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Allen C. Pennington's Wind-Up Math


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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]

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"[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]

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