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Title: Best number of lands vs nonlands in a deck?
Date Posted: Fri Jan/13/12 at 6:45pm

Jingbo
Posts: 72
Joined: 21-Dec-11

I remember reading (way back in elementary school) in a rule book that 20 lands and 40 non-lands is a good starting point.  I've always subconsciously used this rule of thumb when building decks, but now I want to know the truth.  What is the ideal number of lands/nonlands in a deck given different definitions of "ideal" in this context?

Suppose you were set on having 20 lands in your deck.  What number of nonland cards maximizes the chance of getting either 2 or 3 lands in your starting hand (7 cards)?  To clarify this means you don't want 4 lands or 1 land (only 2 or 3).  The answer here is 36 nonland cards for a 56 card deck and the chance of either 2 or 3 lands in your starting hand is 0.5984035.  With a standard 60 card deck the probability of this is 0.5934801.  I suppose these are close...

What simple definitions of "ideal" can you come up with?  Perhaps I can calculate some more probabilities with simple enough definitions and we can attack this problem.
Date Posted: Fri Jan/13/12 at 9:06pm

PinkiePie
Posts: 157
Joined: 10-Sep-11

25 gives you the ideal first hand, but depending on your curve and your other acceleration, you can use more or less!
Date Posted: Fri Jan/13/12 at 9:12pm

Jingbo
Posts: 72
Joined: 21-Dec-11

what is your definition of ideal?  What does 25 nonlands optimize?


[Edited by Jingbo on 13/Jan/12 at 9:12PM]
Date Posted: Fri Jan/13/12 at 9:25pm

gericault5
Posts: 2788
Joined: 13-Oct-09

I don't think there is an "ideal" definition as it changes with every deck.  For example, I have a deck where the highest mana cost is 3, so I find that 18 is enough,.  In another deck the mana payments for abilities plus cost of cards is high so I run 25.  A mono deck will have less land then an equilvant costing multi-color, while a deck with other forms of mana makers(llanowar elves for example) can get away with a lower land count then one without.

I do agree with Pinkie, 24-25 is a good start and modify from there based what is in the deck
Date Posted: Fri Jan/13/12 at 9:25pm

krowbar28
Posts: 434
Joined: 18-Oct-10

I usually run 24 land. You can get away with 22-23 in wenie decks, and up to 26 in more mana sensitive decks like ramp decks.
Date Posted: Fri Jan/13/12 at 9:42pm

Turbine
Posts: 10194
Joined: 26-Oct-09

Everything I've seen says 24. Depends on the deck though and alternate mana sources.

[Edited by Turbine on 13/Jan/12 at 9:45PM]
Date Posted: Fri Jan/13/12 at 10:53pm

Jingbo
Posts: 72
Joined: 21-Dec-11

@
gericault5: the point was to make up many oversimplified definitions of "ideal" in the interest of examining naive mathematical models.

I haven't played magic in a long time (until very recently) so my original post didn't make much sense because I fixed the land count at 20 and used the nonland count as variable... which doesn't make sense if you go below 40 because of the 60 card minimum.  The numbers were correct tho.

Anyway it seems this 24 count is a naive solution.  I think with some thought it could either be justified with more advanced methods or a different number could be.
Date Posted: Fri Jan/13/12 at 11:07pm

Jingbo
Posts: 72
Joined: 21-Dec-11

I computed (just now) that the probability of getting either exactly 2
or exactly 3 lands in your starting hand is maximized with 21 lands (in a
60 card deck) and is 0.5963197.  With 24 lands, this probability is
0.5781189.  In this respect 21 lands is superior. 

The
probability of 4 lands in your starting hand is 0.1964482 with 24 lands
and 0.1416259 with 21 though.  This probability is maximized at
0.3122098 with 34 lands (I wouldn't do that though haha)
Date Posted: Fri Jan/13/12 at 11:44pm

DyingJester
Posts: 1771
Joined: 16-Dec-08

Good god dude...just ow...can I get that explanation in english! Please?
Date Posted: Sat Jan/14/12 at 12:04am

Narcinek War-Rider
Posts: 1283
Joined: 16-Jun-11

It all depends. In decks with high costing cards I'd say 24 lands. In low costing decks and decks with mana ramp I'd say only 20.
Date Posted: Sat Jan/14/12 at 12:21am

Jingbo
Posts: 72
Joined: 21-Dec-11

Just from examining the data, it seems that 24 lands provides a good
balance of probabilities.  For instance, with 24 lands: there is a
50.52% chance of getting exactly 3 or 4 lands in your first hand and
ONLY a 6.93% chance of getting 5 lands.

the probability of 4 or 5 lands in the first 10 draws (including the 7 of your starting hand) is maximized at 51.19% with 27 lands.  It is 48.7% for 24 lands.
Date Posted: Sat Jan/14/12 at 12:58am

DyingJester
Posts: 1771
Joined: 16-Dec-08

Okay...sorry I asked...
Date Posted: Sat Jan/14/12 at 1:39am

Turbine
Posts: 10194
Joined: 26-Oct-09

It's not that hard math. I did similar for fun in 8 grade.
Date Posted: Sat Jan/14/12 at 9:43am

gericault5
Posts: 2788
Joined: 13-Oct-09

Well, I am not a math savant but i would think that, because the decks curve determines the land count, you can't come up with an ideal land count without taking into account that curve.
Date Posted: Sat Jan/14/12 at 10:03am

Narcinek War-Rider
Posts: 1283
Joined: 16-Jun-11

When I build a deck I determine the number of lands in my deck by majority mana cost.



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