The rain was still falling in Wales, and Alice and Bob were terribly bored of having to stay inside the caravan. With just a deck of cards to entertain them they had played all of the card games in their repertoire – several times over.
Suddenly Alice had an idea for another game they could play. Putting aside 21 cards, including the aces (“Too ambiguous,” she said…) and the two jokers, she dealt out two hands – one for her and one for Bob.
To start the game off, Alice laid down three cards – the jack of diamonds, the three of hearts and the four of clubs:
“So that scores me 24 points,” she said with a flourish, before replenishing her hand.
“Oh,” said Bob, “so we’re playing properly then? In which case, I’ll play these…” Bob laid three of his own cards on the table (three of diamonds, six of hearts, king of clubs):
“That’s 26, I think you’ll find,” Bob said smugly, picking up three more cards.
Alice grimaced. “Fine, well I’ll do this then…” This time Alice laid down five cards (six of spades, four of diamonds, five of diamonds, king of spades, five of spades):
“25 points,” she announced, collecting 5 more cards from the deck.
Bob smirked. “Oh Alice, I hate to do this to you again…” he said, laying down five cards himself (two of spades, two of hearts, three of spades, king of hearts, five of clubs):
“That’s 33 points – read ‘em and weep…” Bob sat back with his arms behind his head, thoroughly gloating. It was with some discomfort therefore that when he looked across at Alice he saw she was smiling and shaking her head.
“Oh Bob,” she said. “Oh Bobby Bobby Bob Bob… You’ve made two big mistakes there. For starters, you could have got yourself 7 points more if you’d played the five of clubs first. But more importantly, because you’ve played those cards, I can play these…” Alice laid down five cards (queen of spades, three of clubs, two of diamonds, two of clubs, five of hearts):
“…and that scores me 84 points.”
QUESTION: Make sense of the cards played and the rules of this game to tell me – what game are Bob and Alice playing here? Furthermore, explain Bob’s double-mistake. Please include an explanatory diagram in your solution.