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The Caller · The Fourth Evening: The Prize Table

By the fourth evening Hạnh had begun to have ideas, which her mother said was the most dangerous thing that could happen to anyone in the family.

The idea came to her on the walk to the Green. The tent had been full every night, but the fair had six nights, and the fourth and fifth were always the quiet ones, her uncle said, when the novelty had worn off and the big last night was not yet here. People stayed home on the fourth night. The lantern fund took less.

What the tent needed, Hạnh decided, was a reason to come.

The prizes were all donations. That was how it had always been done. The fruit stall gave mandarins, the bakery gave a box of candied fruit, the noodle woman gave a voucher for two bowls, somebody's aunt gave a hand-knitted scarf. They sat on a folding table at the side of the tent, under a string of red lanterns, and the winner of each game chose one. They were nice prizes. They were not the kind of prizes that made people walk across the Green on a cold night.

A rice cooker would be. There was a good one in the window of the electrical shop by the market, with a little screen and a voice that told you when the rice was ready, and it cost six hundred thousand đồng. Hạnh had seen people stop to look at it.

She could see it already: the rice cooker on a little stand by the tent flap, with a ribbon round it, and a hand-painted sign. People on the path would slow down, the way they slowed down outside the electrical shop. They would come in to look and stay to play. Children would drag their parents in. The fourth night would be the fullest of the fair, and the lantern fund would be so pleased that it would ask her to call again next year, and the year after that, and she would be the caller who had saved the quiet nights.

She had the whole thing worked out by the time she reached the fountain. She had even chosen the colour of the ribbon.

So when she got to the tent, she found the lantern woman, who kept the fund's tin, and the hardware man, who had turned the cage every night since the third, and Ông Sáu with his tea, and she told them.

"One big prize," she said. "The rice cooker. Put it on a stand by the door. People will see it from the path. We'll pay for it from the fund, and the fund will get it back, because more people will come."

The hardware man said that was a good idea. The lantern woman frowned, but she frowned at most things.

"How many cards in the big game, on a quiet night?" said Ông Sáu.

"About fifty," said Hạnh. "If the rice cooker brings people, more."

"And a card for the big game is a gift of ten thousand to the lanterns," said her uncle. "So fifty cards bring in how much?"

That was easy. "Five hundred thousand."

"And the rice cooker costs?"

"Six hundred thousand." Hạnh heard it as she said it, and kept going anyway. "But more people will come."

"Perhaps," said Ông Sáu. "Let us say fifty come. Now here is my question. If you took the rice cooker and shared it out, fairly, among all fifty cards, how much would each card get back?"

Hạnh looked at him. "You can't share out a rice cooker."

"No," he agreed. "But you can share out what it costs. One card wins it. Forty-nine do not. On average, each card gets back the prize divided by the number of cards. Six hundred thousand among fifty."

She worked it out. "Twelve thousand."

"For a card that costs?"

"Ten thousand."

The lantern woman stopped frowning and started writing on the back of her hand.

Hạnh felt the idea come apart in her hands, the way a paper lantern comes apart in rain. If every card, on average, gave back twelve thousand for ten thousand paid, then the people in the tent would be playing with the lantern fund's money. The more who came, the more the fund would lose. The fair would buy a rice cooker so that somebody could take it home, and the lanterns, which were the whole point, would pay for it.

"So with that prize," said Hạnh slowly, "every card gives back more than it costs. On average. The fund loses a hundred thousand even if fifty come, and more if more come."

"And with the prizes we have?" said Ông Sáu.

They looked at the prize table. The lantern woman had a list. She had a list of everything. The mandarins, the candied fruit, the voucher, the scarf, a set of tea bowls, a bag of sticky rice. Priced at what they would cost in the market, together they came to about three hundred thousand.

"Three hundred thousand among fifty cards," said Hạnh. "Six thousand a card. Each card gives back six thousand, on average, and leaves four thousand for the lanterns."

"Which is why," said the lantern woman, who had finished the sum on her hand at the same time, "it has always been done with donations."

Hạnh turned to the committee and said it plainly, because her uncle was looking at her in the way that meant it was her turn.

"The rice cooker would make the lanterns pay for the fun," she said. "The donated prizes give back about six thousand of every ten thousand, and the rest buys the lanterns. That's a fair price. People know they're giving to the lanterns. They come for the evening, not for the rice cooker."

The hardware man scratched his head. "Seems a shame," he said. "It's a good rice cooker."

"Then buy it for your wife," said the lantern woman, and the tent, which had begun to fill up behind them, laughed.

They kept the prize table as it was. Before the first game, Ông Sáu took the chalk and wrote on the board, in his neat teacher's hand, two lines side by side:

A card: 10,000 to the lanterns. The prize table: given by your neighbours.

It was a quiet night, as he had said. Forty-six cards in the big game. The voucher for two bowls of noodles went to the chess men in the front row, who had won together on their shared card and argued for ten minutes about who would get the second bowl.

Walking home, Hạnh asked her uncle whether he had ever wanted a big prize, in thirty years.

"Once," said Ông Sáu. "In nineteen ninety-six. A bicycle."

"What happened?"

"Exactly what you worked out," he said. "Only I worked it out afterwards."

The question for your own table

When you pay for a raffle ticket, a lottery, or a prize draw, do you know what share of the money comes back as prizes? Where could you find out?

Something to do

Next time there is a raffle at school or a fair, ask how many tickets are sold and what the prizes are worth. Work out together what each ticket gives back, on average.

Across the table

The story in three lines. On a quiet night of the fair Hạnh wants to buy a 600,000-đồng rice cooker from the lantern fund as the big prize, to draw a crowd. Her uncle asks what each of fifty cards would give back on average: 12,000 for a 10,000 card. Hạnh sees the lanterns would pay for the fun, and the committee keeps the donated prizes.

One question to ask. "If you shared the prize out among every ticket, what would each one get?"

One thing to do at the table. Invent a raffle: ten tickets at a price you choose and a prize you choose. Work out what each ticket gives back on average. Change the prize until it feels fair for the people and for the cause.

The grown-up layer. What a ticket is worth on average is the prize shared among all the tickets, its expected value. A prize worth more than everything taken in makes every ticket worth more than its price, so somebody else is paying. Fair price and prize are set together. Hạnh wanted a crowd; her uncle let the sum show what the crowd would cost. This is the fourth lesson of the Whetstone course Thinking in Odds.

The Honest Page

  • Known. Fifty cards at 10,000 đồng bring in 500,000. A 600,000 prize shared among them is 12,000 a card, more than each costs; a 300,000 prize is 6,000 a card.
  • Known. The average a ticket or a bet pays back over many plays is called its expected value: the prize times the chance of winning it. (source)
  • Disputed. Why people buy a ticket whose expected value is less than its price. One explanation is that they do not know the odds; another is that the thrill and the hope are worth something to them, which makes the choice sensible after all. (source)
  • Legend. That a big enough prize always pays for itself by bringing a bigger crowd. It is said at every fair; the sum depends on how many come.

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