Topic is, that you can't GSZ for an Arbor turn 1 without an initial mana, nor does it help with your landdrop turn 2Quote:
Originally Posted by Dice_Box
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Topic is, that you can't GSZ for an Arbor turn 1 without an initial mana, nor does it help with your landdrop turn 2Quote:
Originally Posted by Dice_Box
And I'm not saying that you should use GSZ to tutor up a Dryad. I'm saying that running 12 lands gives you a 38.1% chance to have only one non-Cradle/Arbor land in your opening hand as opposed to a 33.9% chance in a deck running 14 lands. This, combined with the amount of non-Arbor dorks we run, would allow you to GSZ to Quirion Ranger on your second turn instead of having a second non-Cradle/Arbor land in that same hand more often, leaving you with one more business card then the 14 land build would have :smile:.Quote:
Originally Posted by Dice_Box
What? Wait? You're losing me here.....
14 lands....
Okay. You got numbers. But as my old math teacher used to say : I can't say you're right without seeing your equation.
My issue here is, not all the lands are just there for mana. I mean, you have so many fetches, not because we need colour fixing but because we need to feed our Planeswalker. The other mana is normally a mix of Basic and Dual lands, all of which we can not cut. So talking about dropping to 12 is fine, but what are you cutting, Duals, basics or DRS food? All of them seem like bad choices to me.
There is more to this equation that just percentages.
Sent from my mobile, forgive spelling and grammatical errors.
Which is why I offered to post the numbers :).
I got those by writing a bit of code that would take 250.000 random opening hands and storing the number of times a hand had exactly 0, 1, 2, 3, 4 or 4+ lands in it. By then dividing those results by 2.500, you get the actual percentages.
The numbers are as follows:
Using 14 land in a 60 card deck:
13,98% chance of having exactly 0 lands in hand
33,88% chance of having exactly 1 land in hand
32,15% chance of having exactly 2 lands in hand
15,45% chance of having exactly 3 lands in hand
3,98% chance of having exactly 4 lands in hand
0,58% chance of having over 4 lands in hand
Using 12 land in a 60 card deck:
18,98% chance of having exactly 0 lands in hand
38,10% chance of having exactly 1 land in hand
29,24% chance of having exactly 2 lands in hand
11,20% chance of having exactly 3 lands in hand
2,23% chance of having exactly 4 lands in hand
0,25% chance of having over 4 lands in hand
So, by your maths, I am either the luckiest man on Earth or have the worst opening hands this side of the Earth will bear.
Lol well it's not math, it's the result of an algorythm taking 250k sample hands and simply counting how many hands contained exactly X or Y lands. It's just raw computing power :smile:.
Don't forget it's more complex than that though - even though the percentage of you having only 1 land in your opening hand may be 34 to 38% (approx.), the percentage of you having 2 lands rises significantly if you count your Cradles as lands after having at least one more land in your hand. In that case, the probability of you having 2 lands in your hand shoots up to the percentages belonging to decks running 16 or 18 lands, which take it to 33,55% for a 60 card deck containing 16 lands or 33,68% for a 60 card deck containing 18 lands.
So that gives you either a 34+34=68 (on 14 "real" land) or 38+34=72% (on 12 "real" land) chance you have 1 OR 2 lands in your opening hand that you can live with :smile:. And yes, in this example I'm ignoring the cases where you'd only have 2 Cradles in hand :smile:
The math and formula is totally wrong as it appears.Quote:
Originally Posted by Echelon
You should have noticed that the bolded part makes abolutely no sense as it implies that running less lands increases your chance to draw 1. The whole calculation should have been about having "at least" 1, 2, 3, etc lands in your Hand as a deck with 60 lands would have a whooping 0% in the bolded parts as you asked for "exactly"
Of course it sums up to 100%, the algorythm examined the cases where you'd have either 0, 1, 2, 3, 4 or more then 4 lands in your opening hand. It would be totally wrong if it didn't add up to 100%, since the algorythm examined all possible cases, lol. Other cases then that simply do not exist, since a hand cannot contain -1 land and the >4 lands statement also covers the 7-land hand :smile:Quote:
Originally Posted by Lemnear
Didn't put it right. Edited the post to make it clearQuote:
Originally Posted by Echelon
The at-least numbers can be gotten by summing up the numbers :smile:, that doesn't make the individual numbers wrong. And ofcourse the chance of you drawing exactly one land card in your opening hand increases by decreasing the number of lands in your deck (to a certain point, ofcourse) simply because you draw more lands less often. It isn't all that strange :smile:Quote:
Originally Posted by Lemnear
Also, the at-least numbers aren't all that exciting. When you have at least 1 land in your hand, the possibility exists you'll have a hand containing 7 lands. It's much more interesting to know how often you'll have 1 or 2 lands in your hand, or somewhere between 1 and 3, since you'd take a mulligan if your hand contained less (0) or more (4+) lands :)
And ofcourse a deck consisting of 60 lands would get a 0% on having exactly drawing 1 land in it's opening hand, it's simply impossible for a deck containing 60 lands to have exactly only one land card in it's opening hand. It'd also have a 100% in the more-then-four category, which would be correct :smile:. And in that same respect, it'd score 100% in every at-least-this-many category :smile:, rendering your arguement mute.
