See the top rated post in this thread. Click here

Page 1 of 8 123 ... LastLast
Results 1 to 13 of 101

Thread: Probability theory

  1. #1
    Senior Member Gramazeka's Avatar
    Join Date
    Dec 2011
    Location
    Ukraine
    Posts
    1,438


    Did you find this post helpful? Yes | No

    Probability theory

    In one box, 2 times more money than in another. We opened one of them, there is $ 100, should we open the second one? How to maximize EV ?
    "Don't Cast Your Pearls Before Swine" (Jesus)

  2. #2


    Did you find this post helpful? Yes | No
    The EV for both envelopes is the same, so no need to swap.

  3. #3
    Senior Member Bubbles's Avatar
    Join Date
    Sep 2015
    Location
    South West
    Posts
    957


    Did you find this post helpful? Yes | No
    I first thought box 1 has 100$. EV to stay is 100$.
    Box 2 will have either 50 or 200$.
    (50+200)/2=125
    On average, our EV to switch will be 125$, 25$ more than staying.

    This didn't seem correct. We know someone opening their first boxes and another person always opening the second one will have the same amount in the end after many boxes. I had to Google to find out what the answer was. I'll not spoil it.


    Sent from my SM-G955U using Tapatalk
    Last edited by Bubbles; 02-18-2018 at 07:32 AM.

  4. #4


    Did you find this post helpful? Yes | No
    Definitely, open the second box and keep the money from both boxes.

  5. #5


    1 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    It's a math teaser. Start here: https://en.m.wikipedia.org/wiki/Two_envelopes_problem

    Kind of like Monty Hall, but with two choices instead of three.

  6. #6
    Senior Member
    Join Date
    Dec 2011
    Location
    3rd rock from Sol, Milky Way Galaxy
    Posts
    14,158


    Did you find this post helpful? Yes | No
    You really don't have any information that is relevant to the problem after opening the first box. One box has a smaller amount, S, and one the larger amount, L. The expected value of either box, assuming each has an equal chance of containing either amount, is:
    EV = 1/2*(S +L)

    Since L =2*S:
    EV = 1/2(S + 2*S) = 3*S/2

    Knowing the value of one box doesn't change the EV's of each box. It just gives the EV of both boxes two possible values that are still equal and equally likely. One if the revealed amount ends up being the smaller amount and another if it ends up being the larger amount. Only one is reality and you don't know which one. You can't say I like this EV better so I will or won't switch. You only know the amount in the box you chose, A. These two events have the same probability:

    If A = S: in which case you gain S by switching
    If A = 2*S: in which case you lose S by switching.
    Since the two events listed above have equal probability so switching has as an effect of zero (1/2(S + -S)).

    Since there is no EV gained in switching, it becomes a problem like Don's coin flip scenario. A preference as to whether you prefer a $100 sure thing or switching to the other box that either has $50 or $200. Since $100 is a trivial amount I would probably take the unrevealed amount in the other box. If the revealed box contained a life changing amount I would keep it.

  7. #7


    1 out of 2 members found this post helpful. Did you find this post helpful? Yes | No
    The question was how to maximize EV. It wasn't a question about utility. To that end Miestro's answer makes the most sense... Haha

  8. #8
    Senior Member
    Join Date
    Dec 2017
    Location
    Round about the 49th
    Posts
    146


    Did you find this post helpful? Yes | No
    Interesting....I linked over to the wikipedia on this and it was too much to take in before morning coffee.

    While not identical, does this bear any relation to the double up option offered on some VP games? I suppose that is more like you have one envelope in hand with $X and are offered the option to exchange to one of two others, one with $2X and one with $0X. If you take the offer you have a random shot at double or nothing.

  9. #9


    Did you find this post helpful? Yes | No
    Seems like there is a clear gain in EV by switching because the average payout from box two is going to be $125.

  10. #10


    1 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    Quote Originally Posted by Three View Post
    You really don't have any information that is relevant to the problem after opening the first box. One box has a smaller amount, S, and one the larger amount, L. The expected value of either box, assuming each has an equal chance of containing either amount, is:
    EV = 1/2*(S +L)

    Since L =2*S:
    EV = 1/2(S + 2*S) = 3*S/2

    Knowing the value of one box doesn't change the EV's of each box. It just gives the EV of both boxes two possible values that are still equal and equally likely. One if the revealed amount ends up being the smaller amount and another if it ends up being the larger amount. Only one is reality and you don't know which one. You can't say I like this EV better so I will or won't switch. You only know the amount in the box you chose, A. These two events have the same probability:

    If A = S: in which case you gain S by switching
    If A = 2*S: in which case you lose S by switching.
    Since the two events listed above have equal probability so switching has as an effect of zero (1/2(S + -S)).

    Since there is no EV gained in switching, it becomes a problem like Don's coin flip scenario. A preference as to whether you prefer a $100 sure thing or switching to the other box that either has $50 or $200. Since $100 is a trivial amount I would probably take the unrevealed amount in the other box. If the revealed box contained a life changing amount I would keep it.
    Seriously, and I mean this in the nicest way - who the fuck cares?

  11. #11
    Senior Member
    Join Date
    Dec 2011
    Location
    3rd rock from Sol, Milky Way Galaxy
    Posts
    14,158


    Did you find this post helpful? Yes | No
    Quote Originally Posted by Meistro123 View Post
    Seems like there is a clear gain in EV by switching because the average payout from box two is going to be $125.
    You are right. If the amounts are unknown in both boxes the values of S and L are undefined variables twice or half of each other. Once you know the value of one box that changes since S is either 1/2 that particular value or twice that particular value. So basically S no longer equals S in each of the two possibilities. So the other box would on average contain 1.25 times the value of the known box. That was bothering me when I did my analysis but I didn't understand why. Thank you for getting me to finish my line of reasoning.
    Last edited by Three; 02-18-2018 at 12:14 PM.

  12. #12


    Did you find this post helpful? Yes | No
    For utility, everyone will have a different answer. For EV, however, there is no difference. This is a classic high school math problem... Maybe this link will be easier to understand.

    https://brilliant.org/wiki/two-envelope-paradox/

  13. #13


    Did you find this post helpful? Yes | No
    I'll always take the chance to double and change envelopes. Fck the math.

Page 1 of 8 123 ... LastLast

Similar Threads

  1. The Theory of Blackjack
    By moses in forum General Blackjack Forum
    Replies: 2
    Last Post: 09-03-2013, 05:18 PM
  2. More Voodoo theory
    By Ikerus in forum The Disadvantage Forum
    Replies: 48
    Last Post: 01-26-2013, 10:25 AM
  3. Brick: BJ theory
    By Brick in forum Blackjack Main
    Replies: 5
    Last Post: 02-19-2005, 03:20 PM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

About Blackjack: The Forum

BJTF is an advantage player site based on the principles of comity. That is, civil and considerate behavior for the mutual benefit of all involved. The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage. To maximize our success, it is important to understand that we are all on the same side. Personal conflicts simply get in the way of our goals.