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Subject: Drawing colonist probabilities rss

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Dan Likos
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The probabilities P(x) of drawing x colonists when attempting to found a colony are as follows (with the 2012 version, i don't know if the 2004 edition has different cards)

P(2) = (7/30)(6/29) = 4.8%
P(3) = (7/30)(13/29) + (13/30)(7/29) = 20.9%
P(4) = (7/30)(10/29) + (13/30)(12/29) + (10/30)(7/29) = 34%
P(5) = (13/30)(10/29) + (10/30)(13/29) = 29.9%
P(6) = (10/30)(9/29) = 10.3%

I am pretty sure these are correct. I don't know if these have been done before and are old news but here you go anyway.

These probabilites assume you don't know any of the expedition cards, but even when you do they will be close,

I will do the probabilites when you get to draw three cards in a bit.
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Dave Eisen
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2004 edition is in fact different: the deck has an equal number of cards with 1, 2, and 3 colonists on them.
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Sophia Lechner
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I've been playing around with this a bit in Excel, and found a good rule of thumb that lends itself to quick calculation.

Focus on the probability of getting 4 or more colonists from the deck in two draws. From a fresh deck, this is ~74% (roughly, 3-1 odds FOR success on founding Quilon with your starting colonists - as a historical note, the old odds were exactly 2-1 for). Starting with 74%, for each 1 colonist or 3 colonist card that gets taken out of the deck, add 3% or subtract 2% respectively from the odds of pulling at least 4 colonists on two cards. This isn't perfect, but it's within 1% over quite a large range.

Playing with these numbers really makes me heavily value a clove plantation in the first turn auction. Even though progressing my colonist track only raises my chance of successful founding by ~26% (from ~74% to 100%), it also adds about 1 to my expected # of remaining colonists in the event of a successful founding (from 0.68 to 1.69).

If I don't get a clove plantation, I want to draw an expedition card before I try to found Quilon - 3.5 out of 10 cards will help me found it (2 colonists, 3 cards for founding, progress with money, progress with ships (counting this as half because I'd like to use this for better than a one spice saving)).
 
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