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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19 Responses to “Free Invoice Template using Excel – Download”

  1. Doug H says:

    Nice post! Invoicing for the small biz or solo entrepreneur is something I see a lot of interest in. Also there are great templates from http://office.microsoft.com/en-us/templates

  2. Abhay says:

    This is awesome.

    I would need a little more. e.g. say I generate a Inv. # 1 with all the details. Once done I can click a button all the relevant details gets stored in some table. Further, when i generate a new invoice those details gets stored in same table but just below the previous invoice.

    Is their a way to do this?

  3. Hui... says:

    Daily dose of Excel held a competition in 2005 for this same topic
    It obtained 9 solutions which are shown:
    http://dailydoseofexcel.com/archives/2005/10/27/invoice-app-the-results/

  4. parimal says:

    How can i removed Dollar Sign, As want to use this in india.
    Please reply.

  5. parimal says:

    Also if possible then can i use Indian Rupee Sign and how?

  6. Gaurang Mhatre says:

    Hi Chandoo,

    Thanks for sharing this invoice template, Let me tell you this template will definitely help me since I got a process to handle where this invoice piece comes. Just a small doubt, can we store all the invoice details in PRODUCT & SERVICES sheet. So that whenever I select an invoice number from invoice sheet I can take print out and I can share it as well. Can we do that?? Since I will be dealing with this on monthly basis.
    It would be great if you can help me with this.

    Thanks in advance for your help!

    Regards,
    Gaurang Mhatre

  7. shrikant says:

    Hi Chandoo,

    I was thinking learning excel is quite tuff task but your blog proved me wrong. You made it very interesting. Thank you. Also the template you have provided for Invoice is very helpful to us.

  8. AKIN KARAMAN says:

    Thanks thanks thanks.. Very helpful. 🙂

  9. Trevor Gordon says:

    Hi i love the speadsheet but would like to ask how do i get it to add the description into the invoice as well

  10. Anuj says:

    Hi Randy, I tried to download one of your link "https://www.dropbox.com/s/2yvo0o2tgq9quhe/Medical_Massage_and_Salon_Application-Free.xlsm" However, i found the link unavailable. Can you please help me get the new link or can you please send this VBA file on my Email-ID.

  11. Kapil says:

    Hi, is there any chance that this can work with the "Products & Service" sheet outside of the Invoice sheet. I create multiple invoice files for the numerous clients. Updating the product sheet for each of them maybe a task. Hence, I want to create a MASTER FILE from which data can be picked up without having to insert new data in each of the invoice files.
    Possible? Or am I asking for the moon 😉

  12. Kadr Leyn says:

    Thank you so much for tutorial.
    This example can be reviewed for the example of the advanced invoice that made with excel userform :https://youtu.be/Qr-4of-38DI

  13. Trevor Gordon says:

    Good Day
    i love this template may i ask if it could be modified to have the following
    when you lookup a item code in the next column to the right it brings up the description then the quantity, unit cost, discount and then total otherwise i love the template

    Item Code Description Quantity Unit Cost Discount Total

  14. Denise Konopka says:

    When creating an Invoice template in Excel are you able to utilize the auto row height and wrap feature when the cell is a merged cell? I need to have a number of cells merged together to allow for enough space to type in the description of work performed (lets say cells A-D are merged in each row) however it seems that I am unable to utilize the auto format feature. To work around this I have to manually increase the row height after each entry. Is there a better solution for this? Thank you!

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