A researcher wants to determine whether a proclaimed psychic really has any special abilities.
Four decks of regular playing cards are shuffled together so that the researcher has $208$ cards in a pile. Half the cards are colored red, and the other half are black. As the researcher looks at each card, the blindfolded psychic calls out the card’s color.
At the $5\%$ level of significance, what is the least number of cards the mind reader must call correctly to show that he is not merely guessing?