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/sci/ - Science & Math

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3369918 No.3369918 [Reply] [Original]

I am sure some of you play magic the gathering. I am having an argument online with someone about it.


You know those fetch lands from onslaught and Zendikar? What he is proposing is that when you fetch his play group uses a proxy of that land so that they do not have to shuffle their library. Then the next time they search their library or draw it, they replace it with the real one.


By not thinning your deck you are circumventing the game are you not?

Example

Situation 1 (with "proxies"): You're drawing from 58 cards left in your deck, you have played 4 fetches so far in the game, and fetched up imaginary lands. You need a mass removal spell, of which you run 5. You have none in hand and need to draw one or you'll lose the game. Your chance of drawing a mass removal spell is 5 out of 58 cards, or 100(5/58)=8.62%.

Situation 2 (normal): You're drawing from 54 cards left in your deck, you have played 4 fetches so far in the game, and fetched up real lands and put them into play. You need a mass removal spell, of which you run 5. You have none in hand and need to draw one or you'll lose the game. Your chance of drawing a mass removal spell is 5 out of 54 cards, or 100(5/54)=9.26%.

Until you actually draw the fetched land with your proxy-method, the statistical probability of drawing a card you need is less than if you had just manned up and played the game.


However he is saying that my example is false since if you draw the card, you just draw an new one. No change in probability. I think that is wrong.

>> No.3369954

derp

>> No.3369961

Did you really just get that butt frustrated and type all that shit out over a card game?

>> No.3369991

>>3369961


Sorry for posting a thread about math on the science and math board. How terrible of me to assume this is the board for math discussion.

>> No.3370014

Their method is wrong. Assume your library has three cards remaining: two lands and a The Abyss (why not).

If you play the way you're supposed to play, then when you use a fetch land it will remove one of the lands. The two remaining cards will be shuffled, and your library will be in one of the following two configurations:
1. Land, The Abyss
2. The Abyss, Land

Thus your chance of drawing a land next turn is 1/2.

But if you do it their way, then you leave the land where it is. Now your library will be in one of three configurations:
1. Land, Land, The Abyss
2. Land, The Abyss, Land
3. The Abyss, Land, Land

In case 3, the next card is The Abyss. In case 2, the card they draw will replace the proxy, so they must draw another card to replace it - which will be The Abyss. So there is a 2/3 chance of drawing The Abyss and a 1/3 chance of drawing an actual land.

>> No.3370017

The fuck is a fetched land?

>> No.3370088

>>3370017


lands

>> No.3370114

OP and the other guy are wrong.
Suppose we have a 58 card deck with 4 proxies. The probability that one of the 5 cards we want is on top is 5/58. The probability a proxy is on top is 4/58. If a proxy is on top then the probability the next card is one we want is 5/57, and the probability of a proxy is 3/57. In the event of a proxy the next card will be one we want with probability 5/56, and a proxy with probability 2/56. Again in the event of a proxy we'll find what we want with probability 5/55 or a proxy with probability 1/55. Finally if the 4th card was also a proxy the probability of finding what we want next will be 5/54.

To get what we want we need the following to be true:

(Mass removal on top) OR (Proxy followed by Mass Removal) OR (2 Proxy followed by Mass Removal) OR (3 Proxy followed by Mass Removal) OR (4 Proxy followed by Mass Removal).

We add probabilities over the OR's, and multiply the implicit AND's within the parenthesis.

Probability of Mass removal on top: 5/58
Probability of Proxy then Mass removal on top: 4/58 * 5/57
Probability of 2 Proxy then Mass removal on top: 4/58 * 3/57 * 5/56
Probability of 3 Proxy then Mass removal on top: 4/58 * 3/57 * 2/56 * 5/55
Probability of 4 Proxy then Mass removal on top: 4/58 * 3/57 * 2/56 * 1/55 * 5/54

We add them all together:

5/58 + 4/58 * 5/57 + 4/58 * 3/57 * 5/56 + 4/58 * 3/57 * 2/56 * 5/55 + 4/58 * 3/57 * 2/56 * 1/55 * 5/54 = 5/54,

which is exactly the probability you gave in the second scenario.

That said, it's stupid to go through this much work, because the "if you draw a proxy it essentially didn't exist" explanation is perfectly valid and essentially performs this calculation.

>> No.3370121

you really care that much in casual? yes the probability changes, but ever so slightly.
The actual shuffling is more important than the removal of one land card. especially if you're playing cards that manipulate the top of your library

>> No.3370122
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3370122

>>3369918

you are not the first to consider this question, people have done a fair amount of statistics regarding fetch lands, see

http://forums.mtgsalvation.com/showthread.php?t=201981
or
http://www.mtgdeckbuilder.net/Blogs/ViewBlog/142

>> No.3370144

>>3370014

Is actually
1.) Land 1, Land 2, Abyss
2.) Land 1, Abyss, Land 2
3.) Land 2, Land 1, Abyss
4.) Land 2, Abyss, Land 1
5.) Abyss, Land 1, Land 2
6.) Abyss, Land 2, Land 1

It's still 50% you dumb fuck

>> No.3370156

>>3370122


Thats not what I am talking about. Read my whole post again instead of reading fetch land and thinking I am talking about that article which I have already read.

>> No.3370159

>>3370114
Your calculations assume that the deck is randomized/shuffled after drawing the proxy, which is not what OP seems to be suggesting. If no shuffling happens, then some library configurations will be more likely than others, as illustrated in
>>3370014

>> No.3370164

Not if land 1 and land 2 are identical, dumb fuck

>> No.3370179

>>3370144
Not if land 1 and land 2 are identical, dumb fuck

(sorry for the double post; forgot to mention the post to which I responded)

>> No.3370187

>>3370164
Sorry forgot to mention. This is highlander.

Assume you are fetching for dual lands.

>> No.3370202

In that case, their method works. But it does not work for regular games.

>> No.3370216

>>3370202


Really? So their method works only in singleton and only if they are not fetching basic lands.

fuck me

>> No.3370252

>>3370216
If you want to search for a card, and your library has multiple copies of that card, it fails. Otherwise, it works.