2012 has been the most awesome year since we started Chandoo.org.
The credit for this goes to our community of Excel users – that is you.
For practically every day of 2012, you have inspired me (and all of us at Chandoo.org) to learn something new, share and make you awesome. I know I say this many times, but I can never feel enough – Thank you for your support to Chandoo.org.
Apart from you, there are many other amazing people & companies that played a role in our success. In this post, let me highlight them & express my sincere gratitude.
People who helped me in 2012:
Teachers & Gurus:
Running a business, website & family requires a lot of motivation, fresh ideas & learning. Thanks to several wonderful teachers & inspiring individuals who gave me the strength I need this year.
Excel & Visualization Teachers:
Jon Peltier, Dick Kusleika, Debra Dalgleish, Mike Alexandar, Daniel Ferry, Robert Mundigl, Hui, Francis, Rob Collie, Bill Jelen and many more.
Chandoo.org Forum Members:
Hui, Sajan, NarayanK, BobHC, Faseeh, SirJB, Luke and all other regulars & Ninjas who contribute to my Excel knowledge everyday.
Business & Motivation
Andy Sernovitz, Darren Rowse, Yaro Starak, Avinash, Brandon Pearce, Alok, Pat, Chris, MrMoneyMustache, Jacob, Patrick and many more.
Technology
Amit Agarwal, John Gruber and many more sourced thru FlipBoard, Twitter & Pulse
Authors
As I was traveling quite a bit (1.5 months each in Thailand & Australia and few weeks with in India) I could not read as much as I wanted to. But I did manage to read & learn from some amazing authors, books. Special thanks to these wonderful authors.
- Chris Guillebeau $100 Startup
- Sam Walton Made in America
- Daniel Kahneman Thinking Fast & Slow
- Benjamin Graham Intelligent Investor
- Bill Bryson Down Under
- John F. Love McDonalds – Behind the arches
- Danielle S. Fairhurst Business Analysis using Excel
- Rob Collie DAX Formulas for PowerPivot
- Bill Jelen PowerPivot in Excel
And many other…
Note: All the book links to Amazon are affiliate links. That means, if you purchase something after clicking on them, I get a few cents 
Partners, Affiliates & Supporters
To make Chandoo.org successful, I collaborate with many great minds in this industry. Some of these remarkable people are,
Chandoo.org Partners
- Danielle at Plum Solutions (and her assistant Susan) helped me arrange first ever Excel & Dashboard classes in Australia.
- Paramdeep at Pristine Education (and their staff) helped us offer various financial modeling training programs thru Chandoo.org.
- Daniel Ferry at ExcelHero.com helped me offer Excel School training along with his academy so that many of you could become awesome in Excel.
- Ankush at ActiKnow Consulting for helping many of our clients with custom Excel solutions.
Our Affiliates:
This year was great for many of our affiliates too. Thanks to their support, we had more customers and they had more revenues. Some of our most prominent affiliates are,
Dashboard Spy, Francis, Daniel Ferry, Debra Dalgleish, Philip, Ken Puls, Oscar, Jimmy Pena, Victor Chan, Alan Murray and many more.
Our Supporters:
Many people selflessly spend their time & energy promoting our cause – to make you awesome. My sincere thanks and love goes to,
Hui, SirJB, BobHC, Luke, Faseeh, Sajan, Narayank and all our Forum regular members & Ninjas.
Special thanks to Fabrice, Robert, Oscar & others who regularly to link to us and spread the good word.
Press:
Special thanks to Kumara Swamy from Telegraph India for featuring me in an article this year.
Customers & Readers
This year, close to 5,000 of you blessed me with your product purchases from us. More than 55,000 of you are now part of our RSS / Newsletter community. Many more continue to join us each day. Thank you so much for inviting me in to your life & taking time to learn from us.
Many thanks to KPMG, Renault Nissan, Ecobank, SEEK, and many other corporate clients for supporting us this year.
I am also thankful to our Excel forum members.
Special thanks to
- Attendees of various live classes conducted by me this year in Perth, Sydney, Melbourne, Brisbane & Chennai.
- People in Sydney, Melbourne, Brisbane & Perth who met me when I was in Australia.
- People in Chennai who met me for coffee.
- Hui & Family, Danielle & Family for sharing some of my evenings very nice and memorable.
Our Staff
Most of what we did at Chandoo.org not even remotely possible without of staff. I am amazed at their level of commitment and support to our mission to make you awesome. My heartfelt thanks to,
- Ravindra: for helping with various training enrollments, emails & customer service
- Vijay: for teaching VBA
- Sameer: for answering student doubts in training programs
- Sujatha: for providing customer care & email support
- Pothi: for taking care of our server & site infrastructure
- Chittibadrayya: for taking care of all the book-keeping & accounting aspect of our business
Special thanks to Neel (our iPhone developer) too.
