Washington State University © 2009 1Dr Holt’s CCPM GamesSixesBASIC Sixes Game• Sixes is a quick game to demonstrate the reasons individuals feel justified in adding safety to individual task estimates. It makes it very clear why this has been done and why it was critical and necessary for people who try to keep their promises. (Helps people understand why they act the way they do.)• Sixes demonstrates how the inflated safety imbedded in individual task estimates required by BAD STATISTICS can be safely removed and replaced with a relatively small project buffer for much better project performance in spite of the same, continued highly skewed probability distributions associated with of individual tasks. (Helps people understand the simple actions needed for the system to dramatically improve.)Advanced Uses of the Sixes Game• The advanced portion of Sixes allows inquisitive individuals to further investigate and consider the impacts of variability on project systems. • They can also help teach specific principles important to Project Management:– Dealing with Erroneous Reporting (not reporting complete with the task is complete)– Dealing with An Errant Task.– One area is the impact of reduced variability– One area is the impact of assemblyWashington State University © 2009 2BEFORE YOU PLAY, Understand the Structure of Individual Tasks•The beta curve is widely accepted by academics to represent the theoretical distribution for individual tasks.•When working on a different problem, I simulated a case with a high degree of rework. Amazingly, I found the same shape curve; the Beta Distribution.Task Duration with 70% Rework 0204060801001200102030405060708090100110120130140150160170180190200Flow TimeNumber of OccurancesBeta Distribution0 Time 0 Prob of OccrMode (Most likely)Median (50% below)Mean (average)85% Estimate•In words, the process stared with Task A which had 70% rework. When Task A finally finished, there was a 40% chance of a short path through Task B and a 60% chance of a long process through Task C and Task D. In this case all Tasks had a Mean of 10 days and a Standard Deviation of 4 Days. •A simulation of 1000 runs shows the Mean time from Start to Done is 49 days with a Standard Deviation of 30 days. But the Maximum time was over 200 days and an 85% time of 80 days. Median about 40 days. We see the same Beta Distribution. The cause is the high amount of Rework. We now see a core problem for individual tasks and great opportunity!Task ATaskBTaskCTaskDDone70% Rework40%60%PassNoYesStartDuplicating the Beta Distribution with DiceIt‟s possible to simulate the Beta Distribution results using fair die. Here is a simple simulation of two processes. One process is rolling a single die (representing the a normal process with wide variation, mean 3.5 days, standard deviation 1.7) producing a number from 1 to 6. The other process is rolling the die and counting the number of rolls until there is a six rolled (the probability of rolling a six in one roll is 0.166. The probability of rolling a six is exactly two rolls is 0.139. And the probability of rolling a six in two rolls or less is 0.305. There is a 95% probability of rolling a six in 17 rolls or less (and a 5% chance it will be more than 17). When you add these two processes together (the number rolled on a single fair die + the number of rolls needed to roll a six), you get a distribution that resembles the Beta. A distribution that has a general, predictable portion and an un-predicable portion causing the long tail.Below is a sample of 500 trials of a single die plus Sixes.While it‟s possible to do create the Beta Distribution used in projects in this way, its cumbersome in a game.So, in the Sixes Game, we ignore the predictable part (the fair die predictable part) and just focus on the unpredictable portion of project tasks. Removing the predictable part doesn‟t seem to detract from the Sixes Game at all and simplifies things.Now that you have the background, you are ready to play Sixes!500 Trials of a Single Die + Sixes024681012141618201 3 5 7 9 11 13 15 17 19 21 23 25 27 29Washington State University © 2009 4Playing the Sixes GameGiving the Group the deeper understanding of the actions of a fair die:• Gather a group of interested people. Ten to twenty people is good. Give each person a fair die.• First, review the characteristics of a fair die. Make sure they all know the probability of rolling a six is 1/6thor 16.7%.• Ask them how many times they expect to roll the dice to get a six. What is the minimum number of rolls necessary to get a six:? (1) What is the maximum number of rolls to get a six? (No upper limit).• To better understand this, let‟s make a histogram to see how many rolls it takes you to get a six. Each of you roll your die until the get a six. Count how many rolls it takes. The leader plots the Histogram of the data points. If you don‟t have at least 20 people, have some people repeat their rolling until you get at least 20 data points (20 is easy to use since each data point represents 5%) • Make the Histogram. You may get something like below. In this case two of the rolls were beyond 20! So, to be 90% (18/20), you would have to estimate 17 rolls!• And yet, 60% of the time (by this Histogram), it only took five rolls or less.• If the distribution of the histogram is not clear enough, ask them to do it again to get 20 more data points. You need to plot 40 or 50 samples on the same histogram to get a good understanding for the distribution. You will find that about 1/6th(17%) are sixes on the first roll and about 50% of the time, it takes 4 rolls. 2/3rd(67%) of the time, a six occurs within six rolls. But an 85% comfort level takes about 10 rolls and 95% at 17.• Explain, it’s not the person rolling the dice but the nature of the process.• Ask if any one rolled a six on the first time and the second time. If they did, have every one watch them to see if they can do it again.500 Tries to Roll a Six01020304050607080901357911131517192123252729Number of RollsOccurancesSeries3Histogram for Rolling a Six00.511.522.533.544.51 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Number of Rolls NeededNumber of Occurances25 27Washington State University © 2009 5Sixes Game• The Game:Now people understand the probability distribution of rolling a Six, you are ready to do a project. The