byak Posted January 19, 2012 Report Share Posted January 19, 2012 ever wondered about the probability of going off with Wind-Ups? [quote][b]Part 1: List of Combos[/b] Defined as any combination of X cards that make the opponent discard at least 3 cards from their hand (usually resulting is some kind of field presence as well). I'm not going to explain how every combo plays out, or I will be here forever. Most of the combos look similar, so if you understand one you should understand all of the others. Tour Guide + Shark Tour Guide + Reborn Tour Guide + Foolish Hunter + Shark Magician + Shark Rat + Shark + Shark Rat + Shark + Reborn Rabbit + Shark + Shark Rabbit + Shark + Reborn Shark + Shark + Shark Shark + Shark + Reborn Foolish + Rat Foolish + Reborn + Shark Foolish + Reborn + Hunter Foolish + Reborn + Rabbit Foolish + Reborn + Magician Foolish + Reborn + Sangan Foolish + Reborn + Tour Bus Notes: - I might have missed a combo or two since I'm not exactly a Wind-Up (zen)master yet. If I did miss one, someone point it out. - Usually tacking on a Wind-Up Factory to any of these combos results in a stronger field presence or the opponent discarding more cards. However, I don't think any combos actually need the Factory. That being said, Factory is still awesome in the mirror and gives you value when you don't combo off. [b]Part 2: The Combo-Oriented Build[/b] For those looking to combo off as consistently as possible, I'd recommend this skeleton. Monsters: 3 Tour Guide from the Underworld 1 Tour Bus from the Underworld 1 Sangan 3 Wind-Up Shark 3 Wind-Up Magician 2 Wind-Up Hunter 3 Wind-Up Rat 2 Wind-Up Rabbit Spells: 3 Wind-Up Factory 1 Monster Reborn 1 Foolish Burial You obviously want staples, backrows, etc, but I'm only listing cards that can be involved in the combo. You also play Upstart Goblins to increase your probabilities even further, but I don't see most builds playing them, so I won't list them. [b]Part 3: Combo Probabilities[/b] Notes: - 40 card deck - You're going first - Hand traps will be factored in in another part - Some combos will be listed as one in order to make the math easier - Calculated using: [url="http://stattrek.com/Tables/Hypergeometric.aspx"]http://stattrek.com/...rgeometric.aspx[/url] Tour Guide + Shark/Reborn = H(40,3,6,1) * H(39,4,5,1) = 0.394331983805668 * 0.43616490984912 = 0.1719937741672238 Tour Guide/Rat + Foolish + (not opening both Hunters) = H(40,6,6,1) * H(39,1,5,1) * (1 - H(38,2,4,2)) = 0.649616765406239 * 0.128205128205128 * 0.9914651493598862 = 0.0825733824795105 Shark + Hunter = H(40,3,6,1) * H(39,2,5,1) = 0.394331983805668 * 0.242914979757085 = 0.095789145863725 Shark + Magician + (not opening both Hunters) = H(40,3,6,1) * H(39,3,5,1) * (1 - H(38,2,4,2)) = 0.394331983805668 * 0.345223766276398 * 0.9914651493598862 = 0.1349708997311629 Rat/Rabbit + Shark + Shark/Reborn = H(40,5,6,1) * H(39,3,5,1) * H(38,3,4,1) = 0.57712368238684 * 0.345223766276398 * 0.290659080132764 = 0.0579099882838618 Shark x2 + Shark/Reborn = H(40,3,6,2) * H(38,2,4,1) = 0.0536437246963556 * 0.20199146514936 = 0.0108355745474858 Foolish + Reborn + Shark/Hunter/Rabbit/Magician/Sangan/Tour Bus = H(40,1,6,1) * H(39,1,5,1) * H(38,12,4,1) = 0.15 * 0.128205128205128 * 0.797466639571903 = 0.0153358969148443 [u]Total[/u]: 0.5694086619878141 But wait, there's more! [b]Part 4: Calculating Overlap[/b] We don't exactly have a 56ish% first-turn combo here. We still need to subtract out overlap (ie the probability that we draw a hand that qualifies for two or more combos). Tour Guide + Reborn/Shark + Foolish + (not opening both Hunters) = H(40,3,6,1) * H(39,4,5,1) * H(38,1,4,1) * (1 - H(37,2,3,2)) = 0.394331983805668 * 0.43616490984912 * 0.105263157894737 * 0.995495495495495 = 0.0180230555196569 Tour Guide + Shark + Hunter = H(40,3,6,1) * H(39,3,5,1) * H(38,2,4,1) = 0.394331983805668 * 0.345223766276398 * 0.20199146514936 = 0.0274976581948711 Tour Guide + Shark + Magician + (not opening both Hunters) = H(40,3,6,1) * H(39,3,5,1) * H(38,3,4,1) * (1 - H(37,2,3,2)) = 0.394331983805668 * 0.345223766276398 * 0.290659080132764 * 0.995495495495495 = 0.0393899912091714 Tour Guide + Shark + Rat/Rabbit + Shark/Reborn = H(40,3,6,1) * H(39,3,5,1) * H(38,5,4,1) * H(37,3,3,1) = 0.394331983805668 * 0.345223766276398 * 0.445641129851656 * 0.224158368895211 = 0.0135988728865341 Tour Guide + Shark x2 + Shark/Reborn = H(40,3,6,1) * H(39,3,5,2) * H(37,2,3,1) = 0.394331983805668 * 0.0403034613560929 * 0.157657657657658 = 0.0025056443039523 Foolish + Reborn + Shark/Hunter/Rabbit/Magician/Sangan/Tour Bus + Tour Guide/Rat = H(40,1,6,1) * H(39,1,5,1) * H(38,12,4,1) * H(37,6,3,1) = 0.15 * 0.128205128205128 * 0.797466639571903 * 0.421492921492921 = 0.006463971994352 Tour Guide/Rat + Foolish + Shark + Hunter + (not opening the 2nd Hunter) = H(40,6,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,2,3,1) * (1 - H(36,1,2,1)) = 0.649616765406239 * 0.128205128205128 * 0.290659080132764 * 0.157657657657658 * 0.944444444444444 = 0.0036044416796835 Tour Guide/Rat + Foolish + Shark + Magician + (not opening both Hunters) = H(40,6,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,1) * (1 - H(36,2,2,2)) = 0.649616765406239 * 0.128205128205128 * 0.290659080132764 * 0.22985842985843 * 0.998412698412698 = 0.0055554219259906 Tour Guide + Foolish + Rabbit + Shark + Shark/Reborn = H(40,3,6,1) * H(39,1,5,1) * H(38,2,4,1) * H(37,3,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.128205128205128 * 0.20199146514936 * 0.22985842985843 * 0.161904761904762 = 0.0003800322722367961 Rat + Foolish + Shark + Shark/Reborn = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,1) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.20199146514936 = 0.0029681395445423 Shark + Hunter + Magician + (not opening the 2nd Hunter) = H(40,3,6,1) * H(39,2,5,1) * H(38,3,4,1) * (1 - H(37,1,3,1)) = 0.394331983805668 * 0.242914979757085 * 0.290659080132764 * 0.918918918918919 = 0.0255845267783086 Rat/Rabbit + Shark + Shark/Reborn + Hunter = H(40,5,6,1) * H(39,3,5,1) * H(38,3,4,1) * H(37,2,3,1) = 0.57712368238684 * 0.345223766276398 * 0.290659080132764 * 0.157657657657658 = 0.0091299531078161 Shark x2 + Shark/Reborn + Hunter = H(40,3,6,2) * H(38,2,4,1) * H(37,2,3,1) = 0.0536437246963556 * 0.20199146514936 * 0.157657657657658 = 0.0017083113025315 Foolish + Reborn + Shark + Hunter = H(40,1,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,2,3,1) = 0.15 * 0.128205128205128 * 0.290659080132764 * 0.157657657657658 = 0.0008812428798204042 Rat/Rabbit + Shark + Shark/Reborn + Magician + (not opening both Hunters) = H(40,5,6,1) * H(39,3,5,1) * H(38,3,4,1) * H(37,3,3,1) * (1-H(36,2,2,2)) = 0.57712368238684 * 0.345223766276398 * 0.290659080132764 * 0.20199146514936 * 0.998412698412698 = 0.0116787562002709 Shark x2 + Shark/Reborn + Magician + (not opening both Hunters) = H(40,3,6,2) * H(38,2,4,1) * H(37,3,3,1) * (1-H(36,2,2,2)) = 0.0536437246963556 * 0.20199146514936 * 0.20199146514936 * 0.998412698412698 = 0.0021852194617904 Foolish + Reborn + Shark + Magician + (not opening both Hunters) = H(40,1,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,1) * (1-H(36,2,2,2)) = 0.15 * 0.128205128205128 * 0.290659080132764 * 0.20199146514936 * 0.998412698412698 = 0.0011272588834916 Shark x2 + Shark/Reborn + Rat/Rabbit = H(40,3,6,2) * H(38,2,4,1) * H(37,5,3,1) = 0.0536437246963556 * 0.20199146514936 * 