MATHEMATIC - PROBABILITY IN YUGIOH

Now we shall see what ban list can do.

Assume your deck size is 40. If you run 3 copies of X card, what's the probability that you draw at least 1 copy in your opening turn?

Let probabilty of drawing at least 1 copy = p(A),

Case 1: drawing 1 copy
P(A1) = (3C1)(37C5)/(40C6)=0.3407

Case 2: drawing 2 copies
P(A2) = (3C2)(37C4)/(40C6) =0.0516

Case 3: drawing 3 copies
P(A3) = (3C3)(37C3)/(40C6) =0.0020

Hence P(A) = 0.3407 + 0.0516 + 0.0020 = 0.3943(40%)


If you run 2 copies of X card,
Let probability of drawing at least 1 copy = P(B)

Case 1: drawing 1 copies
P(B1) = (2C1)(38C5)/(40C6) = 0.2615

Case 2 : drawing 2 copies
P(B2) = (2C2)(38C4)/(40C6) = 0.0192

Hence P(B) = 0.2615 + 0.0192 = 0.2808(28%)


If you run 1 copy of X card,
Let probability of drawing at least 1 copy = P(C)

P(C) = (1C1)(39C5)/(40C6) = 0.15(15%)


Now it's clear that limiting does make difference...