What Condition my Condition(al) is in!

The hardest land to speculate impact on in Delver's mana base was Glacial Fortress. It's condition that a plains or island be ont he battlefield presented some troubling math that I hope I deduced correctly. If anything, though, it was fun to work.

Ths first chart is the probability that any land drawn is a plains or island:

	# Island or plains drawn
Drawn:	>=1	0	1	2	3	4	5	3+
1	47%	53%	47%	0%	0%	0%	0%	0%
2	74%	26%	53%	21%	0%	0%	0%	0%
3	88%	12%	42%	37%	9%	0%	0%	9%
4	95%	5%	28%	42%	22%	3%	0%	25%
5	98%	2%	16%	37%	33%	11%	1%	44%
6	99%	1%	8%	28%	37%	21%	5%	63%

So, if you draw 1 land in your opener, there's a 47% chance it is a basis land. When you draw 2 lands, there's a 53% chance just 1 of them is basic, and a 21% chance both are basic.

Next is the chances of drawing a Glacial Fortress as your lands:

	# Glacial Fortress Drawn
Drawn:	>=1	0	1	2	3	4	3+
1	21%	79%	21%	0%	0%	0%	0%
2	39%	61%	35%	4%	0%	0%	0%
3	53%	47%	43%	9%	0%	0%	0%
4	65%	35%	47%	16%	2%	0%	2%
5	74%	26%	47%	23%	4%	0%	4%
6	82%	18%	44%	30%	7%	0%	7%

There's a 21% chance that the first land drawn by the deck is a glacial fortress. 35% chance that one land drawn is a glacial fortress by the time two lands are drawn.

Conditionally, if you have 2 lands drawn, the probability of it being a glacial fortress AND a basic land is 21%. If you have 3 lands drawn, the chance of having 1 glacial fortress and at least 1 basic is 37%. Whether it'll be first or second is a mystery to me. I am not that good at this math, yet.

Next, I want to determine whether 0,1,2,3, or 4 glacial fortresses would be best based for the deck. I'm just going to speculate on this and try to use some sort of deductive reasoning. I made a chart that will compare 8 criteria for combinations of Plains, Island, and Glacial Fortresses in a Delver deck.

1.% First land tapping for {U}
2.% First land being Glacial Fortress
3.% First land being a basic land
4.% Having a land that taps for {W} by 3rd land drawn
5.% Having a fortress and basic by land drop 2
6.% Having a fortress and at least 1 basic by land drop 3
7.% Having the Geist in hand to play by 9th drawn card
8.% Having the Delver or Ponder in hand to play in opening hand

There is a lot of combinations here, too, because we have to determine what basics we'd replace the fortresses with. There's:
UUUU, UUUW, UUWW, UWWW, WWWW
GUUU, GUUW, GUWW, GWWW
GGUU, GGUW, GGWW
GGGU, GGGW
GGGG

15 column chart! :D

No, just kidding. I want to maximize my chances of castign 1st turn Delver. It's the name of the deck! So I only want combinations that have maximum {U} tapping power. That's:

UUUU, GUUU, GGUU, GGGU, and GGGG

5 columns. I have a :(

	Land Combo
Crriteria	UUUU	GUUU	GGUU	GGGU	GGGG
1	84%	84%	84%	84%	84%
2	0%	5%	11%	16%	21%
3	68%	63%	58%	53%	47%
4	62%	70%	77%	83%	88%
5	0%	7%	13%	18%	21%
6	0%	14%	25%	33%	37%
7	51%	51%	51%	51%	51%
8	68%	68%	68%	68%	68%

You have 16 more percentage points of having your first land tap for {U} than having a delver or ponder in your opening hand. Applying the same metric, 16 pecentage points more than the 51% chance of having Geist in your hand by the 9th card drawn is 76%. The first combination that has a 76% or greater chance of having a {W} as the third land drop is GGUU. If you treat this proportionally, though, you'd be looking at a percentage drawing {W} starting at 68%, which is GUUU.

I'm just going to state that while its good to have the highest percentage possible of having {U} and {W} sources in the deck, the loss of tempo that could be generated by running 4 Glacial Fortresses is not worth that maximization. Delver should have ran either 1 Fortress, and 3 extra islands, instead, or 2 fortresses and 2 islands.

What's just so bad is I can't test this theory since Delver does not exist as a deck archetype yet. However! Having this chart and knowing the conclusions I drew from it, and why, contribute to my budding manifest on deck design.