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P.D. ACTIVITY (or how I learned to 'cook' the dice and never say die):

A die is a mechanical device designed to provide an equal probability that, when rolled, any of the six sides will face upward when the die comes to rest.

You mission, should you choose to accept it, will be to first 'cook' your own die, perform some trials then 'freeze' your die and roll some more. Depending on your results, you will join the 'winners' or 'losers' group, do some more trials and then analyse the results.

To perform the experiment (detailed below), requires

  • A spreadsheet for storage of two discrete data sets (Part-1 & Part-2)
  • Minimum of two dice (required for comparison between two groups)
  • A fridge/freezer (to cool dice down to to between +5 to +10 Celsius)
  • Source of hot (near boiling) water (to heat dice to between +70 to +90 Celsius)
  • An infrared thermometer (optional but best).

NOTE: NEVER EXPERIMENT WITH HEAT UNLESS YOU HAVE ADULT TO HELP YOU

  • Allow heated dice to cool before touching them with bare hands.
  • Use caution when dealing with any hot substance.

To reduce risk of burning, this experiment will use hot water in a mug istead of an oven and baking tray to soften the dice. This will reduce the efficacy, but the bias will be significant over a reasonable number of trials (30 or more).

Video 1. Eureka - Heat Versus Temperature


Methods to Affect Rolling Die Outcomes:

Traditional six sided dice are still used in a huge range of games where multiple random outcomes are required to be provided in a fair and predictable way.

Over the centuries, many people have tried different ways to 'load' a die, to make it fall more often on a number of their choice.

In this experiment, you will learn how to use HEAT to affect the odds - or to do what is known as 'loading' the dice in your favour.

A 'loaded' die, also known as a 'weighted', 'cooked' or 'crooked' die, can be used to amaze, confuse, or to conquer your friends (or enemies).

By altering the weight distribution in a die, you can get it to land more often on the side of your choice. See How To Load & Test Dice.

  1. 'Floaters' are dice that have had their weighting altered by hollowing out a portion of the die. The hollow section of the die will be off centre in order to bias the die’s rolling properties in a certain way. These types of weighted dice earned their name because they float instead of sink when placed in a glass of water.
  2. Another type of die has a semi-solid material inside of it. This material must have a melting point just below your body temperature. Usually, wax is used as the substance. When the cheater clutches the die in her hand, the wax inside of the die will melt and shift to whichever side is currently facing down. This allows the cheater to modify the die in whichever way she chooses and increase the chance that this side will face up after the die is rolled.
  3. Standard plastic dice can also have their weight properties modified. When a plastic die is heated in an oven with a desired face pointing upwards, the internal plastic will soften and gently pool at the bottom of the die. When done correctly, this type of loaded weighted die will be indistinguishable from a legitimate die.

Source: http://www.onlinecraps.net/craps/cheating/loading-dice/weighted/ and http://www.ehow.com/how_4494964_make-trick-dice.html

'Frozen Moments' - A Dice Rolling Experiment:

A number of dice will be 'cooked' (see above) to bias the probability in favour of the number 'one'

Our 'null hypothesis' is that the probability of predicting the outcome of a 'cooked' dice roll will NOT be significantly different from dice that have been 'frozen' with the opposite face pointing upwards.

Our hypothesis is designed to compare results where:

  1. The 'cheater' has biased a die by 'cooking' it with the 'one' face pointing up
  2. The 'cheater' has further biased a die by 'freezing' it: As heat rises, during the time taken to complete the 'freezing' process the internal plastic will be slightly more fluid at the top of the die and this will slightly increase the density at the base of the die - adding to the bias resulting from the earlier 'coooking' process.
  3. To evidence the temperature layering effect of the frozen die, use an infrared thermometer to measure and record the temperature difference between top and bottom of die on removal from the freezer.

How To Cook Dice

Do not use an oven: You may get burnt or end up with melted plastic everywhere

Do not use a microwave: A microwave will not melt the die the correct way and will most likely warp the plastic and make it unplayable. It's also dangerous.

You MUST get assistance from a teacher/adult:

  • Place your die into the bottom of a mug with the 'one' side facing up.
  • Pour some hot water from a jug or similar similar water heater into the mug until it covers the die by at least 50mm.
  • When poured, the water temperature should be close to boiling. The ideal temperature is around 70 to 90 degrees Celsius (depending on type of plastic).
  • Use your infrared thermometer to measure and record the temperature.

This should heat and soften the plastic enough to change the shape/balance of the die. The number that was facing up, out of the mug/cup should occur slightly more often than the other numbers when the die is rolled over a large number of trials.

Experimental Method:

Our experiment will compare two sets of dice: One 'cooked' set and one 'frozen' set.

We will start by 'cooking' a number of dice and use a whiteboard marker or similar pen to mark the 'one' face with a number which can be used to uniquely identify each die (this will be used later to allocate the die and record ownership by nominated trial group/person).

Run a number of dice rolling trials as per the procedure listed below and record your results.

There are two parts to the trial: See 'Part 1' and 'PART 2' below:

PART-1:

For Part-1, a minimum of ten trials should be run for each die (a total of forty or more rolls is desirable).

