Animals - big or small, feathered or furred - jostled each other as they each tried to get within reading distance of the handful of posters wrapped around tree trunks about the busy jungle market place.
Snow Ears was forced to burrow his way out of the crush after he had put up the last poster that said, "Five Houses for Five Lucky Winners. Roll the dice to see if you have the winning streak. 200 seeds for a 3-dice roll. Numbers 333 gets a new home."
A week before, Goose had complained to SCales about the slow sales of his newly constructed homes at the edges of Upper Valley Ridge, and Scales persuaded him to put them up for a competition. Scales also added that the exercise was a good way to observe the behavior of animals who considered themselves as either winners or losers. He reckoned that the fees they would collect from the dice rolls would be more than enough to compensate for the cost of the houses. Goose agreed with the plan and was also excited to see the result of the observation.
Snow Ears's nose twitched as he studied the swarming crowd. He wished that he could take part but Scales told him that if he were to win a home, the other animals might accuse him of cheating. The rabbit let out a heavy sigh as he turned his back on the crowd and hopped back to the office.
"Did you make sure to put up the posters where everyone could read them?" Scales asked the moment Snow Ears's head popped into the office-lair.
"Yes, Dr. Scales. I was almost crushed to death by the crowd."
"Ah. It was that well received? Why that is excellent!!"
"Is there anything else I need to do before the day of the competition?"
"Yes. Get as many writing leaves as you possibly can. I want you to observe the animals' temperament before and after they roll the dice. Use a scale of 1 to 10, with 1 for extremely unhappy and 10 for extremely happy. Since you will be the yardstick, I am afraid I can't allow you to have assistance."
"Oh, that is all right Dr. Scales. I think I can manage."
But as Snow Ears made his way back to his burrow hole, he began to wonder if Scales would be interested in getting extra statistical data for his research. So he readied an extra stack of leaves and asked his neighbor Squirrel if he would like to help take down the dice numbers that face up at each roll. He promised to teach Squirrel about Random Variables, so the exercise would be a good experience for him.
On the day of the competition, Snow Ears and Squirrel had to squeeze their way to the booth because of the huge crowd waiting there, although it was not even 6.00 am yet. Two hours later Scales and Goose arrived. Snow Ears was pleased to note that Scales had brought dice with three different colors - yellow, blue and white. He advised Squirrel to write down the numbers facing up based on the order of color which was yellow first, blue second and white third. He told him to record down as much information as he could into each leaf because he only had one small stack for the extra data.
A long orderly queue began to form and each animal was allowed a maximum of 5 throws. If any should wish to throw more, then it should go to the back of the line and wait its turn.
That day Snow Ears recorded 50,286 throws. That amounted to a collection of 10,057,200 seeds for Scales. The game only ended when the fifth house found a winner. Snow Ears rubbed his tired paws together as he thought over the day. The crowd had moved fast, in fact, faster than he had hoped. But something irked him.
Three dice. Each dice had 6 sides, so that meant that the probability of a number coming face up at any one time was 1/6. Since each dice was independent of each other, meaning that the result of Yellow will not affect Blue which will not affect White in any way, then each dice has a 1/6 probability of showing the number 3 face up.
P (Yellow showing 3 face up) = 1/6
P (Blue showing 3 face up) = 1/6
P (White showing 3 face up) = 1/6
Hence the probability of all three showing the number 3 at one time is
P (Yellow) ∩ P (Blue) ∩ P (White) = 1/6 x 1/6 x 1/6 = 1/216
He was experienced enough to know that in real life the numbers will not match exactly, but he was also familiar with playing dice and he knew that the results will always be quite close to the calculated probability. Especially if the dice had been rolled a large number of times. However, the day's 50,286 rolls meant that the average win had turned up only after the 10 thousandth roll. He tugged one of his ears as he wondered if the Random Variable Formula he used was wrong.
Scales slithered to his side and said, "What an exhausting day it has been. Good job Snow Ears."
"Thank you Dr. Scales."
"I notice that Squirrel has been here all day with you? You didn't ask him to help you with the observation scale did you? It could have compromised the data."
"Oh no sir. I asked him to help on a different data: The dice throw. I thought that you might be interested to know which numbers turned up most often."
"That was totally unnecessary. Those are nothing more than schoolwork data. You have wasted a lot of good writing material as well as Squirrel's time."
"I am sorry, sir."
"Well don't waste anymore time on that. Throw those data away and concentrate on the ones I asked you to collect."
"Yes, sir." Snow Ears immediately stuffed the data Squirrel collected into a hole and placed his observation sheets into 5 wheel-barrows that Scales had rented from Grocer Hare. They didn't need the sixth barrow, so the hare asked Snow Ears to send it back to his shop before pushing a barrow in front of him and going after Scales, Goose, Squirrel and Chipmunk who were already on their way to the office-den.
Once their voices had faded in the distance, Snow Ears dug up the leaves he had stuffed into the hole and filled them into the extra wheel-barrow. Then he covered the hole back with litter left behind by the crowd so that by the time birds came by to look for insects, there was already a high pile of leaves for them to rummage through.
Snow Ears pushed the barrow to his home, emptied it then continued onto Grocer Hare's store where the accountant, Doormouse, was waiting. He left it there, and after a brief chat about the day, he returned to his hole and studied the sheets that Squirrel had filled. He totaled up the throws based on color and number and came up with the following table.
| Number | Yellow | Blue | White |
| 1 | 16,728 | 8,396 | 4,497 |
| 2 | 19,612 | 8,399 | 4,495 |
| 3 | 253 | 8,376 | 199 |
| 4 | 4,421 | 8,388 | 4,428 |
| 5 | 4,525 | 8,392 | 11,556 |
| 6 | 4,747 | 8,335 | 25,111 |
Snow Ears began to rub on his ear again. The Yellow dice was obviously skewed to numbers 1 and 2, while the white dice appeared to be skewed to 5 and 6. Only the blue dice showed normal behavior. After some more thought, Snow Ears decided not to tell Scales about the dice because Squirrel may not have collected the data properly. He slept restlessly that night.
Scales returned to the site after Goose left his office. He watched the crows scratch about the rubbish hole in search of worms and insects. After they were done, he slithered towards the heap and realized that none of the shredded leaves about the area were the palm ones that Snow Ears had used for data collection. He turned back to his den, seething with rage.