Use this if you want exact percentages:
http://www.geneprof.org/GeneProf/too...rgeometric.jsp
Sent from my mobile, forgive spelling and grammatical errors.
No, it's just wrong for the point we're talking about. We were talking about the chances to have Initial mana sources in hand for the configurations of 12/60 and 14/60 and not a mathematical prove that having less copies of a card(type) in a deck reduces the chance of drawing multiples which you did here and I think is abolutely pointlessQuote:
Originally Posted by Echelon
@Lemnear: Use it, it gives the same numbers I do :laugh:
Any invariance in my number is due to the fact that a sample size of 250k is actually still too small to explore all possible hands in a 60 card deck, but it's close enough
I don't care about just initial mana sources all that much, I care more about having exactly the right amount of manasources I want as often as possible, simultaneously having as many business cards as possible in my hand whilst having that exact right amount of mana sources/lands :smile:Quote:
Originally Posted by Lemnear
Btw, sorry for the double post
Lemme flash up the Cray-1 sitting in the basement of the office here.
Ill do some super-elf calculations myself.
While I appreciate your attempt, this is rather pointless. First, you should use a proper algorithm and not use brute-forced numbers although I admit that the variance might be negligible. The page you are looking for to do this kind of calculation can be found here: http://stattrek.com/online-calculato...geometric.aspx.Quote:
Originally Posted by Echelon
Population size = 60 (or...61? :wink: )
Number of successes in population = 14 (or 12)
Sample Size = 7
Number of successes in sample (x) = 1 (for exactly 1 land)
It also shows the cumulative probability which helps a lot.
Second, and this is the actual reason: you seem to enjoy theorycrafting a lot and there's nothing wrong with that. But when you actually play the game, you realize that you'd actually have to weigh different % in different ways, e.g. multiplay them with a "gravity"-factor as I'd call it. For example a hand with 0 lands might come up at like 18,98% of the time but will outright lose the game in about >90% of the time. And even that number is again depending on whether you are on the play or draw. On the other hand, a hand with 5 lands, while still bad, has a way higher average win percentage.
TL/DR: What this means is that one is missing out on overall win% if he is as narrowly focused on increasing the chance of getting the perfect hand with the perfect number of lands and best mixture of spells, as you are. I'd go as far as to call this The Belcher Approach that is not suitable for a deck that is really well equipped for grinding out the long game.
And now we didn't even talk about the opportunity cost of adding that Elvish Pioneer yet. What I am saying is that all these factors are are borderline calculateable and you shouldn't waste your time on calculating the best configuration beyond a certain point as you'll get nothing of practical value out of it.
/Edit: did some editing of minor mistakes, so you might wanna re-read.
Indeed I do like my theorycrafting. Be that as it may, I also acknowledge that there's more to Magic then just crunching numbers. Heck, that's why I bother bringing up running an Elvish Pioneer or replacing an Elvish Visionary with a Fierce Empath :smile:.Quote:
Originally Posted by Julian23
You'd have to admit though, when having a hand that contains 5 land, you take a mulligan the same as you would a no land hand, which effectively renders the win chance of the 5 land hand to 0 as well :smile:
On another note, if you are mulling every 5-land hand, you are doing it wrong. I'm inclinded to mulligan 5 lands but that again is dependant on a crazy amount of factors, especially the matchup and whether it is pre or postboard.Quote:
Originally Posted by Echelon
Forest
Fetchland
Fetchland
Bayou
Gaea's Cradle
DRS
Wirewood Symbiote
Is something I will very likely keep against Canadian Threshold for example and a lot of other decks. I'd go as far as to say that against an unknown opponent, I think I'll always keep this on the draw, even if the 5th land isn't a Cradle.
Because there are quite a few scenarios where 5 lands is still a valid keep (as opposed to 0 lands), 5-land hands still carry a way higher win% than 0 land hands, which will almost always be a mulligan. Therefore, since it is EV that we are actually chasing, you have to account for that in your calculations, which you don't. If you don't (and I think it's not worth/possible), I believe your time is much better spend playtesting with regards to EV in the first place. If that's what you're looking for, of course.
In response to this whole theory crafting deal,
If you think you're on to something in theory, just actually try it out in practice against a real opponent. Sure your sample size is going to be quite small compared to the your code, but you'll actually get to see what happens when you take your opponent into account with this land deal. In a perfect universe always having 2 land and not any more seems sweet, but if your opponent is playing something as simple as wasteland how often do you get fucked over because you aren't running just a few more lands? Or if you want to actually cut lands from the deck, are you cutting fetches? That just makes deathrite worse. There are way more factors to consider than just simple percentages. Bottom line for me is that theory is useful, its hard to consider all the factors you need to in order to make good deck building decisions.