  1. First, 'cook' three dice as per instructions above, using the number 'one' as the preferred face (the face pointing 'up'). Don't forget to mark the 'one' face with a unique number to identify each die.
  2. Allocate each die to a specific person/group and record ownership (using the ID marked on the dice at the time of 'cooking')
  3. Three dice will be placed with the 'six' face up and the 'one' face down
  4. The person/group allocated to each die will record the result of the roll and also, record the temperature of the top and bottom of the die after each trial (using infrared thermometer).
  5. At the end of this first part of the experiment, all results must be entered into a spreadsheet against the name of the specific person/group responsible for that particular dice.
  6. Count the results to identify the number of 'successes' - the total number of times (if any) that the number 'one' has been rolled for each of the experimenters/groups during the trials in Part-1.

PART-2

For Part-2, a minimum of ten trials should be run for each die (a total of forty or more rolls is desirable).

Using the results from Part-1 above, divide the 'Part-1' experimenters into two new groups:

  1. A 'winners' group having the highest number of successes in 'Part-1' and a 'losers' group with the lowest number of successes in 'Part-1'
  2. Before running more trial dice rolls, each die belonging to a member of the low scoring. 'losers' group should be placed into a refrigerator/freezer cabinet with the 'six' side facing up.
  3. These 'frozen' dice should be left in the freezer for a minimum of five minutes. and then removed (the dice only need to be cooled to harden the plastic at a temperature of 5 - 10 degrees Celsius- The dice do not need to be actually frozen.
  4. A new set of trials should be run, with the same number of trials as performed in 'Part-1'.

On completion of the minimum number of trials (as defined above), the new results must be added to the spreadsheet so that these results can be clearly differentiated but compared accurately with the earlier trial results.

Example spreadsheet entries:

Name Group Die ID Die roll result Temp TOP Temp Bot Win=1 or Lose=0
Rhonda N/A 1 3 25.1C 25.1 C 0
Arthur N/A 2 1 25.2C 25.1 C 1
Fred N/A 3 2 26.1C 25.0 C 0
Jill N/A 4 2 26.1C 25.2 C 0
Jan N/A 5 1 25.2C 25.1 C 1
Rhonda N/A 1 3 25.1C 25.1 C 0
Arthur N/A 2 1 25.2C 25.1 C 1
Fred N/A 3 2 26.1C 25.0 C 0
Jill N/A 4 2 26.1C 25.2 C 0
Jan N/A 5 1 25.2C 25.1 C 1

Table 1. Results of PART-1 trial set

  • When the die roll result is the same as the biased face, then mark as a win
  • The unique 'ID' for each die that was assigned when die was first 'cooked'

Name Group Die ID Die roll result Temp TOP Temp Bot *Win=1 or Lose=0
Arthur winner 2 4 11.1C 9.3 C 0
Fred loser 3 1 10.3C 9.0 C 1
Rhonda loser 1 2 15.6C 16.9 C 0
Rhonda loser 4 1 15.6C 18.0 C 1
Jan winner 5 1 25.2C 25.1 C 1
Arthur winner 2 4 11.1C 9.3 C 0
Fred loser 3 1 10.3C 9.0 C 1
Rhonda loser 1 2 15.6C 16.9 C 0
Rhonda loser 4 1 15.6C 18.0 C 1
Jan winner 5 1 25.2C 25.1 C 1

Table 2. Results of PART-2 trial set (showing groups of 'winners' & 'losers')

  • When the die roll result is the same as the biased face, then mark as a win
  • The unique 'ID' for each die that was assigned when die was first 'cooked'

Discussing & Writing Up The Results:

On completion of the data entry, each group must provide a written discussion, summary and conclusion.

  1. How did the the experimental results relate to the original hypothesis?
  2. In general, did the results of the 'losers' group in Part-2 improve, decline or remain the same compared with their results in Part-1
  3. In general, did the results of the 'winners' group in Part-2 improve, decline or remain the same compared with their results in Part-1
  4. Why do you think this happened?

In summary, what would you change or what new experiment do you think should be performed to improve this experiment?

References

Neuroscience Survey

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Also see:


Video 1. Veritasium - Punishment Vs Reward & Regression to the mean

Unfortunately, much of the effect claimed by alternative medicine can often be explained simply as regression to the mean: When Aunt Jane's acne gets better after rubbing mint leaves on her face, that's “anecdotal evidence” based almost entirely on regression to the mean. Many symptoms will come and go in an apparently random fashion if recorded in an objective way - headaches, for example, tend to disappear without the aid of any treatment over time. People seek treatment when their symptoms are particularly severe, when they are at their respective “top”.

Regression to the mean, therefore, suggests that if symptoms are excessively severe this week, then next week they should be less severe simply by random fluctuations. If treatment is only sought when these symptoms are at their worst there will almost always be a coincidental recovery. This appears even if the treatment has no effectiveness whatsoever.

A placebo control group in a controlled trials removes the effect of regression to the mean. Both groups, on average, experience a tendency to regress to the mean. If the treatment group shows a statistically significant increase in the speed that symptoms regress, it can be attributed to the effects of the treatment, not the placebo effect or regression to the mean

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first. To avoid making incorrect inferences, regression toward the mean must be considered when designing scientific experiments and interpreting data.


 
 
teaching/stem/st2-2016/pd-dice-activity.txt · Last modified: 16/02/2016/ 08:53 by 127.0.0.1