Okay. Your point is decent. But here's where your logic is flawed.Originally Posted by Manhattan
You're assuming that not only will you not draw another land, but that you will not draw another card that will benefit from having the extra speed. Given my current list, I can draw one of the following cards from my deck and benefit from the Gemstone Caverns:
Land (20 remaining)
Goblin Lackey (4 remaining, allows turn one Vial/Lackey)
Aether Vial (3 remaining, allows turn one Vial/Vial)
Warren Weirding (3 remaining, allows a turn one Weirding)
Goblin Piledriver (4 remaining, allows a turn one Piledriver)
Mogg War Marshal (4 remaining, allows a turn one War Marshal)
So in 38/53 draws, which is just shy of 72% of the time, I can gain some benefit off of the Gemstone Caverns in that instance. And that's for each draw. And that's excluding Gempalm Incinerator, because the only situation I can imagine wanting to Cycle Gempalm on turn one here instead of dropping the Vial is if my opponent led with a Lackey or a Welder.
Now, I acknowledge that in many cases with that opening hand, you're going to want to drop the Aether Vial on turn one. In which case you've at least made the thing invulnerable to Daze. In this case, 27 of the 53 draws still benefit you greatly on turn one, which is still over 50%.
Additionally, this isn't factoring in that the average CMC of my sideboard cards is 1 (Therapy, Relic, etc.), which makes Caverns even more likely to benefit from the acceleration.
Instead of running either Port or Caverns i'm running my mono-red list with 18 mountains + 4 Wasteland. The reason for running so many red sources:
I'm playing 6 cards that require RR (4 Warchief + 2 Chieftain) and I want to consistently have the mana for one when I play my third land.
I'm testing Frenzied Goblin as a 2-of to give me a higher chance of playing something on the first turn. I know it's just 1/1 when I play it at the start but even then it's solid because it makes Incinerators and/or Piledrivers happy later on. Also, the ability Frenzied Goblin has can just be silly at times giving your Piledriver(s)/Lackey(s) clear way to kind of just win the game asap.
Tacosnape, I stand corrected. I had overlooked that possibility. However the argument, while diminished in probability of occuring, still stands in principle. Sometimes you do draw Caverns at the right time and still can't do something broken with it.
We're already talking about a situation that is only relevant 1 out of 8 games you'll have the chance for something to "truly shine and win you the game" (something I seriously doubt but again, lets say it does, for science sake) whereas 7 out 8 games it'll be worse then a mountain, a rishadan port or a mutavault.
Your reply to this was that the above lands aren't any good either. Is the real argument here that you're under the impression that Port and Mutavault are bad cards (bad as in, as bad as gemstone caverns)? Both on the play and on the draw (as the cards are in the deck both on the play and on the draw) because if that's your whole argument here then you're just plain wrong, Port has won goblin players all over the world many games and Mutavault is a fine card to use when you're in a meta that's full with aggro and tribal (control non existent). Are you saying that they can't be used every game? Because that's fine, lets say for port that it's pretty much always a good card on the play (3/8) and 50% of the time it's good on the draw (2/8) that's grossly underestimating its efficiency. That's still scoring better then Barry's Cavern.
With Gemstone Caverns I'm less concerned starting with it in my opening hand on the draw as I am topdecking it one turn 1. Man, that's always a killer non-topdeck. How often does that happen? 2/53 ~ 4%.
In the hand described, I would pitch the Matron to Gemstone Mine and play the Vial unless I draw a better 2-drop.
Rishadan Port is probably just as good in that sample hand as Caverns anyway. It's even better when you don't draw your third land in the next two draws or if you would be on the play with that hand.
I think your calculation is flawed. The probability of drawing at least one caverns in an opening hand of 7 cards is:
1 - ((56 choose 7) / (60 choose 7)) = 0.399499626
So it's near 40%. Probability is such a fun thing... people have done similar things in the past though, don't worry.
