Spades is the strongest suit in many card games.
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The probability of each suit in a standard deck of cards is 13 in 52, or 1 in 4, or 0.25.
The first card can be anything. That means that there are 51 cards left and 39 of them are not the same suit as the first one, therefore P(not same suit) = 39/51 = 13/17.
1/13
The minimum number of cards that must be dealt, from an arbitrarily shuffled deck of 52 cards, to guarantee that three cards are from some same suit is 9.The basis for 9 is that the first four cards could be from four different suits, the next four cards could be from four different suits, and the ninth card is guaranteed to match the suit of two of the previously dealt cards. The minimum number, without the guarantee, is 3, but the probability of that is only 0.052, or about 1 in 20.
5. Assuming the first four are all different suits, the 5th card must be a duplicate suit. If any prior to the 5th card is not a new suit, it is garunteed to be a duplicate of a prior suit.