No Ambiguous Doll Collections

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Posts: 11
Joined: 03 October 2022, 08:06

No Ambiguous Doll Collections

Post by calculatorStore »

TLDR: Nothing to see here move along ;)

I was curious if there were any ways to collect dolls so that you would need to care which ones were discarded.

According to the wiki
When you have a set of Doll cards whose Curse values add up to exactly 6, immediately dispel those Doll cards.
Note: For all card types that dispel cards of their own type the game will automatically dispel the cards with the highest Curse values, as there is no valid reason to select any other cards.
This makes sense to automatically dispel a "2" instead of 2 "1"s, but what if you would want to keep a different combination of cards in your reserve (ie a pair of "2"s vs a "1" and "3"). This would matter if there was a "3" or "4" in room if you wanted to dispel a second sum of "6". But do any of these cases actually exist? (Short answer No)

Long answer:
There are 81 (3^4) possible "states" of having 0,1,or 2 cards of values "1","2","3", or "4". But not all of these are possible to start in since they will have a combination of cards that add to "6". These are "4+2", "4+1+1", "3+3", "3+2+1", "2+2+1+1".

Eliminating states which already have a combination that adds to "6" these leaves only 21 possible starting combinations.

Of these combinations we need to find ones where if you add an additional card it creates 2 or more possible sums of "6". It turns out there are 3 states like this:
  • Start with "1","3","4" add "2". Dispel "4+2" or "3+2+1". ("4" is strictly better to discard than "3" and "1")
  • Start with "1","3","4","4" add "2". Dispel "4+2" or "3+2+1". ("4" is strictly better to discard than "3" and "1")
  • Start with "1","1","2" add "4". Dispel "4+2" or "4+1+1". ("2" is strictly better to discard than "1" and "1")
In all cases the choice to keep is always one card vs two that sum to it, so they are safe to automatically dispel.

Note: If the Doll's needed to add to "8" in order to dispel them, you could start with "1","2","2","3" and add a "4" and actually need to be able to choose between discarding the "4+3+1" or "4+2+2". But that's not what the card says, so good job game and BGA developers. Thanks for all the hard work!
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