Riddle Keeper

You have in front of you a large jar of black and white jelly beans. You repeatedly reach in and pull out two random beans. If you pull out two beans of the same color, you put one white bean back in, if they are a different color, you put one black bean back in.

Assume that you have sufficient number of extra black and white beans to do this trades — if your first pick is two black beans, you reach into your “extras” pile for a white and put it back into the jar.

As you repeat this process, eventually there is only one bean left in the jar. What color will it be? More specifically, what is the minimum amount of information you will need about the contents of the jar in order to determine the color of the final bean?

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