Simulating Dice throws – the correct way to do it in excel

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dice-throws-excel-simulating - correctlyIf you ever had to simulate random outcomes in excel sheet, you might have already heard of about the spreadsheet function rand(), this little function generates a random fraction between 0 and 1 whenever you use it. So I usually write =round(rand()*12,0)int(rand()*12)+1 if I need a random number between 0 to 12. Of course, if you have analysis tool pack installed like I do, then we can use randbetween(0,12) to do the same.

In order to simulate a dice throw, thus you can use round(rand()*5,0)int(rand()*6)+1.

So, what would you do if you need to simulate the face total when you throw 2 dice?

round(rand()*10,0)int(rand()*11)+2 ?

Wrong

Why? Apparently a random number between 2 and 12 (1 is not possible as the minimum you can get when you throw two dice is 2) doesn’t simulate 2 dice throws properly.

The CORRECT way to do this is instead generate 2 individual random numbers and add them up, like:

round(rand()*5,0)int(rand()*6) + 1 + round(rand()*5,0)int(rand()*6) + 1

Here is why this is correct way to simulate dice throws using random number generator functions:

I have ran these 2 random functions each for 2500 times and plotted the distribution:

excel-simulate-dice-throw-distribution

As you can see, the left plot of int(rand()*11)+2 tells that each of the 11 possibilities (2,3,4,5,6,7,8,9,10,11) are equally likely. But that is not what happens when you throw a dice, you see an awful lot more 5,6,7,8 than you see a perfect 12 or 2. And there is a reason for that, the distribution of 2 dice throws is actually a bell curve, and when you use int(rand()*6) + int(rand()*6) + 2 the distribution is bell curvish.

Update: Thanks to Jon for pointing out that round() is not the choice if you want random integers, you should use int instead. See his explanation in the comments and the illustration here.

I have used this logic to simulate monopoly board game and prove that it is not really that random.

More on games: Bingo / Housie ticket generator excel sheet

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13 Responses to “Gantt Box Chart Tutorial & Template – Download and Try today”

  1. Oli says:

    Hi Chandoo

    As one of your students I have followed your detailed example through with great success. However, Excel is acting in an unexpected way and I wonder if you could take a look?
    http://cid-95d070c79aef808e.office.live.com/self.aspx/.Public/Gantt%20Box%20Chart.xlsm
    On my version, I have to type 40239 (Which equates to 2 Mar 2010) to get the chart to display 31 May 2010 (which should be 40329)!!??

    Have I done something wrong or is Excel acting up?

    Thx
    Oli
    PS Your example file in 2007 displays correctly.

  2. Dave says:

    Hi,

    I like this idea a lot, but I agree the name is a little drab.

    As an American I may just be seeing things, but to me the combination of lines and bars on your chart looks like a bunch of cricket bats.

    Maybe you could work that into a catchier name. 🙂

    Cheers!

  3. Bob says:

    Here is some code I use to keep the axis synched.
    It may be useful to some of your readers
    It is based on a comment I saw on Daily Dose of Excel.

    Function SynchGanttAxis(Cname, lower, upper)
    'Sets the X min and X max for Category axis

    Application.Volatile

    On Error Resume Next
    '
    'Top Horizontal Axis
    With ActiveSheet.Shapes(Cname).Chart.Axes(xlCategory, 1)
    .MinimumScale = lower
    .MaximumScale = upper
    End With

    'Bottom Horizontal Axis
    With ActiveSheet.Shapes(Cname).Chart.Axes(xlValue, 2)
    .MinimumScale = lower
    .MaximumScale = upper
    End With

    End Function

    Function SynchVerticalAxis(Cname, lower, upper)
    Application.Volatile
    On Error Resume Next
    ' Excel 2007 only
    'Right hand vertical axis
    With ActiveSheet.Shapes(Cname).Chart.Axes(xlValue, 1)
    .MinimumScale = 0
    .MaximumScale = upper
    End With

    End Function

  4. Chandoo says:

    @Oli.. Can you check your file again.. I see 40329...

    @Dave: Even I saw things.. the bars actually looked like lollipops. How about calling this lollipop chart - now that would be yummy and goes along the tradition of naming charts after eatables (bar, pie, donut...)

    @Bob: Superb stuff... thanks for sharing 🙂

  5. Mike H says:

    Hi Chandoo
    This looks really good and I think it can also be applied to show project phases / milestones.

    Question: Thinking further could this be amended to display a project lifecycle (Idea through to Implementation say 7 phases) on one bar / row? Just imagine 20 projects within a programme all on one chart one bar each showing their respective lifecycle stages i.e. on one page.

    Idea: As the Gantt Box Chart this is quite intensive to set up re formatting etc how about the added extra of once you have completed this to "Save as template" i.e. saves the formatting and layout of the chart as a template so you can apply to future charts. Simple to do and will save the time formatting etc again and again and again.
    Therefore tip: Click on your chart demo and then click on Save As template icon (2007) - edit file name and click on save. Ready to use / apply via Templates in Change Chart Type window.

    Thanks and be very interested if the lifecycle question can be resolved

    Mike

  6. Oli says:

    How embarrassing.

    I was obviously suffering from numerical dyslexia. I was one of those days.

  7. Chandoo says:

    @Mike H: You can easily make this chart to work like a generic project lifecycle plan chart. All you have to do is,

    1. in a separate sheet define the steps of lifecycle and various dates in a table (with 5 columns for each of the projects you have).
    2. now use a control cell to input the project name you want to show in the chart
    3. based on the input, use OFFSET Formulas to get the correct data
    4. Rest is same as the tutorial above

    For more info on the dynamic charting visit http://chandoo.org/wp/tag/dynamic-charts/ and http://chandoo.org/wp?s=OFFSET

  8. Your solution is really smart but in the en Excel isn't meant to do stuff like this. I, as a former PM, always thought is was frustrating that you had to do stuff like this for something simple like a Gantt chart. So I built Tom's Planner. And would like to plug it here. I think it really solves the problem you are trying to solve in the most efficient way. Check out http://www.tomsplanner.com for a free account or play around with the demo.

  9. Lopi says:

    Hi there,
    Chandoo - this is really a very nice and helpfull chart - I adopted it, so I can report a forecast or the delay of a certain task (coming from my role as an auditor for projects).
    One topic I´m currently struggeling with: I do have a project lasting for lets say 12 month. For a management reporting, I want to have kind of snapshot, lets say one month back and 2 month in the future. I tried with the offset formula, but failed. Any idea?
    Thx
    Lopi

  10. [...] Ein viel geliebter Klassiker ist die Erstellung von GANTT-Diagrammen mit Excel. Wir hatten das Thema wiederholt schon hier. Chandoo.org hat sich mal wieder mit einer neuen Variante hervorgetan: Das GANTT-Box-Chart. [...]

  11. David says:

    Hi Chandoo - fantastic xls. One thing I can't figure out how to do is adjust the alignment of the vertical axis. I would like to left align so that I could indent to represent sub tasks. Can that be done? Or is there a better way?

  12. Paul says:

    I've been trying to work out if there's a way to show weekends on the graph. The closest thing I've got is to add them on a secondary axis, but then I haven't been able to keep both axis lined up together! Any ideas?

    Following on from this - is it possible to show things like holidays?

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