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Spark & Whetstonethe grown-up commons

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Small Stakes: Fifteen Buttons

The power went at ten past eight on a Tuesday in their third week in the flat, and it did not come back.

It was not only them. Kezia went to the window and saw that the launderette below was dark, and the chip shop opposite, and the streetlights all the way down to the Green, where the pond showed up faintly silver against the black grass. Somewhere a dog was barking about it. The fridge gave a long, sad sigh and went silent.

"Candles," said Sim.

"We don't own candles," said Kezia.

"Everybody owns candles."

"We've lived here three weeks," said Kezia. "We own a kettle, two mugs, a frying pan your mum gave you, and the drawer."

The drawer was the kitchen drawer to the left of the cooker. It had come with the flat. When they moved in it had already been full of things left by people who had lived there before, and neither of them had had the heart to empty it. Over three weeks they had added to it. It was the place where things went when you did not know where else they went.

Sim found it by feel and pulled it out entirely, and they took it to the table and went through it by the light of his phone, which was on eleven per cent.

There was a ball of garden string. There was a pencil, a very short one, chewed. There was a takeaway menu for a pizza place that no longer existed. There were two birthday candles, one blue and one pink, which they lit and stood in a saucer, where they gave a light about the size of a thumbnail. There were four spoons that did not match anything. And at the very back, in a small glass jar that had once held paprika, there were buttons.

Kezia tipped them onto the table. She counted them in the candlelight. Fifteen.

"Right," said Sim, turning his phone off to save it. "Well. That's the evening sorted."

"Doing what?"

"I don't know," said Sim. "Something with buttons. We'll play for a pound a game. Make it interesting."

Kezia looked at him across the two tiny flames.

"No," she said. "No money."

"It's a pound."

"It's always a pound," said Kezia. "And then it's always about the pound." She had grown up in a house where the adults played cards for coins on Friday nights, and she had liked it, mostly, and she had also watched her uncle stop laughing about halfway through every evening. "We'll play for the washing-up. Loser does it. That's the stakes."

Sim considered this. The washing-up was, at that point in their friendship, a genuinely serious matter.

"Done," he said. "What's the game?"

Kezia had a game. She had learned it at primary school, though she could not have said from whom, and she had taught it to children since, in wet playtimes, with pencils or lolly sticks or crayons.

"Fifteen buttons in a row," she said, lining them up by the candles. "We take turns. On your turn you take one button, or two, or three. Your choice. Whoever has to take the last button loses."

"That's it?"

"That's it."

They played. The first game was over in about a minute. Sim took three, Kezia took one, Sim took two, Kezia took three, and suddenly there were only a few buttons left and Sim was frowning at them in the candlelight, and he took two, and Kezia took one, and Sim was left looking at the last button.

"Washing-up," said Kezia.

"Again," said Sim.

They played again, and again. It was absurd how much fun it was. There was nothing to it, fifteen buttons and a saucer of birthday candles, and yet every game ended with somebody groaning or laughing, and every game they leaned closer over the table to watch each other decide. Kezia found she was watching Sim's face more than the buttons. He chewed his lip when he was thinking. He hummed when he thought he was winning. She had lived with him for three weeks and had not known either of those things.

"That's the point of small stakes," she said, when he asked why she was smiling. "Nobody's watching the money. So you watch each other."

It was a lovely theory. It lasted about forty minutes.

Sim had gone quiet. He was not humming. He had picked up the chewed pencil and was writing numbers on the back of the dead pizza menu, very small, by the light of the pink candle.

"Hang on," he said. "Hang on, hang on."

"What?"

"If there's one button left and it's your turn, you lose. Yes?"

"Yes."

"So you want to leave the other person one button," said Sim. "And if there are five, and it's their turn, then whatever they take, one or two or three, you can take enough to make four between you, and leave them one." He was writing faster. "And if you leave them nine, you can do the same and get them to five. And thirteen gets them to nine." He looked up. "Thirteen, nine, five, one. Leave them one of those, and you can't lose. Ever. From fifteen, you take two. Then you've left thirteen."

"You're making that up," said Kezia.

"Play me," said Sim.

She played him. He took two. She took one. He took three, which left nine. She tried everything. He won.

He won the next game. And the next. He won six in a row, and each one was exactly the same: he would take whatever made the total between them four, and the buttons would go down thirteen, nine, five, one, and Kezia would be left looking at the last button on the table, and Sim would say, very quietly, "Washing-up."

On the seventh game, she did not want to play.

It was strange. It was the same game. Same buttons, same candles, same flatmate. But it was not a game any more. It was a sum. She knew, before they started, exactly how it would end, and so did he, and there was nothing left to watch. Sim was not even pleased. He had stopped humming somewhere around the fourth win.

"It's broken," he said, a bit sadly, putting the pencil down. "I broke it."

"You solved it," said Kezia. "That's not the same. A solved game is just finished."

"Can you unfinish it?"

Kezia looked at the buttons. Then she pulled them all back into a row. Fifteen.

"New rule," she said. "You can take up to four."

Sim stared at her. Then he grabbed the pencil.

"No," said Kezia, covering the menu with her hand. "You've got to work it out while we're playing. That's the deal. Or it's the washing-up for a week."

So they played again, by the light of two birthday candles that were very nearly out, and this time Sim chewed his lip and lost twice before he started to see it, and Kezia won once by luck and once on purpose, and they argued about whether a game counted if the pink candle went out halfway through. And somewhere around midnight, the fridge shuddered and hummed back into life, and every light in the flat came on at once, and both of them shouted.

Neither of them got up to switch the big light off. They played one more game first.

The question for your own table

When a game stops being fun, is it because you've lost, or because you've solved it? What one rule would make it a game again?

Something to do

Put fifteen buttons, coins or dried beans in a row. Take turns taking one, two or three; whoever takes the last one loses. Play until one of you works out how always to win, and then change the rule to "up to four" and start again. Play for the washing-up, never for money.

Across the table

The story in three lines. A power cut in their third week in a first flat leaves Kezia and Sim with a drawer: string, a pencil, birthday candles and fifteen buttons. Kezia refuses to play for money ("then it's always about the pound") and teaches a button game for the washing-up instead. Sim solves it (leave thirteen, nine, five or one) and wins six in a row until it stops being a game; Kezia changes one rule and they have an evening again.

One question to ask. "Why did the game stop being fun when Sim started winning every time?" Then: "What does playing for nothing change?"

One thing to do at the table. Fifteen of anything in a row; take one, two or three; last one loses. When someone finds the winning pattern, let them explain it, then change the rule to "up to four."

The grown-up layer. The game is a version of Nim, and it can be solved: with take-up-to-three, leave one more than a multiple of four. Solving a game finishes it; changing one rule starts it again, which is the design habit behind TableForge's Shelf. Playing for nothing at all keeps the attention on the person opposite.

The Honest Page

  • Known. This is a version of Nim, one of the oldest studied games. Games like it can be solved: one player can always win with the right moves. (source)
  • Known. When you may take one, two or three and the last button loses, you want to leave one more than a multiple of four: thirteen, nine, five, one. From fifteen, take two.
  • Known. When you may take up to four, you want to leave one more than a multiple of five: eleven, six, one. From fifteen, take four.
  • Disputed. Where the name Nim comes from. It was named in 1901, perhaps from the German word nimm, 'take!'; nobody is sure. (source)
  • Legend. That the drawer in every first flat contains exactly fifteen buttons. Ours did.

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