You run a single Allure of Darkness and ten DARK monsters, and you want to open Allure with something to banish. Ask for exactly one Allure and at least one DARK:
| Group | In deck | Min | Max |
|---|---|---|---|
| Allure of Darkness | 1 | 1 | 1 |
| DARK monsters | 10 | 1 | 4 |
Hypergeometric draw odds
Will you open it?
Every ratio argument ends the same way: how often does this deck actually put the right cards in your hand? Set the deck, name the cards that matter, and read the real number.
Your deck
Main deck only — leave the Extra Deck out of it.
The cards that matter
Group your cards by the job they do, then say how many of each you want to see in hand.
Everything else
28
0
4
Terraforming fetches Dragon Ravine, so treat all five as the same card. Pair that with your six Dux and Phalanx and ask for at least one of each:
| Group | In deck | Min | Max |
|---|---|---|---|
| Ravine + Terraforming | 5 | 1 | 5 |
| Dux or Phalanx | 6 | 1 | 5 |
The trick is grouping. Any cards that are interchangeable for the combo you are testing belong on the same line, and a searcher counts as a copy of whatever it fetches.
How the number is worked out
Your deck is a finite pile, and each card you draw is gone from it, so the odds shift with every draw. That is precisely what the hypergeometric distribution describes, and it is what this page computes: the exact figure, not a simulation and not an approximation.
Groups are counted together, so a hand only passes when it meets all of your requirements at once. The percentage is the share of every possible opening hand that would pass.