Talk:Monte Carlo method

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Hello. The current revision says "It's well known that Monte Carlo methods were central to the simulations required for the Manhattan Project." Since there weren't electronic computers, how were the simulations carried out? Who was responsible for setting them up? Since the publications generally used to establish credit for the method date from the 50's, it seems this sentence needs to be clarified. Happy editing, Wile E. Heresiarch 15:11, 4 Mar 2004 (UTC)

I believe there were computers in that time. Consider the Atanasoff–Berry Computer, for example. -Stimpy 21:24, 30 November 2006 (UTC)
The calculations on the Manhattan Project were carried out on desk calculators by human computers initially, later they were performed using IBM unit record equipment programmed with control panels. Many many punch cards were used for input, output, and intermeediate results. -- RTC 18:42, 31 July 2007 (UTC)
There is something strange with Ulam's claim to have invented Monte Carlo methods in 1946. Without going back to Buffon or Pearson, Monte Carlo methods had already been used by Fermi and later by the Manhattan Project (probably already with Metropolis and Von Neumann, though the articles were published much later on). So the idea was in the air. However there is no denying that the increasing power of the computers helped, to make this method widespread. The article by Metropolis was published, I think, in 1949, though he must have had the idea long before.
This article is interesting It shows that the researchers at Los Alamos were perfectly aware of the "statistical sampling" technique, which is actually just another name for Monte Carlo methods. Their idea was just to give it a new life thanks to computers. It also tells how Fermi had had the same idea 15 years before.

Just querying whether 'To be written' should be in the article, or here? Something I've been thinking about actually: Do we keep a strict dichotomy between wiki and metawiki (ie, the content, and writing about it) with their respective namespaces, OR do we do whichever is considered most efficient for improving the article? As always, just throwing ideas about. nsh 22:18, Mar 19, 2004 (UTC) (talk)

In 2002 and before, to-do notes in articles were exceedingly popular. They're not so fashionable anymore but they're not against policy. -- Tim Starling 05:34, Mar 20, 2004 (UTC)

There's some advice to the effect that omissions should be noted. I find this unrealistic (in particular in mathematical topics, where completeness is unlikely, to say the least).

Charles Matthews 12:59, 12 Jun 2004 (UTC)

This article links to the disambiguation page for degree of freedom. I think it should link directly to the degree of freedom (statistics) page, but I don't know enough to be sure. Hopefully someone else does.

I think degrees of freedom (physics and chemistry) is the best page to link to, and I changed the article accordingly. Others may differ. -- Jitse Niesen (talk) 10:55, 7 September 2005 (UTC)

What's wrong with including GAs? They are a reasonably good method for optimisation in many-dimensional spaces. -- Tim Starling 07:59, Mar 31, 2004 (UTC)

Hi, I changed the reference from "central limit theorem" to "law of large numbers" in the description of the rate of convergence in numeric integration. The law of large numbers is the theorem about convergence of a sample mean to the population mean, and the central limit theorem is about convergence in distribution of a sample mean to a normal r.v. Since normality doesn't matter here, the LLN is the correct theorem. It's not quite obvious because it's applied to the square of the sum and not the sum itself. Gray 23:06, 17 June 2006 (UTC)

Simple Description[edit]

This article is quite technical. It would be nice to have a simpler layman's description too. -- 11:51, 20 September 2005 (UTC)

I'm not sure every scientific topic should have a layman's description. That could cause ( was course) some very long articles. However, I remember a teacher introduced Monte Carlo simulations with this example: Imagine you are walking on a beach and suddenly find that you can't remember the numerical value of pi. What can you do? Draw a square and a circle within the square, with the circle as large as possible. Then throw a number of sandgrains (say 1000) randomly in the square (I guess you would have to find a different color of sand to tell the difference). Since we know the ratio between the area of the circle and the area of the square is pi/4 we can find an approximation to pi by counting the grains outside (or inside) the circle and the deviation can be found from the number of grains.
This could be illustrated with a square, a circle and a number of "randomly" distributed dots, and used as an illustration for this article, with the explanation in the image text. Do you think that would be relevant? Zarniwoot 10:00, 24 January 2006 (UTC)


How about adding some words about the use of a monte carlo method to find factors. Eiler7 10:55, 4 February 2006 (UTC)

yeah... high precision numeric analysis, simulated.... analytic memories, stuff like that: it might evn work... ... Florin Matei, Romania — Preceding unsigned comment added by (talk) 10:45, 25 November 2011 (UTC)


Perhaps I'm missing something, but the article seems to lack a description of what the Monte Carlo method is, instead only describing applications. AaronSw 03:35, 30 May 2006 (UTC)

