Hypergeometric Nightmare - Enter the Dungeon and Wishes
General forum
Posted on Aug. 20, 2017, 7:41 p.m. by Lord_Khaine
I've recently become obsessed with the idea of using Enter the Dungeon alongside Death Wish and Burning Wish to play a game that never truly ends, until I decide to pull off some jank combo.
Enter the Dungeon combos with the Wishes in that if you cast a Wish in the subgame, the exiled Wish goes back into your library once you end that subgame - along with the card you wished for. This allows Burning Wish and Death Wish to act as copies 5-12 of Enter the Dungeon, and actually more since casting them in a subgame means you can still use the new copies in the main game, or another subgame.
My problem is when I try approaching hypergeometric distribution to figure out how many copies of Enter the Dungeon I'm likely to pull into the game from my collection.
You see, in the main game, I have the following:
Population size: 60 (cards in deck)
Successes in population: 12 (4 Enter the Dungeon, 4 Burning Wish and 4 Death Wish)
Sample size: 9 (initial hand of 7 cards, and assuming +2 cards are drawn due to the turns required to play lands to cast the cards)
Successes in sample: 1 or greater.
In the main game, 2 of the 12 cards happening is most likely, at %32.872
Upon starting the first subgame (Subgame 1) from a main game, assuming we had 2 of the 12 in hand, success in the population drops to 10, but the population size is assumed to decrease to 51.
For the first subgame in Subgame 1, the statistics continue the trend of 2 of the successes in the population most likely to appear first 9 cards, the population size decreasing by 9 and the successes in the population most likely to decrease by two when going into the next subgame.
Repeating this pattern, I'm at a roadblock: how do I account for the odds of Wish-ing an additional copy of Enter the Dungeon into my deck in the process?
(Suggestions for the other 48 cards in the deck are appreciated, as long as it isn't duplication spells such as Fork.)
What you need is an algorithm to literally map out say... all the possible iterations for a set number of turns and then calculating out how many succeeded/failed. This is one of those things that an equation alone just can't do
August 21, 2017 12:26 a.m.
Lord_Khaine says... #4
Entrei I'm afraid you may be right. Part of why I'm concerned about the odds of additional Enter the Dungeons entering my deck is that it affects how many I'll need to order beyond the playset I have right now.
Entrei says... #2
Well... subgames make hypergeometric distribution more or less impossible. You can take an average of when a sub game will start and what will be left that can be played, but HGD is just not designed to do what you are doing. Given that HGD is designed to account for probabilities with a set number of variations, it can be used relatively easily. However, adding in a successive, inconsistent change to the population renders it more or less useless.
August 21, 2017 12:21 a.m.