Cactus Game Design Message Boards

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).

 

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...

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).

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?"

We have a whole board for that called "Rulings Questions." Mayhem delenda est.