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## Lucky Cards

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #32515 Fun: (2.68) Difficulty: (2.36) Category: Probability Submitted By: Gizzer Corrected By: Radioguy

After an intense week of play-downs, the National Draw Poker Championship has come down to the final hand between two fierce competitors: Tex Holden, the defending champion; and Rae Sonheim, the unknown of the tournament, who has amazed the spectators with her cool bluffs. In what is the first of a number of amazing coincidences of the night, both players have an equal stake.

Although Tex kept his poker face intact, his excitement mounted as he examined each card he was dealt. The first card he received was his lucky card, the King of Clubs, which he considered a very good omen. Perhaps it was, as each of the next four cards were of the same value as each other, giving Tex one of the best possible hands: four of a kind.

Meanwhile, across the table, Rae waited until all the cards were dealt before looking at her cards. She, too, was pleasantly surprised as she had received four of a kind as well, along with the Queen of Spades, which is her lucky card.

Each player, believing he or she had an unbeatable hand, prepared to end the tournament then and there with a careful strategy designed to win all the chips.

After many rounds of raises and counter-raises, at long last, all the chips were riding on this one hand. The better hand would take the pot, and the trophy.

Tex, having had his last raise called, gleefully displayed his hand first. All eyes turned to Rae, but, as usual her face showed no emotion.

Before the outcome is revealed, can you determine the probability that Tex has retained his title?

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