Websites & Companies that helped me in 2012
I am thankful to Microsoft for making Excel so awesome.
I am also thankful to,
Email & Productivity: Google, iPhone
Website, Hosting & E-commerce: WordPress, GoDaddy, Wishlist Member, KnownHost, Amazon, PayPal, E-Junkie, 2Checkout, EBS
Community & Connection: Twitter, Facebook, Youtube, Skydrive
Software: Paint.NET, Mozy, Notepad ++, Camtasia & Snagit, Skype
There are many other software, companies and websites that help me every day. I am really thankful to each and every one of these. Detailed listing here.
Last but not least…
There is someone else that deserve utmost thanks for everything I do at Chandoo.org.
- My family: Jo & kids support me and Chandoo.org in numerous ways. They shower me with love, humor and support everyday so that I can be awesome at what I do.
- All my close friends & relatives: for supporting me & encouraging me to do better.
PS… something for you:
Here is a nice little surprise for you. Go ahead and download it. Unlock the secret message.
PS: Incase you have difficulty downloading the file, see it in action here.
20 Responses to “Simulating Dice throws – the correct way to do it in excel”
You have an interesting point, but the bell curve theory is nonsense. Certainly it is not what you would want, even if it were true.
Alpha Bravo - Although not a distribution curve in the strict sense, is does reflect the actual results of throwing two physical dice.
And reflects the following . .
There is 1 way of throwing a total of 2
There are 2 ways of throwing a total of 3
There are 3 ways of throwing a total of 4
There are 4 ways of throwing a total of 5
There are 5 ways of throwing a total of 6
There are 6 ways of throwing a total of 7
There are 5 ways of throwing a total of 8
There are 4 ways of throwing a total of 9
There are 3 ways of throwing a total of 10
There are 2 ways of throwing a total of 11
There is 1 way of throwing a total of 12
@alpha bravo ... welcome... 🙂
either your comment or your dice is loaded 😉
I am afraid the distribution shown in the right graph is what you get when you throw a pair of dice in real world. As Karl already explained, it is not random behavior you see when you try to combine 2 random events (individual dice throws), but more of order due to how things work.
@Karl, thanks 🙂
When simulating a coin toss, the ROUND function you used is appropriate. However, your die simulation formula should use INT instead of ROUND:
=INT(RAND()*6)+1
Otherwise, the rounding causes half of each number's predictions to be applied to the next higher number. Also, you'd get a count for 7, which isn't possible in a die.
To illustrate, I set up 1200 trials of each formula in a worksheet and counted the results. The image here shows the table and a histogram of results:
http://peltiertech.com/WordPress/wp-content/img200808/RandonDieTrials.png
@Jon: thanks for pointing this out. You are absolutely right. INT() is what I should I have used instead of ROUND() as it reduces the possibility of having either 1 or 6 by almost half that of having other numbers.
this is such a good thing to learn, helps me a lot in my future simulations.
Btw, the actual graphs I have shown were plotted based on randbetween() and not from rand()*6, so they still hold good.
Updating the post to include your comments as it helps everyone to know this.
By the way, the distribution is not a Gaussian distribution, as Karl points out. However, when you add the simulations of many dice together (i.e., ten throws), the overall results will approximate a Gaussian distribution. If my feeble memory serves me, this is the Central Limit Theorem.
@Jon, that is right, you have to nearly throw infinite number of dice and add their face counts to get a perfect bell curve or Gaussian distribution, but as the central limit theorem suggests, our curve should roughly look like a bell curve... 🙂
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I'm afraid to say that this is a badly stated and ambiguous post, which is likely to cause errors and misunderstanding.
Aside from the initial use of round() instead of int(),.. (you've since corrected), you made several crucial mistakes by not accurately and unambiguously stating the details.
Firstly, you said:
"this little function generates a random fraction between 0 and 1"
Correctly stated this should be:
"this little function generates a random fraction F where 0 <= F < 1".
Secondly, I guess because you were a little fuzzy about the exact range of values returned by rand(), you have then been just as ambiguous in stating:
"I usually write int(rand()*12)+1 if I need a random number between 0 to 12".
(that implies 13 integers, not 12)
Your formula, does not return 13 integers between 0 to 12.
It returns 12 integers between 1 and 12 (inclusive).
-- As rand() returns a random fraction F where 0 <= F < 1, you can obviously can only get integers between 1 and 12 (inclusive) from your formula as stated above, but clearly not zero.
