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Explaining extra truffles
Does the Pig's mood affect the quality of generated truffles? [[User:XaqNautilus|XaqNautilus]] ([[User Talk:XaqNautilus|talk]]) 13:13, 4 February 2018 (UTC)
== Extra Truffles ==
Every time a pig produces a truffle, there is a 2/3 chance of it producing another. The first is guaranteed. We can work out the chances of second and subsequent truffles and add them up. The first ten terms in the infinite sum are
1 + (2/3) + (4/9) + (8/27) + (16/81) + (32/243) + (64/729) + (128/2187) + (256/6561) + (512/19683) + ……
Simplifying to the same denominator as the tenth term
1 + (13122 + 8748 + 5832 + 3888 + 2592 + 1728 + 1152 + 768 + 512 + ……)/19683
which is
1 + (38342/19683)
or
1 + 1.94797……
As you can see, the second to tenth terms add up to almost two, and the sum to infinity is indeed 2. And remember, that's in addition to the guaranteed first truffle.
so, an optimal pig '''will''' produce an average of three truffles per day, in the long run
[[User:One More Day|One More Day]] ([[User talk:One More Day|talk]]) 21:39, 10 November 2018 (UTC)