I totally agree with you. I looked this up because I want to be able to answer the question: "What is a Monte Carlo simulation?" with a two or three sentence summary. I still can't do that after reading the article. (Aug 8, 06)
How doesn't "Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms." answer the question? Would moving the mention of nondeterminism to the first sentence help? Fredrik Johansson 22:27, 8 August 2006 (UTC)
It doesn't, in fact, answer the question. The sentence you quoted gives an extremely broad classification, and then explains the differences with other methods. But it lacks an (adequately) informative definition of what the method really is, or at least how it's supposed to work. Some parts of the article later hint at the fact that MC is a form of evaluation based on repeated simulations from a set of randomized inputs (which is what I think it really is, though I'm not an expert at all - so don't quote me on that), but that info should probably be placed in the intro in a clearer form. 20:55, 8 February 2007 (UTC).
Reading the rest of the talk page, I see that this is not the only request for a simpler explaination. Maybe adding a simple example (like the classic circle area by hit/miss, as suggested somewhere above) after the definition may help. -- Sergio Ballestrero 08:04, 9 August 2006 (UTC)
Good idea. Numerical integration is probably the best example of a Monte Carlo method, and possibly the simplest to understand for non-technical readers. By the way, after reading the definition in the Dictionary of Algorithms and Data Structures, I'm inclined to agree that the one used here could be improved. The following distinction is made between two main types of randomized algorithm: "A Monte Carlo algorithm gives more precise results the longer you run it. A Las Vegas algorithm gives exactly the right answer, but the run time is indeterminate." Fredrik Johansson 13:55, 9 August 2006 (UTC)
And our lead section's definition is conflicted. It says the difference is the process is not deterministic, but typically PRNGs are used, making the process fully deterministic, just similar to a stochastic one. That and I agree the definition isn't really clear. I don't have any good books in front of me or ideas off the top of my head how to make the lead better, but I'll see what I can do. Any proposals for a clearer and more accurate lead would be great. Adding an example is not a bad idea, but the explanation shouldn't depend on it. - Taxman Talk 17:18, 9 August 2006 (UTC)

I absolutely agree that this article could be much clearer by providing just a short, clear answer to the question : What is the key property which makes the Monte Carlo method the Monte Carlo method? I have a good background in CS and maths, and was just looking to this article for a quick refresher on what made something a Monte Carlo simulation. Which I ended up going to google and going somewhere else for. It just needs to be made clear that the Monte Carlo method is and provides a quick way to provide a good, approximate numerical value when actually calculating the exact value is either impossible or too time consuming. 16:13, 17 March 2007 (UTC)

Agreed: It is an incdredibly simply concept make increcedibly obscure and impenetrable by too many f***ing wannabe PhDs over-editing the f***ing article --- I have made a start modifying the article's first intro sentence to explain what the f*** Monte Carlo Menthods actually are: throwing a f***ing dice and measuring the results: nothing f***ing more and f***ing nothing less. Can anything be any f***ing clearer than this people!!!??? BY GOD I'VE ENJOYED THIS!!! (talk) —Preceding undated comment added 09:57, 17 March 2013 (UTC)

Commercial software packages[edit]

This section was accumulating nonnotable specialized software or other links that looked to be linkspam. So I partially cleaned it out and rephrased the lead to include phrasing on general purpose use and notability. My gut feeling is that Crystal Ball and @Risk are the pre-eminent tools and I could see only including them plus other software that is (or becomes) equally well accepted. However, I lack a non-OR source for this so I leave it to the group to comment. Martinp 21:41, 10 July 2006 (UTC)

I'm a little puzzled by external software links on a page like "Monte Carlo methods", a technique, by the way, that is completely software-dependent. Crystal Ball and @Risk are certainly widely-used tools and should be noted here. However, the fact that only spreadsheet add-ins are listed here is very misleading, as it implies that spreadsheets are the state-of-the-art in Monte Carlo simulation. While they are certainly widely used (because spreadsheets are ubiquitous), I find it hard to believe that any academic or practitioner would state that they are state-of-the-art in terms of Monte Carlo simulation tools. We have a tool (GoldSim) that is a general purpose Monte Carlo simulator, but is repeatedly removed from this external software list (while spreadsheet add-ins remain). It is both relevant (the software is completely focused on Monte Carlo simulation) and notable (used worldwide by government, commercial and research organizations, including the very national labs where the Monte Carlo method was first widely used: Los Alamos, Sandia, Argonne, Lawrence Berkeley). I understand the need to limit linkspam, but if you are going to have external software links at all on a topic like this (and I think you should, as without software, the method is not practical), it seems to me that some attempt should be made to be comprehensive regarding the tools that are actually used in the community.

