Question for the Probability Nerds

[Tacosnape]

Here's a question I need to know for a deck I'm in the process of creating.

This is a 60 card deck, and assume a normal 7-card hand with no Mulligans or anything.

I want my opening hand to have the highest probability possible of having exactly one land and six spells in my opening hand.

What number of land in my deck gives me the greatest chance of this happening?

Also, if it's not too much trouble, what are the chances of hitting Exactly 0 or Exactly 2 land with that number, and what do the odds become for 0-land, 1-land, and 2-land opening hands if I run one less Land than the number that gives me the best chance at Exactly 1 land?

[Lukas Preuss]

It's actually quite easy to calculate.

You get the highest probability for having exactly one land in hand if you run 8 lands (roughly 0,4217 or 42,17 percent). 7 lands (41,61%) and 9 lands (41,97%) both have lower percentages.

With 8 lands, a 0-land hand has the probability of 34,64 percent and a 2-land hand has the probability of 18,84 percent.

Edit: Just so you can see what I did: I used the formula of the Hypergeometrical Distribution: http://en.wikipedia.org/wiki/Hypergeometric_distribution and used N=60 (cards in your deck), k=1 (or 0, or 2) (number of lands you want in your opening hand), n=7 (your opening hand of 7 cards) and m=7,8,9, whatever I tried (number of lands you run in your deck).

[freakish777]

You can also play around in MWS' Deep Reasoning/Analysis (or whatever it's called, make a deck with 20 lands and start decreasing). It's math is accurate, it just doesn't show you decimal places which can be important...

[Tacosnape]

It's actually quite easy to calculate.

You get the highest probability for having exactly one land in hand if you run 8 lands (roughly 0,4217 or 42,17 percent). 7 lands (41,61%) and 9 lands (41,97%) both have lower percentages.

With 8 lands, a 0-land hand has the probability of 34,64 percent and a 2-land hand has the probability of 18,84 percent.

Edit: Just so you can see what I did: I used the formula of the Hypergeometrical Distribution: http://en.wikipedia.org/wiki/Hypergeometric_distribution and used N=60 (cards in your deck), k=1 (or 0, or 2) (number of lands you want in your opening hand), n=7 (your opening hand of 7 cards) and m=7,8,9, whatever I tried (number of lands you run in your deck).

Isn't he smart, folks?

Now all I have to do is weigh how well/bad the deck performs with 0 and 2-land hands respectively.

I'll let you run some crazy mathematical formula to figure out how many Lesbian Points you get.:cool:

[TheCramp]

It's actually quite easy to calculate.

You get the highest probability for having exactly one land in hand if you run 8 lands (roughly 0,4217 or 42,17 percent). 7 lands (41,61%) and 9 lands (41,97%) both have lower percentages.

With 8 lands, a 0-land hand has the probability of 34,64 percent and a 2-land hand has the probability of 18,84 percent.


Lukas's math is correct, and for all those who are intrigued by such things you can use the following on line calculator to do this sort of calculation:

http://www.adsciengineering.com/hpdcalc/

[Maveric78f]

You can also play around in MWS' Deep Reasoning/Analysis (or whatever it's called, make a deck with 20 lands and start decreasing). It's math is accurate, it just doesn't show you decimal places which can be important...

Quote for falsity. MWS random generator is bad. It has been proven that the land number probability curve generated by MWS is biased (you tend to draw more lands than normally, but it may depend on your deck) and squized (don't know the english term for that, the curve's top is not high enough, which shows that MWS stacks cards of the same type). The "squize" anomaly is defendable because it's probably the case IRL but the bias has no justification.

[freakish777]

Quote for falsity. MWS random generator is bad. It has been proven that the land number probability curve generated by MWS is biased (you tend to draw more lands than normally, but it may depend on your deck) and squized (don't know the english term for that, the curve's top is not high enough, which shows that MWS stacks cards of the same type). The "squize" anomaly is defendable because it's probably the case IRL but the bias has no justification.

Learn to read. Tools-> Deep Deck Analysis.

Gives you statistical likelihood of drawing a particular card, or combination of cards, in your deck, by the nth draw. Their math (on that portion of the application) is correct, even though they don't go to decimal places.

[Nihil Credo]

Quote for falsity. MWS random generator is bad. It has been proven that the land number probability curve generated by MWS is biased (you tend to draw more lands than normally, but it may depend on your deck) and squized (don't know the english term for that, the curve's top is not high enough, which shows that MWS stacks cards of the same type). The "squize" anomaly is defendable because it's probably the case IRL but the bias has no justification.

Link?