### Brain Teasers

# Snapoker Tie-Breakers

The card game Snapoker is a very complex game for four players, requiring the use of two decks of cards with all odd spades, even hearts, prime diamonds (including aces) and non-prime clubs (including aces) removed. Note that jacks are 11, queens are 12, kings are 13. Two jokers are added to the deck and are each worth 15. The cards are dealt among the four players. A hand starts when the dealer shouts "Let's Snapoker!" Following a frenetic minute of randomly throwing all cards onto the table, and at the dealer's call of "Heeeeeeere, piggy, piggy, piggy!" players are required to grab as many cards as they can. Once all cards have been grabbed, the total value of the cards in each player's hand is added up. Points (4, 3, 2 and 1) are awarded to players on each hand, with the highest card total receiving maximum points. In the event of a tie, the player who can drink a glass of milk through their nose the quickest will receive the greater points. A running score is kept throughout the game. The game is over when someone reaches a total of 518 points or when a fight breaks out, which is a common occurrence.

Assume that all four players are equally matched at card-grabbing such that, following the grab, the cards are evenly distributed amongst all four players. What is the lowest card total at which you can be assured you will not be required to drink a glass of milk through your nose in order to break a tie for the maximum 4 points?

Assume that all four players are equally matched at card-grabbing such that, following the grab, the cards are evenly distributed amongst all four players. What is the lowest card total at which you can be assured you will not be required to drink a glass of milk through your nose in order to break a tie for the maximum 4 points?

### Answer

If all four players hold the same number of cards, the lowest card total that would never require a tie-break is 142.If all four players hold the same number of cards, the highest single hand card total at which a tie-breaker might be needed is 141. In this case, the two players who would be required to drink milk through their noses would each have had a hand consisting of a joker and two 8s, 9s, 10s, jacks, queens and kings. Any score above 141 can not be duplicated in a single hand of Snapoker, thus making 142 the lowest total to which a tie-breaker will not need to be applied.

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