The Caller · The Third Evening: Twice
The big game came at nine, the last of the night. Everybody stayed for it. The prize for the big game was always the best thing on the prize table, and on the third evening it was a red lacquer box of candied fruit, the kind that families put out for guests at Tết, donated by the bakery at the corner of the Green. People bought a fresh card for the big game even if they had been playing the same tired one all evening. There were forty-one cards in it that night. Hạnh counted them as they were handed in, because her uncle had told her to.
The early games had gone well. Hạnh's voice had settled into something she almost recognised as her own, and she had stopped reading the rhymes off the list for the numbers she knew best. The chess men in the front row had started joining in on the last word of each rhyme, under their breath, the way people do in church. When she sang eighty-eight, which had a rhyme about two fat snowmen, half the tent sang the last word with her, and she laughed in the middle of it and had to start again. Her uncle did not tell her off. He looked, if anything, pleased.
On the second night, the big game had been won by Cô Tám.
Cô Tám ran the flower stall by the fountain, and she was the loudest person Hạnh had ever met. She laughed at everything, including things that were not jokes, and when she won the big game on the second night she had stood on her chair and waved the prize, a basket of oranges, over her head until the young father at the back asked her, politely, to stop, because his baby was awake.
On the third night, at about a quarter past nine, with forty-one cards in play and the tent tight with people, Hạnh turned the cage and sang sixty-four, and Cô Tám shrieked.
She had filled her row. Again.
She was on her chair before Hạnh had put the ball down. The tent laughed, mostly. Some of it clapped. And from the back, under the clapping, Hạnh heard a man say, not quite quietly enough, "Two nights running. That's not luck. That's fixed."
It was the hardware man. He had his arms folded.
A few heads turned. Somebody said, "Shh." Somebody else said, "Well, he's got a point." And the laughter in the tent changed, the way milk changes in hot tea, into something slightly sour.
Hạnh felt it go. She was the caller. It was her cage, or at least it was in her hands. If people thought it was fixed, they would think she had fixed it, or her uncle had, for a friend. And Cô Tám was still on her chair, waving the red box, not noticing anything at all.
There was an easy way to make the sourness go. Hạnh could say, kindly, to the whole tent, that just to be fair, Cô Tám might sit out the big game tomorrow night, and give somebody else a chance. Cô Tám would not mind. She would laugh. Everyone would feel better. Hạnh opened her mouth to say it.
"How many cards in the big game?" said Ông Sáu.
He was sitting beside her with his tea, as he had every night. He asked it in his teacher's voice, the one that sounded like a question even when it was an answer.
"Forty-one," said Hạnh. She had counted.
"About forty," said her uncle. "So tonight, before the first number, what chance did Cô Tám have?"
"About one in forty."
"And what chance did whoever won last night have of winning again tonight? Whoever it was."
"The same," said Hạnh. "One in forty."
Ông Sáu nodded. "And how many nights are there in the fair?"
"Six."
"So how many times can somebody win two nights in a row?"
She counted on her fingers, under the table. The first night and the second. The second and the third. The third and the fourth. The fourth and the fifth. The fifth and the sixth. "Five," she said.
"Five chances," said her uncle, "each about one in forty. Put them together and it is about five in forty. About one fair in eight, somebody wins the big game twice running." He drank his tea. "I have called this fair for thirty years. It has happened to somebody in about four of them."
Hạnh looked out at the tent. It was quieter now, waiting.
What had happened was rare. It was rare for Cô Tám, who had about one chance in forty tonight of standing on her chair again. But it was not rare for somebody. With forty people and six nights, somebody being lucky twice was not a strange thing at all. It was an ordinary thing, happening to a loud person.
She stood up.
"It's rare for Cô Tám," said Hạnh, to the tent, and her voice did not shake. "But it isn't rare for somebody. With forty cards and six nights, about one fair in eight, someone wins the big game twice running. This year it's her."
Cô Tám, who had heard none of the muttering, beamed and bowed.
The hardware man unfolded his arms, then folded them again. "Still," he said.
Ông Sáu stood up too, slowly, because his knees did not like folding chairs. He picked up the cage by its handle and walked down the side of the tent to the back row, and held it out to the hardware man.
"There is one more game before we close," he said. "Would you turn it for us?"
The hardware man looked at the cage. Then at the tent, which was watching. Then he took it.
He turned it three times, carefully, exactly three, the way he had watched Hạnh do it. A ball rolled to the door. He took it out and read it out, without a song, because he did not know the songs. Nineteen. He turned it again. Seventy-seven. Again. He was not a bad caller, Hạnh thought; he had a good loud voice from shouting the price of nails.
The last game of the night was won by the young father at the back, on the eleventh number, with one hand, without waking the baby.
Cô Tám did not win. She clapped louder than anyone.
Afterwards, as they put the cage back in its box, the hardware man came to the table.
"Thirty years, you said," he said to Ông Sáu. "And four times somebody won twice?"
"About that," said Ông Sáu.
The hardware man nodded slowly. "I'll turn it again tomorrow," he said, "if you like."
"I'd like that very much," said Ông Sáu, and the hardware man went off into the dark of the Green looking, Hạnh thought, almost pleased.
The question for your own table
When something unusual happens to someone you know, a lucky streak, a coincidence, a run of bad days, do you ask how rare it is for them, or how rare it is for somebody?
Something to do
Ask everyone at the table their birthday. With twenty-three people, two share a birthday more often than not. With a family, count how many pairs of people you have, and see how many chances that gives.
Across the table
The story in three lines. Cô Tám wins the big game of the fair two nights running, and someone at the back says it's fixed. Hạnh nearly asks Cô Tám to sit out. Her uncle counts with her: about one chance in forty a night, five chances in a six-night fair, so about one fair in eight somebody wins twice, and then he hands the cage to the doubter to turn.
One question to ask. "Is it rare for her, or rare for somebody?"
One thing to do at the table. Each person rolls a die six times and writes the results. Look for anyone who rolled the same number twice in a row. Count how many of you did.
The grown-up layer. A coincidence can be very unlikely for one named person and quite likely for somebody in a crowd, because there are so many people and so many chances. The famous example is that among twenty-three people, two probably share a birthday. Hạnh wanted to calm the tent by moving the winner. Her uncle calmed it by counting, and by letting the doubter turn the cage. This is the third lesson of the Whetstone course Thinking in Odds.
The Honest Page
- Known. With about forty cards in the big game, whoever won last night has about one chance in forty of winning again tonight. A six-night fair has five pairs of nights in a row, so somebody winning twice running happens in about one fair in eight.
- Known. In a group of just twenty-three people, the chance that two share a birthday is more than one half. Coincidences in a crowd are more common than they feel. (source)
- Disputed. Why people so often see a pattern or a cheat in a run of luck. Psychologists disagree about how much is a habit of attention and how much a sensible suspicion that is usually wrong. (source)
- Legend. That a lucky person stays lucky, for a night or a season. Players at every kind of table have said it; the cage does not keep track of who is holding the card.
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