I have a set of items. These items are (pseudo)randomly placed into buckets. The buckets are ordered and items placed in them are ordered. After all of the items are placed in buckets, the items are read back out of the buckets starting with the first item in the first bucket, then the second item in the first bucket, and so one until there are no more items in the bucket. Then the items are read from the second bucket and so on.
For example, I have three buckets, and the items a
through e
. a
is inserted into bucket 2:
1 2 3 a
b
into bucket 1
1 2 3 b a
c
into bucket 2
1 2 3 b a c
and so on until we have the following buckets
1 2 3 b a d e c f
The items are then read out as the list b
, e
, a
, c
, f
, d
.
A naïve examination seems to say that items inserted first have a higher chance of being first and items inserted last have a higher chance of being inserted last. This makes me fairly certain that the list has less entropy than just shuffling the items with an algorithm like fisher-yates, but how do I calculate the difference in entropy?