As surprising as it may seem at first thought, the answer is 2/3, NOT 1/2.  You can confirm this experimentally by clicking on the buttons below to simulate a large series of trials: (requires a JavaScript-enabled browser):

Card Number (1=Black1/Black2, 2=White1/White2, 3=Black/White):
Top of Card:
Bottom of Card:
Total Draws:
Draws in Which Top and Bottom Colors Match:
Draws in Which Top and Bottom Colors Differ:
Percentage of Draws in Which Top and Bottom Colors Match:

Surprised at the result?  Most people adamantly assert (even after hours of contemplating the problem) that the answer is 50%, reasoning that "there are two possibilities: the underside is either BLACK, or WHITE, thus the odds are 50/50 that the underside matches the top".  However, they are confusing possibilities with probabilities.  Yes, there are two possibilities (i.e., two possible outcomes), but the probabilities of each are NOT equal.  Give it some more thought, before pressing the button below for an explanation.

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