This is probably the toughest puzzle yet so I'll just let the
last puzzle keep running a bit longer. Respond to this thread if the puzzle wording is at all unclear.
Face-Up Poker
Quote:
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Originally Posted by Rules of Face Up Poker:
The Game
Face-Up Poker is played with two players and a standard 52-card deck. Cards are not dealt at random as in standard poker, instead each player may select any cards he wants from a face-up deck. Each player may always see what the other has drawn. Hands are valued as in standard draw poker.
The Play
Play begins with the first player selecting any 5 cards of his choosing from the deck. The second player does the same with the remaining cards. The first player then discards any number of cards from his hand to the discard pile (just as in draw poker) and then selects that same number of new cards from the deck. The second player does the same.
The Winner
The player with the highest poker hand wins. If both players have the same hand the game is a draw.
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Ricky and Steve are playing one another in a game of Face Up poker. Ricky is first to act and Steve second. For his starting hand Ricky has 2,598,960 different choices, only some of which would positively secure him the best possible outcome.
So:
Let
X = The number of possible starting hands that Ricky could select in order to secure himself the best possible outcome.
Let
Y = The highest 5-card card total of all the possible starting hands that Ricky could select in order to secure himself the best possible outcome. (Ignore suits and count Jacks as 11, Queens as 12, Kings as 13, and Aces as 1. For example, 2C 7D 8S KC AH would be a card total of 2+7+8+13+1=31.)
X * Y = ?