I have reviewed my math independently and corrected most of it. However your numbers most certainly are incorrect. Gut reaction alone tells me that a two-off is not going to sit in my opener 40% of the time.
I'd also like to add two more numbers I left out before.
Probability of drawing both Caverns on the play with 9 additional draws:
(16/60)x(15/59)=6,8%
Probability of drawing both Caverns in the consecutive 10 draws of an onthedraw-game: (10/53)x(9/52)=3,3%
@tivadar I think you just made the mistake of assuming 4 Gemstones Caverns while there's only 2 in the deck. Actually, I'm 100% positive you did.
And because I decided to not be lazy, the correct number is 0,221468927, so 22%.
edit, @ above, excel is giving me a different number, and so is the MWS calculator. I'm using the hypergeometric distribution. I guess the flaw in your calculations is that as soon as you draw a card and it isn't the Caverns, it means that the chance increases from 2/60 to 2/59, etc. Check out this for an explanation.
Considering you're on the draw 50% of the time it means it can be used in 11% of your games which ~equates to 1 out of 10 games instead of 1 out of 8 games.
Sorry, yeah, I was assuming 4 and didn't take the time to read. But yeah, you're right, 1 - ((58 choose 7) / (60 choose 7)) = 0.221468927. Not so bad really. Note that this is the probability of not having zero caverns, so it accounts for both 1 and 2. Note that this is somewhat different than 7/30ths, but close to it still.
Actually that is the exact number that I come up with when I calculate the probability of drawing at least one Caverns and then subtract the probability of drawing both:
7/30-(1/60)x(1/59)=0,22146892655367
That would suggest that you calculated the number of getting exactly one Caverns.
Just logically you can see that 7/30 is not correct. Sure, the chance of drawing one with the first card is 1/30 (2/60) but when that card is drawn and it wasn't a caverns your card pool decreases, so the next chance isn't 1/30 but instead 2/59, and the next chance to draw one if you didn't 2/58 which is again bigger then 1/30. But it doesn't work like this.. and it's hard to explain with my english knowledge how it does work but if you want to know just check out the link I gave you.
I added both chances, the chance of drawing one is 20.96% and the chance to draw 2 is 1.19%. I have no idea how you got the same number but that's really odd.
That's the same approach I used at first. The way I look at it now is this:
I have 60 cards infront of me. Each has a 1/30 of being a Caverns. I take 7 random cards from these 60. I now have 7 times a 1/30 chance of having a Caverns.
2/60 This is the probability of a card being a Caverns
2/59 This is the probability of a card being a Caverns if you already identified one card as not being a Caverns.
As you see you are using different amounts of knowledge for judging the cards probabilities of being Caverns. Adding those afterwards is like adding fractions with different denominators.
The reason I initially went for this was because I had seen this approach used for calculating the probability of a sequenze appearing.
http://www.youtube.com/watch?v=p3nvH6gfrTc
Starts at 1:00. However these are obviously two different problems.
Spreadsheet: http://www.megaupload.com/?d=TZ59Y6QL
@Manhattan, your error is that you don't draw cards in a vacuum, you draw hands of 7 cards, as such, you need to calculate the probability of drawing a certain hand. This is called the hypergeometric distribution, it's actually not that difficult, you first look at the chance to draw the card once, this can be the first draw 2nd, 3rd, 4th, 5th, 6th or 7th draw. Then you multiply that by the chance of not drawing the second copy and then add all the probabilities together. So you get 7 different hands:
x - - - - - -
- x - - - - -
- - x - - - -
- - - x - - -
- - - - x - -
- - - - - x -
- - - - - - x
The x's is getting the card on that draw and the minus is not getting the card (look at the above vertically, or horizontally doesn't really matter where each row/column is an instance), needless to say, there's no difference in chance of drawing it the 1st or the 7th draw, so you actually really only need to do this once and multiply it by 7. Then you can do a similar thing for getting 2 copies and multiply it by 7 and then adding the two chances (if you look at my excel sheet, you'll see what I mean).
