Help: statistical probabilities of land draw after Mind Grind vs Sculpt?
Standard forum
Posted on March 9, 2013, 11:17 a.m. by Apoptosis
I need someone with a better command of statistics to answer a question for me. Please, if you don't know statistics, don't confuse the matter.
Some cards just make you mill a certain number of cards, e.g. Mind Sculpt
Other cards make you mill until you hit a land>, e.g. Mind Grind. Intuitively, this suggests that the probability of drawing a land on the next draw is less in this case.
The question is whether cards like Mind Grind hold a statistical advantage over cards like Mind Sculpt in denying your opponent access to lands. For now, let's forgo why you want to use mill to deny lands as opposed to maximizing your mill.
Here is the problem asked in a more statistically neutral manner:
A deck of sixty cards has 24 blue cards and 36 red cards. 10 cards are drawn and 3 or 4 blue cards are removed.
Seven cards are then removed from the remaining. What is the probability of drawing a blue card next?
Cards are drawn until 1 blue card is drawn. What is the probability that the next card will be blue?
Cards are drawn until 2 blue cards are drawn. What is the probability that the next card will be blue?
What would be the answers for #1-3 if you started with 22 blue cards and 3 were in the first 10?
Thanks!
also posted this question here:
http://answers.yahoo.com/question/index?qid=20130309083637AA3zI9l
March 9, 2013 11:37 a.m.
Epochalyptik says... #4
It's impossible to answer your question properly because of the vague wording you use. Statistics requires hard numbers. Saying "3 or 4 blue cards are removed" means we need to do all calculations twice: once for the case where 3 blue cards are removed and once for the case where 4 blue cards are removed.
1 is impossible to answer because we don't know the composition of the seven cards removed.
2 and 3 are impossible to answer because we don't know how many cards were removed in each case.
March 9, 2013 12:09 p.m.
Arachnarchist says... #5
Although, I probably could do the actual statistics, I'm too lazy. But I will do a simplified analysis.
With 24 lands and 36 spells, there is 1.5 spells per land card, so theoretically on average there should be 1 or 2 spells between each land card. So for each mill until a land is hit you will mill approximately 2.5 cards. Also a card like Mind Grind will always end the mill on a land, so if the lands were evenly spaced, the next card or two should be a spell, thus denying your opponent (theoretically) a land for at least a turn.
With 22 lands, the odds go up slightly for Mind Grinding. As there are now almost twice as many spells as lands, there should be two spell cards between each land much more than there will be one.
March 9, 2013 12:14 p.m.
ducttapedeckbox says... #6
Enyeto actually did an experiment to make a point for my deck Perfection of Milling. I'm sure you can ask him for the results. It may not be what you're looking for, but it does concern Mind Sculpt with Mind Grind.
March 9, 2013 12:22 p.m.
Bobgalarneau says... #7
Based on the statistics of arachnarist, for a mind sculpt you will mill 2 or 3 lands. In my opinion there is no way it could serve you better than mind grind. Simply because the later can be used as a mana sink for a huge mill....
March 9, 2013 12:28 p.m.
Epochalyptik says... #8
Also, I'm moving this to Standard to promote more discussion.
March 9, 2013 12:39 p.m.
Looking at the cards, Mind Sculpt always mills 7, that's plan and simple 7, over 10% of their deck. With Mind Grind it is random. so you could mill just 2-3 cards, or you could mill a solid 12 you never know. In my personal experience at a fnm I cast Mind Grind with x=4 (total cmc 6) and actually helped the other player... His next four cards were lands and he already had a decent amount of land on the field. so it got him to his better spells faster, though he was denied 4 lands, but at the point i think he already had 7-8 on the field.
How I set my Dimir deck up was with, 3-4 Mind Sculpt and 1-2 Mind Grind because I prefer the set 7 cards over wasting my whole turn and 6 mana to mill 4... but that's just bad luck on my half.
March 9, 2013 1:47 p.m.
http404error says... #10
The odds are neutral. With Grind, the odds of milling land is fixed - you will always mill X lands. With Sculpt, the land ratio is variable, but centered around the same ratio - namely the ratio of lands to total cards in their library. The only way to accrue statistical advantage is to stack their deck.
Let me restate:
Grind hits a variable number of cards, and a fixed number of lands.
Sculpt hits a variable number of lands, and a fixed number of cards.
The ratio of lands milled to total cards milled will always average the ratio of lands to total cards in their library currently.
The only way to "game the system" is to stack their deck, or let them do it for you. Sculpt will snag a greater or fewer amount of lands cards, but will average the same ratio. That's of course saying nothing about mana efficiency... but that's another statistic entirely.
I can furnish some numbers to clarify if that's the sort of thing that helps you.
March 9, 2013 4:02 p.m.
http404error says... #11
Oh, and to add, milling until you hit a land has no statistical effect on what the next draw will be. It may increase or decrease the chance slightly, but the odds are still centered around neutral effect.
March 9, 2013 4:08 p.m.
In a very simple sense Mind Sculpt is more economical than Mind Grind. In order to mill 7 cards with Mind Grind you're going to roughly have to set X at around 3.
Apoptosis says... #2
A follow-up for each question is: what is the probability of drawing a blue card on the next 5 draws?
March 9, 2013 11:19 a.m.