Grace Black
13:25, February 26
"We will not disclose the result of the Red Game to preserve the fairness of this game. As you know, we will now play the Blue Game in this Part of the Confidence Trick." The croupier took a blue envelope from his pocket. "This blue envelope contains the instructions for tiday's Blue game," The envelope was torn open. "Door Prize."
"Door prizes are given by lottery and contested by guests at a large gathering, say a birthday party for an affluent person. But this game has no random factor, it's more like Hide and Seek. Allow me to explain the rules."
- One player is randomly selected to become the dealer
- This player is given a gold colored token with the word "WINNER!" printed on both sides.
- At the start of each round, the dealer will select one of three boxes to put the "WINNER!" token in, the non-dealer will be unable to see which box the dealer has selected
-The dealer is allowed to wager on any combination of the three boxes. She may wager on one, two or all three. The dealer's total wager may be up to the amount that she currently holds in this game
- The non-dealer may request that a box without the token be revealed publicly at the cost of 25% of the dealer's wager across all three boxes. The revealed box is randomly selected from the two without the winning token.
- The non-dealer makes her wagers. She may only wager on one box and must wager a sum at least equal to the dealer's total wager.
- The boxes are revealed. All of the money that was wagered is divided between the players pro rata based on the amount that each of the players wagered on the winning box. If there is no money wagered on the winning box, then the round is voided and restarted. In the restarted round, the dealer must wager on the winning box.
- The dealer and non-dealer switch roles for the next round
- The game lasts 10 rounds unless someone runs out of money
- Players may communicate between rounds
"Are there any questions?... None, then to familiarize you with the game as it is played, we will play one practice round with each player as dealer. Does anyone volunteer to start as dealer?"
"I will." The minute I said this, two suits walked in each holding an open case which held 150 chips.
"This is the money that you will use for this game, One hundred fifty gaming tokens each worth ten thousand dollars. Each of you will start with one and a half million dollars." As he said this, a third suit came in with a pair of earmuffs and a blindfold. "These serve to prevent the non-dealer from inferring in any way what moves the dealer has made. Mr. Kamisaki, if you will put these on." Naoki put the blindfold over his eyes and the earmuffs over his ears. "Mr. Kamisaki, if you can hear me, tell me which hand I have on my shoulder." Silence. The croupier placed a disc with the word "WINNER!" written on it onto the table. "Miss Black, select the winning box and make your wagers." The boxes were numbered 1, 2, and 3. "Your opponent will not see the order in which you made the wagers." I put the disc into box #3 and wager 20 tokens ($200,000) each on boxes 1, 2, and 3. "Are those your wagers?"
"Yes." The croupier removed the blindfold and earmuffs from Naoki. "You may wager on no more than two of the boxes. You may open one of the two non-winning boxes at the cost of one quarter of Miss Black's total wager of sixty chips, in this case, fifteen chips."
Naoki had two choices:
1. Wager 60 chips with 33% confidence and a return of 75% of the chips on the table (90). Expected Value: (90x1/3)-60=-30 chips, -$300,000
2. Spend 15 chips to reveal one of the boxes and wager 60 with 50% confidence and the same return of 90 chips. Expected Value: (90x1/2)-75=-30 chips, -$300,000
In the long run, neither strategy has an advantage. But he only gets five rounds as non-dealer. To break even, he needed 2 wins with the first strategy or 3 wins with the second strategy. The second strategy is higher percentage.
"60 on Box 3." Naoki put sixty chips on Box #3. The boxes were opened and the winning token appeared under Box #3. He was just lucky, and this was a practice round.
"Box #3 is the winning box. Mr. Kamisaki wagered 60 chips on this box. Miss Black wagered 20 chips on this box. There are 40 chips wagered on losing boxes. 30 would have gone to Mr. Kamisaki and 10 would have gone to Miss Black. The score would have been 180-120 to Mr. Kamisaki after this round. We will switch roles for this second and final practice round. Miss Black, if you will put on the blindfold and earmuffs." The earmuffs go over my ears and the blindfold goes over my eyes.
...
...
...
The blindfold and earmuffs come off and I see Naoki's wagers. 40 chips on each box. He's pushed me all-in with this one. I think about the percentages and the odds.
"You may wager on no more than two of the boxes. You may open one of the two non-winning boxes at the cost of one quarter of Mr. Kamisaki's total wager of one hundred twenty chips, in this case, thirty chips. This will leave you with only ninety chips. In this case, you will go all-in." Wouldn't it be fair to prevent me from opening one of the boxes. Naoki wagered 120, I have 120.
1. Wager 120 chips with 33% confidence and a return of 75% of the chips on the table (180). Expected Value: (180x1/3)-120=-60 chips, -$600,000
2. Spend 30 chips to reveal one of the boxes and wager 90 with 50% confidence and a return of 145 chips. Expected Value: (145x1/2)-120=-47.5 chips, -$475,000
"This is a practice round, no consequences for my actions yet. Open one of the boxes." I paid 30 chips and Box #2 was opened. Empty. 50-50 now. Nothing better or worse than a blind guess.
"90 on Box #3." The boxes were opened...
"Box #3 is the winning box. Miss Black wagered 90 chips on this box and Mr. Kamisaki wagered 40 chips on this box. There are 80 chips wagered on losing boxes. 55 would have gone to Miss Black and 25 would have gone to Mr. Kamisaki. Thirty chips have been spent to even the odds. The score would have stood at 125-145 to Miss Black after two rounds. This practice session is over. We will return the chips to their initial owners and the real game will start. But first you will have three minutes to communicate before the first round of the game."
"How did you know to open a box?"
"Simply put, I had a 1 in 3 chance if I didn't and a 1 in 2 chance if I did. That reminds me. Why didn't you do that?"
"How much do you owe?"
"Why is that important?"
"There is $12 million in this Part of the Confidence Trick and they'll only take back $8 million. This game alone has $3 million on the table and only $2 million will be taken back. That's a million dollars for free. And to answer my question, I myself owe $1.6 million. My friend Takayoshi owes $290,000."
"I owe almost $4 million. My teammate Sylvie owes over $2.8 million."
"That makes over $8.5 million and we have four million to gain." We can't cover half of our debts with the extra money. I owe four million after all. Screw him, I need the money.
Start of Game
Round 1
The croupier showed the same coin used to decide who would play first. "Miss Black, since you volunteered to start as dealer in the practice rounds, you will call this coin toss." The croupier showed both sides of the coin. "Red, or Blue?"
"Blue." The croupier threw the coin in the air, caught it, and slapped it on to the back of his other hand. He lifted the throwing hand from the coin.
"It is Red. Mr. Kamisaki, you will have the choice of dealing first or last."
"I will deal last." The croupier 's assistants put the blindfold and earmuffs on to Naoki's head, leaving me to make my initial wagers and pick the winning door. Box #1, 20 chips per box.
The blindfold and earmuffs came off. "You may wager on no more than one of the boxes. You may open one of the two non-winning boxes at the cost of one quarter of Miss Black's total wager of sixty chips, in this case, fifteen chips." That's exactly what he said in the first practice round. "You must wager at least 60 chips on no more than one box."
Without any hesitation, Naoki said "Box 2, 60 chips."
A pause, then...
"It is time for the moment of truth." All three boxes were opened. Box #1, WINNER!; Box #2, empty; Box #3, empty. "Box #1 is the winning box, Miss Black was the only one to wager on that box. Therefore, she will receive all 120 chips on the table. The score stands at 210-90 to Miss Black. You have three minutes to talk amongst yourselves. Once both of you are ready, Round 2 will begin."