Hearts: Answer to question 10

Q: I win the same number of point scoring cards in each hand, and come last in the game. How small could that number of point scoring cards be, if my final score is less than 20 more than the winner's score?

A: 1 scoring card per hand

As in question 8, I must score at least 7 per hand (on average) to come last. I can do this by alternating, with the Queen of Spades (13 points) in one hand and a single heart in the next (1 point) - 14 points in two hands, or 14 x 14 / 2 = 98 in 14 hands. Then I win another Queen of Spades in the 15th hand for a total score of 111. The others' scores can easily be arranged to end up at only 93 each after 15 hands.