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Hypergeometric Facehuggers

Number crunching related to Aliens and Facehuggers and card drawing.

Numbers selected to present some breakpoints of interest in the process since only scenarios of "D mod h=1" are of note, where D is Deck Size and h is hand size per draw. Note that when h >= D you are guaranteed to die at the start of the next turn.

With Deck size D=12

Draw 6 cards per turn: 50% chance, seeing 6 cards
Draw 7: 41.6%. see 7 cards (8.4% greater chance death but you see 17% more cards)

With Deck size D=15

Draw 6: 20% cumulative chance to make it two turns, seeing 12 cards
Draw 7: 6.6% cumulative chance to make it two turns, seeing 14 cards.
13.4% increased chance of death, but you see 16.7% more cards.

Deck size D=19
Draw 6: 36.8% two turns seeing 12 cards, 5.3% success of 3 turns with 18 cards.
Draw 7: 26.3% two turns seeing 14 cards, then horrible death on 3rd turn.

Deck size D=22
Draw 6: 72% chance one turn seeing 6, 45.45% chance of 2 turns seeing 12, 18% chance of 3 turns seeing 18 cards.
Draw 7: 68.18% chance one turn seeing 7, 36.36% chance two turns seeing 14, 4.5% chance three turns seeing 21 cards.


So I think if we look at the above numbers we can conclude that Clark is a giant sissy, and real men draw the extra goddamn card every turn, because winners don't want to be told the odds.

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