and you get the joker
: if the first card is not a joker). So the probability is 1-1/3=2/3
: You swap. Basically, if you do not swap you are not using the information
: given by the dealer while you do swap you use this information.
|
s*******e
发帖数: 432 | 24 The dealer told you one of the remaining card is not a joker after you
choose the first card.
condition
【在 x*******1 的大作中提到】
: dealer has told u one of two remaining cards is not joker? is it a condition
: ? Is my english too bad?
:
: so
: joker
|
x*******1
发帖数: 28835 | 25 so it becomes fact. only 1/2 the guy picks joker.
【在 s*******e 的大作中提到】
: The dealer told you one of the remaining card is not a joker after you
: choose the first card.
:
: condition
|
m*******r
发帖数: 4468 | 26 did i say that clearly or is that him?
【在 s*******e 的大作中提到】
: The dealer told you one of the remaining card is not a joker after you
: choose the first card.
:
: condition
|
p****a
发帖数: 4829 | 27 you still do not get it.
【在 x*******1 的大作中提到】
: so it becomes fact. only 1/2 the guy picks joker.
|
x*******1
发帖数: 28835 | 28 completely confused. haha
【在 p****a 的大作中提到】
: you still do not get it.
|
s*******e
发帖数: 432 | 29 No. Think in another way, if there are 1000 cards, one of them is a joker
and after you choose the first card, the dealer will point out the 998 cards
of the remaining 999 cards which are not joker. Do you swap ? According to
your logic it is still 1/2 since you only choose from only two cards(notice
the dealer point out 998 cards). Now if you let the number of cards go to
infinity then, you will find that it is definite a good idea to swap since
the chance you do not get a joker at the first ch
【在 x*******1 的大作中提到】
: so it becomes fact. only 1/2 the guy picks joker.
|
p********9
发帖数: 3732 | 30 1. 这是一道面试题。已经用了很多年了。
2. 大概10多年前有人问过我，当时吃dinner。
3. 这道题在面试过程中suppose你用最多3分钟时间而且是直接给出答案。当时饭桌上
就是这个要求。我大概是用了一分钟左右，然后他问为什么，我好像说的是三分之几。
他说，其实他就是面试官，很多人这道题都fail了。
4. 现在重新回忆这道题，我还真是忘了一瞬间是怎么想的。现在仔细思考了一下。 这
道题的思路是这样的：
假设三个ball分别为a,b,c的话，结论是根据你做出的对比。
假设你第一次抽的是b， 第二次还剩下a和c，而a和c之间只有一个确定不是，然后假设
a肯定不是 （a和c任何一个被假设都行），那么c是joker的概率是1/3
before swapping, P(b) = 1/3
after swapping P(b') = 1-P(c) = 1-1/3 =2/3
既然2/3 > 1/3， 那你当然应该swap了 |
|
|
p********9
发帖数: 3732 | 31 补充说明一句：
这道题在面试的时候，suppose你不需要用笔和纸的，因为他给你的只有3个ball。
其实考的就是你的直觉和判断，当时你答对了就是对了，没什么可说的。
这种题，如果做不出来的话，fail的概率大一些。因为后面的面试题要比这个更有挑战
力。
当时他还说了，除了这道题以外，还有的题目就是Texas hold 'em里的一些策略，当然比
这个有灵活度和思考力了。
这个人是复旦数学系科班出身，本硕连读，美国top 5金融专业的。 |
g****r
发帖数: 306 | 32 学理（数学）的还真行
我看到这种拐弯抹角的就头痛
【在 p********9 的大作中提到】
: 1. 这是一道面试题。已经用了很多年了。
: 2. 大概10多年前有人问过我，当时吃dinner。
: 3. 这道题在面试过程中suppose你用最多3分钟时间而且是直接给出答案。当时饭桌上
: 就是这个要求。我大概是用了一分钟左右，然后他问为什么，我好像说的是三分之几。
: 他说，其实他就是面试官，很多人这道题都fail了。
: 4. 现在重新回忆这道题，我还真是忘了一瞬间是怎么想的。现在仔细思考了一下。 这
: 道题的思路是这样的：
: 假设三个ball分别为a,b,c的话，结论是根据你做出的对比。
: 假设你第一次抽的是b， 第二次还剩下a和c，而a和c之间只有一个确定不是，然后假设
: a肯定不是 （a和c任何一个被假设都行），那么c是joker的概率是1/3
|
m*******r
发帖数: 4468 | 33 whose texas holdem theory ?doyle brunson or david sklansky?
当然比
【在 p********9 的大作中提到】
: 补充说明一句：
: 这道题在面试的时候，suppose你不需要用笔和纸的，因为他给你的只有3个ball。
: 其实考的就是你的直觉和判断，当时你答对了就是对了，没什么可说的。
: 这种题，如果做不出来的话，fail的概率大一些。因为后面的面试题要比这个更有挑战
: 力。
: 当时他还说了，除了这道题以外，还有的题目就是Texas hold 'em里的一些策略，当然比
: 这个有灵活度和思考力了。
: 这个人是复旦数学系科班出身，本硕连读，美国top 5金融专业的。
|
p********9
发帖数: 3732 | 34 刚刚review了这些跟贴，看来面试官说的这道题fail率是70%～75%，居然是真的。 |
m*******r
发帖数: 4468 | 35 brunson power system or sklansky small stake hold them ?
【在 p********9 的大作中提到】
: 刚刚review了这些跟贴，看来面试官说的这道题fail率是70%～75%，居然是真的。
|
p********9
发帖数: 3732 | 36 10多年前的dinner，他当时是讲了一些，我得仔细回忆一下啊。那天主要是火锅好吃，
所以我的精力比较倾向于唰羊肉。
他每个月都去一次赌场，这些理论他都熟的。
叫我回忆起来再跟你说。
【在 m*******r 的大作中提到】
: brunson power system or sklansky small stake hold them ?
|
p***r
发帖数: 20570 | 37 well, typical restricted choice problem in bridge....long time no see, man.
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
c********r
发帖数: 133 | 38 这段时间在这儿多瞎玩一阵，过段时间估计又不来了。都好？
man.
【在 p***r 的大作中提到】
: well, typical restricted choice problem in bridge....long time no see, man.
|
f*******e
发帖数: 1161 | 39 换不换都一样，
第一种理解，
1. 当Dealer在放屁，死都不换，1/3概率
2. 如果换，两种情况
a. 第一张是joker，P=1/3 * 0=0
b. 第一张不是joker，P=2/3 * 1/2 = 1/3
所以0+1/3 = 1/3
第二种理解，剩下牌中肯定有一张不是joker，Dealer仍然在放屁，所以换不换的概率相
等，因为是两次独立事件。
我的理解，正确么？
【在 c********r 的大作中提到】
: Of course, you should swap.
: there is 1/3 chance that your current holding is Joke, in this case, you
: lose if you swap,
: there is 2/3 chance that your current holding is NOT joke, in this case,
: you win if you swap,
: so you should swap.
|