Either way, I think we can establish that the times this is effectively is 0.5 * 22.1% so 11% of the time. So lets use 1 out of 10 games as a value for argument (I know it's 1 out of 9, but 1 out of 10 is easier to use).
Last edited by Nessaja; 08-06-2009 at 12:49 AM.
So the chances of drawing 2 is:
(58 choose 5) / (60 choose 7) = 0.0118644068
So yes, about 1.19%
The chances of not drawing 0 (which is drawing either 1 or 2) is still what I posted above:
1 - ((58 choose 7) / (60 choose 7)) = 1 - ((58 choose 7) / (60 choose 7)) = 0.221468927
This makes the probability of drawing exactly 1:
B - A = 0.20960452
Just as a note, probabilities are a slippery thing. I was a math major through college and took a full semester of statistics that involved problems like this and computing them still throws me off sometimes. The above numbers are correct though, I'm fairly certain. I've actually gone through this debate in other decks (primarily involving the chance of drawing Force of Will with another blue card...).
The tricky part comes in considering that when you compute the probability of the second card being a caverns, you have to consider the probability it's a caverns *and* the first card was not a caverns. Basically, it's easier to generate the all or nothing and compute the intermediates from there.
@Nessaja: You assume you're on draw 50% of the time. Good point!
You're on the draw 50% of the time, we're talking about Gemstone Caverns, remember?
Wow. I never imagined that this sort of discussion would happen in the Goblins thread.
...Actually, no matter what the right percentage is, it's still going to be a matter of personal preference. Is 22% too low, too high, or just right? So yeah, it doesn't matter. If the dude wants to run the card, then let him.
The Source: Your Source for "The Source: Your Source for..." cliche.
It's 11%, not 22%.
And I really don't care what anyone in specific is playing, but this topic is here to discuss and develop optimal lists of the archetype of goblins. As such, I don't really see the problem with bringing probabilities and chances (aka, facts) on the table. You can talk about experiences all you like but in the end experiences are a very one sided perspective. Statistics are unbiased and give a factual representation (model) of the truth.
And if Taco doesn't want to discuss it any further that's fine, I'll just be left not understanding why on earth you would run a card that gives a (small) gain 11% of the time and is strictly worse 89% of the time.
I'd like to put my deck up for critique. I'm mostly concerned about my sideboard and only having 8 1-drops that are permanents. Here is the list:
x4 Aether Vial
x4 Swords to Plowshares
x4 Goblin Lacky
x4 Goblin Piledriver
x4 Goblin Warchief
x4 Goblin Matron
x4 Goblin Ringleader
x4 Gempalm Incinerator
x1 Kiki-Jiki, Mirror Breaker
x1 Siege-gang Commander
x1 Lightning Crafter
x1 Goblin Sharpshooter
x1 Goblin King
x4 Rishadan Port
x4 Wasteland
x4 Wooded Foothills
x3 Bloodstained Mire
x4 Mountain
x4 Plateau
-SB:
x4 Disenchant
x4 Tormod's Crypt (looking for Relic of Progenitus)
x4 Blood Moon
x2 Pyrokinesis
x1 Vexing Shusher
And to see which decks I'm having the most trouble with, I created a gauntlet of popular decks and played against myself in a few matches for each deck. These are my win percentages:
Zoo 86%
Goblins (R/B) 86%
Fish 75%
Landstill 63%
Aggro Loam 57%
A.N. Tendrils 57%
Threshold 43%
Ichorid 38%
These obviously are flawed. 57% of win percentage against AdN is something you can't achieve with your MD and SB. I don't know about the other matchups, but I'm willing to test you that you're not going over 30% win against Tendrils.
Currently Playing: Nourishing Lich.Deck
Current Record: 1-83-2
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