0.361647361647362 = 0.0039186569470315 Rat/Rabbit + Shark + Reborn + Foolish = H(40,5,6,1) * H(39,3,5,1) * H(38,1,4,1) * H(37,1,3,1) = 0.57712368238684 * 0.345223766276398 * 0.105263157894737 * 0.0810810810810811 = 0.0017004564259535 Shark x2 + Foolish + Reborn = H(40,3,6,2) * H(38,1,4,1) * H(37,1,3,1) = 0.0536437246963556 * 0.105263157894737 * 0.0810810810810811 = 0.0004578411780627797 [u]New total[/u]: 0.391049209291746 [b]Part 4B: Calculating Overlap From Our Overlap[/b] Of course there's some overlap in our overlap as well. There's a chance that we draw a hand that qualifies for 3 or more combos. We have to subtract this overlap from our overlap. However, since subtracting from a negative is a positive, the second layer of overlap is actually added to the total. [img]http://i1.kym-cdn.com/photos/images/newsfeed/000/001/122/xzibit-happy.jpg[/img] Here are are all of the hands that qualify for 3 or more combos. Tour Guide + Shark + Foolish + Hunter qualifies for... 1. Tour Guide + Shark 2. Tour Guide + Foolish 3. Shark + Hunter P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,1,4,1) * H(37,2,3,1) = 0.394331983805668 * 0.345223766276398 * 0.105263157894737 * 0.157657657657658 = 0.0022591972695317 Tour Guide + Shark + Foolish + Magician + (not opening 2nd Hunter) qualifies for... 1. Tour Guide + Shark 2. Tour Guide + Foolish 3. Shark + Magician + (not opening both Hunters) P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,1,4,1) * H(37,3,3,1) * (1 - H(36,1,2,1)) = 0.394331983805668 * 0.345223766276398 * 0.105263157894737 * 0.22985842985843 * 0.944444444444444 = 0.003110827550908 Tour Guide + Shark + Shark/Reborn + Foolish + Rat/Rabbit qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Foolish 3. Rat/Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,3,4,1) * H(37,1,3,1) * H(36,5,2,1) = 0.394331983805668 * 0.345223766276398 * 0.290659080132764 * 0.0810810810810811 * 0.261904761904762 = 0.0008402519133178142 Tour Guide + Foolish + Shark x2 + Shark/Reborn qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Foolish 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,2) * H(36,2,2,1) = 0.394331983805668 * 0.128205128205128 * 0.0246562351825508 * 0.10952380952381 = 0.0001365220201785293 Foolish + Reborn + Shark/Hunter/Rabbit/Magician + Tour Guide qualifies for... 1. Tour Guide + Reborn 2. Tour Guide + Foolish 3. Foolish + Reborn + Shark/Hunter/Rabbit/Magician P(hand) = H(40,1,6,1) * H(39,1,5,1) * H(38,10,4,1) * H(37,3,3,1) = 0.15 * 0.128205128205128 * 0.722617354196301 * 0.22985842985843 = 0.0031942248158464 Tour Guide + Shark + Hunter + Magician + (not opening the 2nd Hunter) qualifies for... 1. Tour Guide + Shark 2. Tour Guide + Hunter 3. Tour Guide + Magician P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,2,4,1) * H(37,3,3,1) * (1 - H(36,1,2,1)) = 0.394331983805668 * 0.345223766276398 * 0.20199146514936 * 0.22985842985843 * 0.944444444444444 = 0.0059694258409315 Tour Guide + Shark + Hunter + Rat/Rabbit + Shark/Reborn qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Hunter 3. Rat/Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,2,4,1) * H(37,5,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.345223766276398 * 0.20199146514936 * 0.361647361647362 * 0.161904761904762 = 0.0016100547060967 Tour Guide + Sharkx2 + Hunter + Shark/Reborn qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Hunter 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,3,5,2) * H(37,2,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.0382974067184589 * 0.157657657657658 * 0.161904761904762 = 0.0003854837390695822 Tour Guide + Shark + Hunter + Reborn + Foolish qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Hunter 