If you had said either:
"I usually write int(rand()*12) if I need a random number between 0 to 11 (inclusive)",
or:
"I usually write int(rand()*12)+1 if I need a random number between 1 to 12 (inclusive)"
then you would have been correct.
Unfortunately, you FAIL! -- repeat 5th grade please!
Your Fifth Grade Maths Teacher
Idk if I'm on the right forum for this or how soon one can reply, but I'm working on a test using Excel and I have a table set up to get all my answers from BUT I need to generate 10,000 answers from this one table. Every time, I try to do this I get 10,000 duplicate answers. I know there has to be some simple command I have left out or not used at all, any help would be extremely helpful! (And I already have the dice figured out lol)
Roll 4Dice with 20Sides (4D20) if the total < 20 add the sum of a rerolled 2D20. What is the average total over 10,000 turns? (Short and sweet)
Like I said when I try to simulate 10,000turns I just get "67" 10,000times -_- help please! 😀
@Justin
This is a good example to use for basic simulation
have a look at the file I have posted at:
https://rapidshare.com/files/1257689536/4_Dice.xlsx
It uses a variable size dice which you set
Has 4 Dice
Throws them 10,000 times
If Total per roll < 20 uses the sum of 2 extra dice Adds up the scores Averages the results You can read more about how it was constructed by reading this post: http://chandoo.org/wp/2010/05/06/data-tables-monte-carlo-simulations-in-excel-a-comprehensive-guide/
Oh derp, i fell for this trap too, thinking i was makeing a good dice roll simulation.. instead of just got an average of everything 😛
Noteably This dice trow simulate page is kinda important, as most roleplay dice games were hard.. i mean, a crit failure or crit hit (rolling double 1's or double 6's) in a a game for example dungeons and dragons, if you dont do the roll each induvidual dice, then theres a higher chance of scoreing a crit hit or a crit failure on attacking..
I've been working on this for awhile. So here's a few issues I've come across and solved.
#1. round() does work, but you add 0.5 as the constant, not 1.
trunc() and int() give you the same distributions as round() when you use the constant 1, so among the three functions they are all equally fair as long as you remember what you're doing when you use one rather than the other. I've proven it with a rough mathematical proof -- I say rough only because I'm not a proper mathematician.
In short, depending on the function (s is the number of sides, and R stands in for RAND() ):
round(f), where f = sR + 0.5
trunc(f), where f = sR + 1
int(f), where f = sR + 1
will all give you the same distribution, meaning that between the three functions they are fair and none favors something more than the others. However...
#2. None of the above gets you around the uneven distribution of possible outcomes of primes not found in the factorization of the base being used (base-10, since we're using decimal; and the prime factorization of 10 is 2 and 5).
With a 10-sided die, where your equation would be
=ROUND(6*RAND()+0.5)
Your distribution of possible values is even across all ten possibilities.
However, if you use the most basic die, a 6-sided die, the distributions favor some rolls over others. Let's assume your random number can only generate down to the thousandths (0.000 ? R ? 0.999). The distribution of possible outcomes of your function are:
1: 167
2: 167
3: 166
4: 167
5: 167
6: 166
So 4 and 6 are always under-represented in the distribution by 1 less than their compatriots. This is true no matter how many decimals you allow, though the distribution gets closer and closer to equal the further towards infinite decimal places you go.
This carries over to all die whose numbers of sides do not factor down to a prime factorization of some exponential values of 2 and 5.
So, then, how can we fix this one, tiny issue in a practical manner that doesn't make our heads hurt or put unnecessary strain on the computer?
Real quick addendum to the above:
Obviously when I put the equation after the example of the 10-sided die, I meant to put a 10*RAND() instead of a 6*RAND(). Oops!
Also, where I have 0.000 ? R ? 0.999, the ?'s are supposed to be less-than-or-equal-to signs but the comments didn't like that. Oh well.
How do you keep adding up the total? I would like to have a cell which keeps adding up the total sum of the two dices, even after a new number is generated in the cells when you refresh or generate new numbers.
So, how do you simulate rolling 12 dice? Do you write int(rand()*6) 12 times?
Is there a simpler way of simulating n dice in Excel?
I've run this code in VBA
Sub generate()
Application.ScreenUpdating = False
Application.Calculation = False
Dim app, i As Long
Set app = Application.WorksheetFunction
For i = 3 To 10002
Cells(i, 3).Value = i - 2
Cells(i, 4).Value = app.RandBetween(2, 12)
Cells(i, 5).Value = app.RandBetween(1, 6) + app.RandBetween(1, 6)
Next
Application.ScreenUpdating = True
Application.Calculation = True
End Sub
But I get the same distribution for both columns 4 and 5
Why ?
@Mohammed
I would expect to get the same distribution as you have effectively used the same function