Author Topic: Fun with math  (Read 6373 times)

Offline whiteandgold7

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Re: Fun with math
« Reply #25 on: December 14, 2016, 06:47:32 PM »
0
For the odds of drawing both good dominants, there is a 1 in 2 chance that you drew a good dominant the first time since there are 2 good dominants, and 2 evil dominants.  The odds of drawing a good dominant the first time is 2 out of 4 which is also 1 in 2, then the odds of pulling the 2nd good dominant assuming that you have successfully already drawn the first good dominant there is a 1 in 3 chance.

So all in all, the chance of pulling both good dominants is 1 in 6.

That's the math behind the problem, and yes I do find mathematics fun, and that's half the battle in learning.

Steven

Offline Ivek

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Re: Fun with math
« Reply #26 on: December 15, 2016, 04:36:05 AM »
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It seems intuitively that the answer should be 1 in 3 for both. If I tell you one card is SoG, the odds are 1 in 3 you also drew NJ. Likewise, if I told you one card is NJ, the odds are 1 in 3 you also drew SoG. It's therefore reasonable to think that if I tell you one card is a good dominant, that the odds would remain 1 in 3 that you drew the other one. However, because we don't know which good dominant was drawn, there a couple more "losing" combinations that are possible (which are not possible when we know exactly which good dominant we drew).

Here are the 12 two card combinations you can draw: (S=SoG N=NJ C=CM B=Burial)
S-N
S-C
S-B
N-S
N-C
N-B
C-S
C-N
C-B
B-S
B-N
B-C

If we know we drew SoG, we can see there are 6 possible combos that involve SoG. Two of those combos also include NJ so when you know one of the cards is SoG, there is a 2 in 6 (1 in 3) chance that you also hold NJ.

If we only knew we drew a good dominant (but not which one), we see there are 10 combinations that involve either SoG or NJ. Two of those include both SoG and NJ therefore we have 2 "winning" combinations out of a possible 10 which gives us odds of 2 in 10 (1 in 5).

 8)

Yes you are right, my apology, I got it after a little bit of considering the problem. It's just "frustrating math" and not "fun with math".

The whole thing is about that the odds make sense when it comes to the statistics, i.e. repeating the process. So if we would constantly repeat the process of drawing two cards and have a computer/friend to tell us wheter we drew the two evil cards or at least one of the good dominants, then we could consider the cases in which computer told us we drew at least one good dominant and see that statistically in one fifth of that cases we drew both good dominants.

Really interesting fact that it statistically makes difference if the source of information names the specific card from the set of similar cards...

Offline ag4hosea

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Re: Fun with math
« Reply #27 on: December 15, 2016, 05:22:30 AM »
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Calculus killed any interest I had in mathematics long ago. Disliked and Unsubscribed. ;)

And yet your inner calling for mathematics Jesus brought you into this thread. Suppressing that innate love for math Jesus will only leave you unfulfilled and incomplete.  :'(

I fixed it for you. You are welcome  ;D
Your Aussie brother in Christ, Andy :)

Offline Josh

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Re: Fun with math
« Reply #28 on: December 15, 2016, 08:47:26 AM »
+1
I wrote this post up after only reading the first post.  I have no idea who got it right, or if my answer is right (but I think it is).

There are 6 combinations that Justin could have drawn:
-   SoG/NJ
-   SoG/CM
-   SoG/Burial
-   NJ/CM
-   NJ/Burial
-   CM/Burial

If Justin tells me he knows I drew a good Dominant, that means Justin drew at most 1 good Dominant.  That means he didn’t draw SoG/NJ – but he does have one of the other 5 combinations.  Of those 5 possibilities for Justin, only 1 of them leaves me with SoG/NJ – that’s if Justin drew CM/Burial.  Therefore, the odds I drew SoG/NJ is 20% (1 in 5).

If Justin tells me he knows I drew SoG, that means Justin has 2 cards that are not SoG.  There are 3 possible combinations for Justin.  Of those 3 possibilities for Justin, once again 1 of them leaves me with SoG/NJ.  Now my odds of having SoG/NJ is 33% (1 in 3).
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Offline Josh

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Re: Fun with math
« Reply #29 on: December 15, 2016, 08:55:22 AM »
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For the odds of drawing both good dominants, there is a 1 in 2 chance that you drew a good dominant the first time since there are 2 good dominants, and 2 evil dominants.  The odds of drawing a good dominant the first time is 2 out of 4 which is also 1 in 2, then the odds of pulling the 2nd good dominant assuming that you have successfully already drawn the first good dominant there is a 1 in 3 chance.

So all in all, the chance of pulling both good dominants is 1 in 6.

This is correct, but this is the unconditional probability of drawing SoG/NJ.  Once Justin gives you information, it changes the odds of what actually happened, and you are dealing with conditional probability.

Here's how you arrive at the unconditional 1/6 odds, using one of Justin's examples for conditional probabilities:

There's a 5/6 chance that Justin can say (truthfully) "You have drawn at least 1 good Dom".  When this happens, you have a 1/5 chance of getting SoG/NJ.  5/6 * 1/5 = 1/6

There's also a 1/6 chance that Justin can NOT say (truthfully) "You have drawn at least 1 good Dom".  When this happens, you have a 0% chance of getting SoG/NJ, because Justin drew them.  1/6 * 0 = 0

1/6 + 0 = 1/6

QED
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Offline Professoralstad

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Re: Fun with math
« Reply #30 on: December 16, 2016, 12:04:25 PM »
+1
I think what everyone is missing here is that Justin would never willingly give you accurate information in a game of Redemption unless it was to his advantage. Not to say he would lie, as he wouldn't do that either, but really the question you should be asking is not "what are the odds that I drew both dominants?", but rather, "why is he telling me this?"
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Offline STAMP

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Re: Fun with math
« Reply #31 on: December 16, 2016, 12:18:49 PM »
+1
I've always thought these message boards could benefit from a "Fun with English" thread.   ;)
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Offline Minister Polarius

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Re: Fun with math
« Reply #32 on: December 17, 2016, 10:06:30 AM »
+4
We have a whole board for that called "Rulings Questions." Mayhem delenda est.
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