3. Foolish + Reborn + Shark/Hunter P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,2,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.345223766276398 * 0.20199146514936 * 0.0810810810810811 * 0.0555555555555556 = 0.0001238633252021221 Tour Guide + Shark + Magician + Shark/Reborn + Rat/Rabbit qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Magician 3. Rat/Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,3,4,1) * H(37,3,3,1) * H(36,5,2,1) = 0.394331983805668 * 0.345223766276398 * 0.290659080132764 * 0.22985842985843 * 0.261904761904762 = 0.0023820474875962 Tour Guide + Sharkx2 + Shark/Reborn + Magician qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Magician 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,3,5,2) * H(37,2,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.0382974067184589 * 0.157657657657658 * 0.161904761904762 = 0.0003854837390695822 Tour Guide + Shark + Magician + Foolish + Reborn qualifies for... 1. Tour Guide + Shark/Reborn 2. Tour Guide + Magician 3. Foolish + Reborn + Shark/Magician P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,3,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.345223766276398 * 0.290659080132764 * 0.0810810810810811 * 0.0555555555555556 = 0.0001782352543401425 Tour Guide + Rat/Rabbit + Sharkx2 + Shark/Reborn qualifies for... 1. Tour Guide + Shark/Reborn 2. Rat/Rabbit + Shark + Shark/Reborn 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,5,5,1) * H(38,3,4,2) * H(36,2,2,1) = 0.394331983805668 * 0.516712779870675 * 0.0246562351825508 * 0.10952380952381 = 0.0005502328459680653 Tour Guide + Rat/Rabbit + Shark + Reborn + Foolish qualifies for... 1. Tour Guide + Shark/Reborn 2. Rat/Rabbit + Shark + Reborn 3. Foolish + Reborn + Rabbit/Shark P(hand) = H(40,3,6,1) * H(39,5,5,1) * H(38,3,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.516712779870675 * 0.290659080132764 * 0.0810810810810811 * 0.0555555555555556 = 0.0002667731562470593 Tour Guide + Shark x2 + Reborn + Foolish qualifies for... 1. Tour Guide + Shark/Reborn 2. Shark x2 + Reborn 3. Foolish + Reborn + Shark P(hand) = H(40,3,6,1) * H(39,3,5,2) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.0382974067184589 * 0.0810810810810811 * 0.0555555555555556 = 0.00006802654218874969 Tour Guide/Rat + Foolish + Shark + Hunter + Magician + (not opening the 2nd Hunter) qualifies for... 1. Tour Guide/Rat + Foolish 2. Shark + Hunter 3. Shark + Magician P(hand) = H(40,6,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,2,3,1) * H(36,3,2,1) * (1 - H(35,1,1,1)) = 0.649616765406239 * 0.128205128205128 * 0.290659080132764 * 0.157657657657658 * 0.161904761904762 * 0.971428571428571 = 0.0006002498797187291 Tour Guide + Foolish + Shark + Hunter + Rabbit + Shark/Reborn qualifies for... 1. Tour Guide + Foolish 2. Shark + Hunter 3. Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,2,3,1) * H(36,3,2,1) * H(35,3,1,1) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.157657657657658 * 0.161904761904762 * 0.0857142857142857 = 0.00003214986830607565 Rat + Foolish + Shark + Hunter + Shark/Reborn + (not opening the 2nd Hunter) qualifies for... 1. Rat + Foolish 2. Shark + Hunter 3. Rat + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,2,3,1) * H(36,3,2,1) * (1 - H(35,1,1,1)) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.157657657657658 * 0.161904761904762 * 0.971428571428571 = 0.0003643651741355239 Tour Guide/Rat + Foolish + Hunter + Shark x2 + Shark/Reborn qualifies for... 1. Tour Guide/Rat + Foolish 2. Shark + Hunter 3. Shark x2 + Shark/Reborn P(hand) = H(40,6,6,1) * H(39,1,5,1) * H(38,2,4,1) * H(37,3,3,2) * H(35,2,1,1) = 0.649616765406239 * 0.128205128205128 * 0.20199146514936 * 0.0132561132561131 * 0.0571428571428571 = 0.00001274306207276905 Tour Guide + Foolish + Shark + Magician + Rabbit + Shark/Reborn qualifies for... 1. Tour Guide + Foolish 2. Shark + Magician 3. Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,1) * H(36,3,2,1) * H(35,3,1,1) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.22985842985843 * 0.161904761904762 * 0.0857142857142857 = 0.00004687319575073552 Rat + Foolish + Shark + Magician + Shark/Reborn qualifies for... 1. Rat + Foolish 2. Shark + Magician 3. Rat + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.22985842985843 * 0.161904761904762 = 0.0005468539504252478 Tour Guide/Rat + Foolish + Magician + Shark x2 + Shark/Reborn qualifies for... 1. Tour Guide/Rat + Foolish 2. Shark + Magician 3. Shark x2 + Shark/Reborn P(hand) = H(40,6,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,3,3,2) * H(35,2,1,1) = 0.649616765406239 * 0.128205128205128 * 0.290659080132764 * 0.0132561132561131 * 0.0571428571428571 = 0.00001833684753663713 Rat + Foolish + Sharkx2 + Shark/Reborn qualifies for... 1. Rat + Foolish 2. Rat + Shark + Shark/Reborn 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,2) * H(36,2,2,1) = 0.394331983805668 * 0.128205128205128 * 0.0246562351825508 * 0.10952380952381 = 0.0001365220201785293 Rabbit + Foolish + Sharkx2 + Shark/Reborn + Tour Guide qualifies for... 1. Tour Guide + Foolish 2. Rabbit + Shark + Shark/Reborn 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,2) * H(36,2,2,1) * H(35,3,1,1) = 0.394331983805668 * 0.128205128205128 * 0.0246562351825508 * 0.10952380952381 * 0.0857142857142857 = 0.00001170188744387394 Rat + Foolish + Shark + Reborn + (not opening both Hunters) qualifies for... 1. Rat + Foolish 2. Rat + Shark + Reborn 3. Foolish + Reborn + Shark P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,1,3,1) * (1-H(36,2,2,2)) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.0810810810810811 * 0.998412698412698 = 0.0011895451273248 Rabbit + Foolish + Shark + Reborn + Tour Guide qualifies for... 1. Tour Guide + Foolish 2. Rabbit + Shark + Reborn 3. Foolish + Reborn + Shark/Rabbit P(hand) = H(40,3,6,1) * H(39,1,5,1) * H(38,3,4,1) * H(37,1,3,1) * H(36,3,2,1) = 0.394331983805668 * 0.128205128205128 * 0.290659080132764 * 0.0810810810810811 * 0.161904761904762 = 0.0001928992098364535 Shark + Hunter + Magician + Rat/Rabbit + Shark/Reborn + (not opening the 2nd Hunter) qualifies for... 1. Shark + Hunter 2. Shark + Magician 3. Rat/Rabbit + Shark + Shark/Reborn P(hand) = H(40,3,6,1) * H(39,2,5,1) * H(38,3,4,1) * H(37,5,3,1) * H(36,3,2,1) * (1 - H(35,1,1,1)) = 0.394331983805668 * 0.242914979757085 * 0.290659080132764 * 0.361647361647362 * 0.161904761904762 * 0.971428571428571 = 0.0015836382820859 Sharkx2 + Hunter + Magician + Shark/Reborn + (not opening the 2nd Hunter) qualifies for... 1. Shark + Hunter 2. Shark + Magician 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,2) * H(38,2,4,1) * H(37,3,3,1) * H(36,2,2,1) * (1 - H(35,1,1,1)) = 0.0536437246963556 * 0.20199146514936 * 0.22985842985843 * 0.10952380952381 * 0.971428571428571 = 0.0002649914088355732 Shark + Hunter + Magician + Foolish + Reborn + (not opening the 2nd Hunter) qualifies for... 1. Shark + Hunter 2. Shark + Magician 3. Foolish + Reborn + Shark/Hunter/Magician P(hand) = H(40,3,6,1) * H(39,2,5,1) * H(38,3,4,1) * H(37,1,3,1) * H(36,1,2,1) * (1 - H(35,1,1,1)) = 0.394331983805668 * 0.242914979757085 * 0.290659080132764 * 0.0810810810810811 * 0.0555555555555556 * 0.971428571428571 = 0.0001218310798967077 Sharkx2 + Hunter + Rat/Rabbit + Shark/Reborn qualifies for... 1. Shark + Hunter 2. Rat/Rabbit + Shark + Shark/Reborn 