its on every map,
Technically adamantine spires spawn 1 in every 2x2 embark tile zone so if your map is only 2xY or Xx2 then it is fully possible for you to not get any adamantine at all.
2x2 is the smallest area you can embark in without hacks. He's right, it is on every map.
Your map doesn't necessarily line up with the 2x2 blocks though. So for example if the embark 2x2 blocks looked like this (assuming this is in the top left corner of the embark screen)
£..£
....
....
£..£
It is fully possible to make a 2x4 or 4x2 fort and still not get any adamantine spires.
£EE£ £..£
.EE. or EEEE
.EE. EEEE
£EE£ £..£
And it doesn't break the 2x2 rule
£.|.£
..|..
--+--
..|..
£.|.£
So it's not that a 2x2 is the only embark size that can get nothing, but a 2x
'anything' embark can potentially end up with zero (though the chance reduces drastically with each additional tile you increase it by) as long as the 2xY embark doesn't line up with the corner of the embark map.
Since your map isn't necessarily aligned, this means that the various embark sizes can have (Arranged by ascending area):
Size Spires
2x2 0-4
2x3/3x2 0-4
2x4/4x2 0-6
3x3 1-4 (smallest guaranteed spire)
3x4/4x3 1-6
3x5/5x3 2-6 (smallest guaranteed dual)
4x4 1-9
4x5/5x4 2-9
4x6/6x4 2-12
5x5 4-9 (smallest guaranteed quad)
5x6/6x5 4-12
5x7/7x5 6-12 (smallest guaranteed six)
6x6 4-16
If you ensure that your embark area aligns with the map (so there is an even number of squares between either the top or bottom edge of your map
and an even number between the left or right edge of your map then the table becomes this:
Size Spires
2x2 1 (smallest guaranteed spire)
2x3/3x2 1-2
2x4/4x2 2 (smallest guaranteed dual)
3x3 1-4
3x4/4x3 2-4
3x5/5x3 2-6
4x4 4 (smallest guaranteed quad)
4x5/5x4 4-6
4x6/6x4 6 (smallest guaranteed six)
5x5 4-9
5x6/6x5 6-9
5x7/7x5 6-12
6x6 9 (smallest guaranteed nine)
And that then gives spire/area ratios of:
Edit: It was pointed out that I had forgotten to include weights in my calculations, and as such the Ratio (avg) calculation is worthless. Feel free to use the min and max though.Size Ratio (max) Ratio (min) Ratio (avg)
2x2 1.000 0.000 .500
2x3/3x2 .666 0.000 .333
2x4/4x2 .750 0.000 .375
3x3 .444 .111 .278
3x4/4x3 .500 .083 .292
3x5/5x3 .400 .133 .267
4x4 .563 .063 .313
4x5/5x4 .450 .100 .275
4x6/6x4 .500 .083 .292
5x5 .360 .160 .260
5x6/6x5 .400 .133 .267
5x7/7x5 .343 .171 .257
6x6 .444 .111 .278
Size Ratio (max) Ratio (min) Ratio (avg)
2x2 .250 .250 .250
2x3/3x2 .333 .167 .250
2x4/4x2 .250 .250 .250
3x3 .444 .111 .278
3x4/4x3 .333 .167 .250
3x5/5x3 .400 .133 .267
4x4 .250 .250 .250
4x5/5x4 .300 .200 .250
4x6/6x4 .250 .250 .250
5x5 .360 .160 .260
5x6/6x5 .300 .200 .250
5x7/7x5 .343 .171 .257
6x6 .250 .250 .250
So in general:
1)Aligning your map raises the minimum while lowering the maximum (with the exception of any map with two odd dimensions such as 3x3, 3x5, 5x5, and 5x7 as they are
always aligned).
2)Unaligned maps have a better overall spire/area ratio then aligned maps do.
Edit: Disproved3)All aligned maps have an spire/area ratio of .25 spires per embark square with the exception of dual odd dimension maps.
Edit: Disproved, All maps have a spire/area ratio of .25.4)The best unaligned maps for finding adamantine in ascending area order are 3x3, 3x5, 4x5, 5x5, and 5x7.
5)The best aligned maps for finding adamantine are any
'even'x
'even' maps