The Caller · The Sixth Evening: The Dice Next Door
On the last night of the fair the Green was full by five o'clock. The last night always was. Families came who had not come all week, grandmothers in their best áo dài under winter coats, small children with lanterns on sticks, teenagers who pretended they had only come because their parents made them and then stayed until the end. The lantern fund had strung extra lanterns across the paths, and the whole Green glowed red and gold under a clear sky.
And next to the lô tô tent, that evening, there was a new table.
It belonged to the youth club. Two older boys and a girl with a clipboard had set it up in the afternoon: a cloth printed with six pictures, a gourd, a crab, a fish, a tiger, a rooster and a prawn, and a plastic bowl with three big wooden dice in it, each die painted with the same six pictures. A sign said BẦU CUA, 1,000 ĐỒNG A GO, FOR THE CLUB TRIP. A small crowd of children was already round it, putting coins on the pictures and shrieking when the bowl was lifted.
Hạnh watched it from the tent flap while the chairs filled up.
She knew the game. Everybody did. Her grandmother had played it with her every Tết, for sweets, on the kitchen floor. You put a coin on a picture, and the three dice were shaken under the bowl. If your picture came up on one die, you got your coin back and one more. On two dice, two more. On three, three more. If it came up on none, the banker kept your coin.
Six nights in the tent had taught her to ask what a game kept. She did not know the answer for bầu cua, but she was suddenly sure it kept something, and that the children did not know.
She felt something rise in her, warm and certain. She had learned more in six evenings than in a term at college. She would go next door now and tell the youth club, kindly but clearly, that the game was a kind of cheat, that it took more than it gave, that it was not right to run it for children, and that they should pack it up and sell cakes instead.
She had taken two steps towards it when her uncle said, behind her, "Count it first."
She turned. He was sitting at the trestle table with a brown paper bag from the noodle stall, flattened, and a pencil.
"You were going to tell them it keeps something," said Ông Sáu. "How much?"
"I don't know yet," said Hạnh.
"Then you were going to say a true thing you could not show." He held out the pencil. "Sit."
She sat. The tent was filling behind them. She had ten minutes before the first game.
"Three dice," said her uncle. "Six pictures on each. How many ways can they land?"
She wrote it. Six for the first die, six for the second, six for the third. "Six times six times six. Two hundred and sixteen."
"Say you put your coin on the crab. In how many of those ways is there no crab at all?"
She thought. No crab meant each die showed one of the other five. "Five times five times five. A hundred and twenty-five."
"And exactly one crab?" said Ông Sáu.
That took longer. The crab could be on the first die, with no crab on the other two: one times five times five, twenty-five ways. Or on the second. Or on the third. "Seventy-five," she said.
"Two crabs?"
Two dice crabs, the third not: one way for the two, five for the third, and three ways to choose which die was not a crab. "Fifteen."
"Three?"
"One."
She added them on the bag. A hundred and twenty-five, seventy-five, fifteen, one. Two hundred and sixteen. Every way the dice could land.
Her uncle did not say anything else. He folded his hands round his tea and waited.
So Hạnh did the rest herself. Suppose you played every one of the two hundred and sixteen ways once, with one coin each time on the crab. In the hundred and twenty-five with no crab, you lost your coin: a hundred and twenty-five coins gone. In the seventy-five with one crab, you won one coin each time. In the fifteen with two, two coins each, thirty. In the one with three, three coins.
She wrote it. Lose 125. Win 75 + 30 + 3 = 108.
"Seventeen," she said. "Seventeen coins lost, for every two hundred and sixteen played. About eight in every hundred." She looked at the bag. "It feels fair. Three dice, so your picture comes up about half the time. But the doubles and the triples don't quite make up for the times it misses. The banker keeps seventeen."
"Seventeen," said Ông Sáu. "Not a cheat. A share. Like ours, only quieter."
Hạnh thought of her grandmother on the kitchen floor, paying out sweets from a tin, and laughed, because her grandmother had always ended Tết with more sweets than she started with.
Hạnh looked at the paper bag for a long moment. Then she stood up, took a drawing pin from the chalkboard, and went next door.
The girl with the clipboard looked up, a little wary. Hạnh did not lecture. She pinned the paper bag to the post at the corner of the table, where everyone could see it, and said, "I worked out what bầu cua keeps. It's seventeen in every two hundred and sixteen. About eight coins in a hundred, for the club trip. I thought people might like to know."
The girl read the bag. One of the boys read it over her shoulder. Then the girl laughed.
"That's less than I thought," she said. "We'll leave it up." And she wrote 8 in 100 goes to the trip on her sign, under the price, in marker pen.
The children went on playing, mostly. A few stopped and read the bag, and one of them, a boy of about ten, did the sum again on his fingers and then looked at the bag with deep respect, as if it had told him a secret.
Hạnh called the last night of lô tô to a full tent, two hundred people in the end, standing three deep at the back. She sang every number. She did not shout one away once. The big game was won by Bà Diệu, on thirty-three, which made the whole tent cheer, and Bà Diệu wrote it in her notebook and underlined it twice.
When the lanterns were coming down, Ông Sáu put the wooden cage in its box and held the box out to her.
"For next year," he said.
"Your voice will come back," said Hạnh.
"Perhaps," said her uncle. "But the room trusts yours now. And you can count."
The question for your own table
When a family game is played for small coins or sweets, does anyone know what it keeps? Would it change the game to write the number on the cloth?
Something to do
Take three dice and choose a number. Roll all three thirty times and keep a tally of how often your number shows on none, one, two or three of them. Compare it with 125, 75, 15 and 1 in 216.
Across the table
The story in three lines. On the last night of the fair the youth club runs a bầu cua table for small coins next to the lô tô tent, and Hạnh is about to tell them it's a cheat. Her uncle asks her to count it first. On a paper bag she finds the banker keeps 17 of every 216 coins played, pins the sum to the stall, and the club writes "8 in 100 goes to the trip" on its sign.
One question to ask. "Why does a game that seems fair keep anything at all?"
One thing to do at the table. With three dice, count with the children: how many ways can three dice land (216)? In how many is your chosen number missing (125)? Work out the rest together.
The grown-up layer. Bầu cua cá cọp feels close to fair: your picture appears about half the time, and doubles and triples pay extra. Counting every way the dice land shows the extra never quite covers the misses, so the banker keeps about 8 cents in every dollar. The story never makes the game look worth playing for money; it puts the number on the cloth. This is the last lesson of the Whetstone course Thinking in Odds, and the end of The Caller.
The Honest Page
- Known. Bầu cua cá cọp is a Vietnamese dice game often played at Tết, with six pictures on three dice and on a mat. A player bets on a picture and is paid for each die that shows it. (source)
- Known. Three dice land 216 ways. A chosen picture misses in 125, shows once in 75, twice in 15 and three times in 1. Betting one coin on each of the 216 loses 125 and wins back 108, so the banker keeps 17, about 8 in every 100.
- Known. The British game Crown and Anchor works the same way, with six symbols on three dice, and keeps the same share for the banker: a player gets back about 92 pence of every pound. (source)
- Disputed. When and where these three-dice games began. Crown and Anchor is said to date from the eighteenth century, but that is not well recorded, and its relatives in China (Hoo Hey How) and Vietnam may be as old or older. (source)
- Legend. That a lucky picture comes up more often for some people than others. Every player has one; the dice do not.
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