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[Mini]

I think (I haven't done the math) you would have about a 1/4 chance to have some in a 1x1 embark.

[Double A]

You wouldn't get any in a 0x0

[Miuramir]

The map is divided into a 2x2 meta-grid of meta-tiles.  Ordinary blue pillars are placed one per meta-grid, randomly.  Thus, 1/4 of the embark squares contain a blue pillar.  A 1x1 embark has a 75% chance of none, and a 25% chance of one.  A 3x3 or larger embark is guaranteed to have at least one.  Due to the grid, however, a 2x2 is a bit complex; it could be aligned with the grid, misaligned horizontally, misaligned vertically, or double misaligned.  If I've done the math correctly, the following works out (rounded to 2 places): Chance none, 20.41%; chance 1, 60.55%; chance 2, 17.77%; chance 3, 1.17%; chance 4, 0.10%; overall average 1.0000. 

To reiterate, a 2x2 embark has an average of 1 pillar, but there's a slightly more than 20% (1 in 5) chance that you don't get any, and you could get up to four (unlikely).  In very round numbers, there's a 1/5 chance of none, 3/5 chance of 1, 1/5 chance of 2, and negligible chances of 3 or 4.