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,2) * H(38,2,4,1) * H(37,5,3,1) * H(36,2,2,1) = 0.0536437246963556 * 0.20199146514936 * 0.361647361647362 * 0.10952380952381 = 0.0004291862370558371 Shark + Hunter + Rat/Rabbit + Reborn + Foolish qualifies for... 1. Shark + Hunter 2. Rat/Rabbit + Shark + Shark/Reborn 3. Foolish + Reborn + Shark/Hunter/Rabbit P(hand) = H(40,3,6,1) * H(39,2,5,1) * H(38,5,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.242914979757085 * 0.445641129851656 * 0.0810810810810811 * 0.0555555555555556 = 0.0001922864107668268 Shark x2 + Hunter + Reborn + Foolish qualifies for... 1. Shark + Hunter 2. Shark x2 + Reborn 3. Foolish + Reborn + Shark + Hunter P(hand) = H(40,3,6,2) * H(38,2,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.0536437246963556 * 0.20199146514936 * 0.0810810810810811 * 0.0555555555555556 = 0.00004880889435804408 Sharkx2 + Magician + Rat/Rabbit + Shark/Reborn qualifies for... 1. Shark + Magician 2. Rat/Rabbit + Shark + Shark/Reborn 3. Shark x2 + Shark/Reborn P(hand) = H(40,3,6,2) * H(38,3,4,1) * H(37,5,3,1) * H(36,2,2,1) = 0.0536437246963556 * 0.290659080132764 * 0.361647361647362 * 0.10952380952381 = 0.0006175848904113325 Shark + Magician + Rat/Rabbit + Reborn + Foolish qualifies for... 1. Shark + Magician 2. Rat/Rabbit + Shark + Reborn 3. Foolish + Reborn + Shark/Magician/Rabbit P(hand) = H(40,3,6,1) * H(39,3,5,1) * H(38,5,4,1) * H(37,1,3,1) * H(36,1,2,1) = 0.394331983805668 * 0.345223766276398 * 0.445641129851656 * 0.0810810810810811 * 0.0555555555555556 = 0.0002732719035897922 Shark x2 + Magician + Reborn + Foolish 1. Shark + Magician 2. Shark x2 + Reborn 3. Foolish + Reborn + Shark/Magician P(hand) = H(40,3,6,2) * H(38,3,4,1) * H(37,1,3,1) * H(36,1,2,10) = 0.0536437246963556 * 0.290659080132764 * 0.0810810810810811 * 0.0555555555555556 = 0.00007023439493305392 Shark x2 + Rabbit + Reborn + Foolish 1. Rabbit + Shark + Reborn 2. Shark x2 + Reborn 3. Foolish + Reborn + Shark/Rabbit P(hand) = H(40,3,6,2) * H(38,3,4,1) * H(37,1,3,1) * H(36,1,2,10) = 0.0536437246963556 * 0.290659080132764 * 0.0810810810810811 * 0.0555555555555556 = 0.00007023439493305392 [u]New total[/u] = 0.4193341676178323 [b]Part 4C: Calculating the Overlap From the Overlap of Our Overlap[/b] [img]http://i2.kym-cdn.com/photos/images/newsfeed/000/001/123/xzibit-wtf.jpg[/img] Xzibit does not like the sound of that idea, and neither do I. There are some hands that qualify for 4 or more combos, but they are extremely improbable (like 0.01% or less). I'm not going to waste even more of my time calculating this (which would be subtracted from the total since (-1)^3 = -1). I'm just going to say that our [u]final probability is somewhere between 41% and 42%[/u]. [b]Part 5: Hand Traps?[/b] Yes, there is a chance that your opponent opens Maxx "C" or Veiler and shuts down your combo for the turn. Here's a table showing the odds that they DON'T open a hand trap based on the number that you think they run. Runs 1 = 0.875 Runs 2 = 0.762820512820513 Runs 3 = 0.662449392712551 Runs 4 = 0.572929204508152 Runs 5 = 0.49335570388202 Runs 6 = 0.42287631761316 If you're trying to figure out the probability that you open combo[i] and [/i]your opponent doesn't have a hand trap, just multiply the two probabilities together. Ex: You think your opponent runs 3 hand traps = 0.4193341676178323 * 0.662449392712551 = 0.2777876646820561 overall. [b]Conclusion[/b] - Wind-Ups are not reliable as a psuedo-FTK deck. Whether Wind-Ups are successful or not is going to be more dependent on their ability to combo off midgame or win without comboing at all. - Wind-Ups have a lot of f***ing combos.[/quote] Link to comment Share on other sites More sharing options...
