Subject: Zvi's Goblin Hatred (fwd) Date: Fri, 12 Jun 1998 15:33:08 -0400 (EDT) From: Scott Greenleaf To: fkusumot@ix.netcom.com I was very impressed with how quickly Zvi Mowshowitz posted his analysis of the Exodus set on the Dojo, and with the thoroughness of this analysis. Skimming through it, I noticed his Goblin Hatred deck. It's listed in his analysis of the black Exodus cards. This deck was cleverly designed, and attempts to get a very early kill via Hatred. The use of Raging Goblin allows for the possibility of a first turn kill. But how probable is this first turn kill? Zvi roughly estimates the probability of a first turn kill at 3%, and the probability of a second turn kill at 30%. The reasoning behind this estimate can be found immediately following his deck listing. Zvi comments that "this kind of math should have gotten the card out of the set." I was suspicious of his estimate, and decided to carefully calculate the probabilities myself. I had already finished some rough calculations when I noticed Theron Martin's analysis of Zvi's deck, entitled "Zvi's Goblin Hatred". Theron correctly points out that the probability of drawing exactly one Dark Ritual (for example) in your first 7 cards is 33.6%, and the probability of drawing exactly one Dark Ritual in your first 8 cards is 36.3%. Zvi used the rough estimate of 50% in place of these numbers. To compute the probability of a first turn kill when you play first, Theron gives a few possibilities of a first turn kill. Then, he reasons that the probability of having a Petal, a Ritual, a Hatred, a Mana Vault, and a Goblin in your opening seven cards should be about (.336)^5, or about .43%. Doing a similar computation for the other possibilities he listed, he arrives at a probability of a first turn kill (if you play first) of .87%. (He leaves out a bit of the detail in his post, but he was kind enough to answer my email request for more detail). Theron's (and Zvi's) computations make one fatal assumption. They assume that certain probabilities are independent of each other. In particular, they assume that the probabilities of "I draw one Dark Ritual in my first seven cards", "I draw one Mana Vault in my first seven cards", "I draw one Lotus Petal in my first seven cards", "I draw one Hatred in my first seven cards", and "I draw one Raging Goblin in my first seven cards" are independent. They aren't. If their assumption were true, that would mean that 33.6% of opening seven card hands with one Dark Ritual will have a Raging Goblin. It would also mean that 33.6% of opening seven card hands with a Dark Ritual and a Mana Vault will have a Raging Goblin. Further, this assumption implies that 33.6% of opening seven card hands with a Dark Ritual, a Mana Vault, and a Lotus Petal will have a Raging Goblin. You get the idea. If common sense doesn't suggest this assumption is false, mathematics does. Another approach is needed. Let me briefly tell you how I computed the odds of a first turn kill, assuming that you play first. The first (and most time-consuming) part is compiling all the different ways a first turn kill can occur with this deck. There are a lot of ways! The only necessary cards are the Goblin and the Hatred. All other cards are optional. You can do it without land or Dark Rituals (Vault, 4 Petals, Goblin, Hatred). You can do it without Lotus Petals or Mana Vaults (2 Rituals, Mox Diamond, 2 lands, Goblin, Hatred). After you figure out the number of combinations that give a first turn kill, you divide that number by the total number of 7 card hands one can draw (60 choose 7). The probability turns out to be .291%, or one first turn kill in every 344 duels in which you play first. Of course, if you draw first, that improves your odds (but not by much, I suspect) but your opponent also may have a blocker, or a Shock, or an untapped Quicksand. The only "reasonable" way I can think of to estimate second or third turn kills is by running a lot of goldfish hands. There are too many cases to consider. Actually, the tutors aren't always helpful for a turn two kill : you don't want to use petals or depletion lands (8 of the 18 lands are depletion lands) to tutor, because you'll probably need the mana. Also, vampiric tutors may drop your life total enough so that you can't kill on turn two. Further, mystical tutors can only get Rituals and Hatreds. So, things get complicated after turn one, and goldfish tests are the only way to get an idea of how many second and third turn kills to expect. Zvi mentioned that he was conducting an extensive goldfish test of the deck in his post, and I hope he posts the results on the Dojo. I suspect that second turn kills don't happen much more than 2% of the time, if that. Before I close this post, I just wanted to list (for the curious), the different first turn kill combinations I compiled. I'm confident that the list is complete, but if I missed anything, please feel free to let me know. G=Raging Goblin H=Hatred L=Land M=Mox Diamond P=Lotus Petal R=Dark Ritual V=Mana Vault *=Anything but Raging Goblin, Hatred, Land, Lotus Petal, Dark Ritual, or Mana Vault. "*" can be a Mox Diamond. The list of combos: GHPPPPV, GHPPPPR, GHLPPPR, GHLPPPV, GHLLMRV, GHLLMRR, GHLPPRR, GHPPPRR, GHPPRRR, GHPPRRV, GHPPPRV, GHPPRVV, GHLPRRV, GHLPPRV, GHLLPRR, GHLPRRR, GHLLPRV, GHLRPVV, GHPPRR*, GHPPRV*, GHLPRR*, GHLPRV*, GGHPPRV, GHHPPRV, GGHPPRR, GHHPPRR, GGHLPRR, GHHLPRR, GGHLPRV, GHHLPRV. I hope my explanation was clear; I know math makes some people's heads run in circles. Please feel free to email me with questions or comments. Scott Greenleaf