Welche the crab Posted January 19, 2012 Report Share Posted January 19, 2012 Saw this on DGz. Very impressive. Link to comment Share on other sites More sharing options...
Premier Alexander Romanov Posted January 19, 2012 Report Share Posted January 19, 2012 @_@ Could this be summarized? Link to comment Share on other sites More sharing options...
Welche the crab Posted January 19, 2012 Report Share Posted January 19, 2012 "[color=#9BA2A9][font=tahoma, helvetica, arial, sans-serif][size=3]- Wind-Ups are not reliable as a psuedo-FTK deck. Whether Wind-Ups are successful or not is going to be more dependent on their ability to combo off midgame or win without comboing at all.[/size][/font][/color] [color=#9BA2A9][font=tahoma, helvetica, arial, sans-serif][size=3]- Wind-Ups have a lot of f***ing combos."[/size][/font][/color] Link to comment Share on other sites More sharing options...
Expelsword Posted January 19, 2012 Report Share Posted January 19, 2012 This was a waste of time, but I admire your spirit. You should just feel it out instead of thinking Link to comment Share on other sites More sharing options...
TheTurtleOnceCalledGod Posted January 19, 2012 Report Share Posted January 19, 2012 Spread this across the interwebz, such that the prices of the wind-ups go down such that they can be done for non-competitive fun builds. They still are not as good as inzectors, knew it, even without the fancy statistics. Link to comment Share on other sites More sharing options...
Just Crouton Posted January 19, 2012 Report Share Posted January 19, 2012 I'm going to believe this because "Allen C. Pennington" sounds like the name of someone who's college educated. [quote name='Charlotte The Witch' timestamp='1327016046' post='5771774'] @_@ Could this be summarized? [/quote] [media]http://www.youtube.com/watch?v=EarU--5cYOE[/media] Link to comment Share on other sites More sharing options...
evilhorus Posted January 19, 2012 Report Share Posted January 19, 2012 Allen C. Pennington sounds like he's related to Buzz Killington http://www.youtube.com/watch?v=XFcqGGMPc3k Link to comment Share on other sites More sharing options...
Expelsword Posted January 20, 2012 Report Share Posted January 20, 2012 Ok, I admit it. I wish my Statistics projects were this cool. Link to comment Share on other sites More sharing options...
Greiga Posted January 20, 2012 Report Share Posted January 20, 2012 I now have respect for Xzibit. And a 40% chance is actually pretty good for a FTK. Link to comment Share on other sites More sharing options...
.Rai Posted January 20, 2012 Report Share Posted January 20, 2012 [quote name='GreigaBeastDS' timestamp='1327021306' post='5771912'] I now have respect for Xzibit. And a 40% chance is actually pretty good for a FTK. [/quote] But Empty Jar is still 70%. Link to comment Share on other sites More sharing options...
Wizarus Posted January 20, 2012 Report Share Posted January 20, 2012 [quote name='.Rai' timestamp='1327021522' post='5771918'] But Empty Jar is still 70%. [/quote] The FTK is just the icing on the cake. Wind-Ups have no problem using their unlimited card advatange to swarm and swing for the game. Link to comment Share on other sites More sharing options...
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