It seems to me that either all software that contains Monte Carlo simulation should be listed in links or non should be. At present wikipedia listing of products acts as an implicit endorsement. And the irony is that the products listed are far from being the most widely used. i.e. the removal of spreadsheet add-ins Crystal-Ball, @RISK and Solver on the one hand and the omission of spss or Stata. —Preceding unsigned comment added by RWillwerth (talkcontribs) 21:40, 20 November 2009 (UTC)


too many hyphens for my taste. The asides should be mentioned later, preferably in separate sentences. then again, it sets the mode for the randomness theme... Ojcit 17:47, 15 September 2006 (UTC)

I don't have a problem with the number of dashes, however the entire article incorrectly and inconsistently uses hyphens, en-dashes and em-dashes.
I agree that that needs to be fixed.
— DIV ( 10:28, 17 July 2007 (UTC))


I came across a book several (~7) years ago (not necessarily new at the time), which I recall clearly stated that the Monte Carlo method was not named after the casino. I struggle to recall precisely what it was named after, but I think it was a conference or workshop held in Monte Carlo. Obviously the casino link 'sounds right', but that doesn't mean that it is right.
—DIV ( 10:56, 17 July 2007 (UTC))

P.S. Do not add a recent reference which makes a passing reference to gambling at the casino, chance, and the random features of this method. The citation needs to be to either one of the first appearances of the term, where its derivation is made clear or to a later publication which has properly studied the etymology.
—DIV ( 07:15, 19 July 2007 (UTC))

It's in MacKeown. If you're claiming that the textbook is wrong, then it's you who needs a reference, not the article. -- Tim Starling 22:03, 20 July 2007 (UTC)
Since this seems to be controversial, citing the page in the text would be helpful. --Rinconsoleao 11:03, 23 July 2007 (UTC)
I don't have the book anymore, but I believe it was in the introductory chapter. The original version of that history section, written by me, was based on that chapter from MacKeown. -- Tim Starling 06:51, 28 July 2007 (UTC)

Twooars has since (08 April 2008) added a very helpful reference to an original journal article by Metropolis, which is obviously beyond question. Thank-you for clarifying this, and I hope my request for confirmation of the claim was taken in the right spirit: in the end the article is better for inclusion of the appropriate reference. —DIV ( (talk) 07:32, 8 August 2008 (UTC))

At some point the lead and the later article have become desynced on this issue: intro says Metropolis named it, later it says von Neumann named it. (talk) 12:29, 3 May 2013 (UTC)
I was confused by this as well at first, but the article is not desynced as the two sections are referencing different things. Metropolis came up with the name "Monte Carlo Method" for this particular statistical sampling method (Metropolis 1987, Anderson 1986). John von Nuemann code named their Los Alamos work on neutron reactions "Monte Carlo" after the name of the method they used in the work (Grinstead & Snell 1997). shalley303 — Preceding undated comment added 19:14, 15 September 2014 (UTC)

Lack of Technical Details[edit]

Sorry - I would add this to the above comments but still working out how to do this.

In my opinion there is insufficient technical detail in this document for it to be of any use - i.e. how does it work and why does it work.

I completely agree. Explanations given do not qualify for more than broad descriptions. I suggest rewriting or at least giving some examples. Ben T/C 18:18, 22 February 2007 (UTC)

Got the idea, but still not clear about how to get the "random numbers". —Preceding unsigned comment added by Genie05 (talkcontribs) 17:38, 3 February 2008 (UTC)


Carlo should be in CAPPS

Ah-huh, but why?    And what is "CAPPS"?   And what is "Eddit"? ;-)p
— DIV ( 10:31, 17 July 2007 (UTC))


I read this article with great interest, and upon finishing it, realized that I still didn't know what computational method a Monte Carlo simulation follows. I would like to know that. It is clear that the author knows his subject, but the article is so full of mathematical terminology that it seems to assume that the reader is highly math-literate. Highly math-literate people probably already know what a Monte Carlo simulation is, and don't need to consult Wikipedia to find out.

"Applied information economics"[edit]

Somebody added a long section on a technique called "Applied Information Economics" which is a variant of a Monte Carlo method apparently used (how often, I'm unsure) in government and private sector cost-benefit analysis. This was previously placed right near the top, which is clearly inappropriate because it is not central to most fields of application of Monte Carlo. I moved it down below the section on history of Monte Carlo, where it makes more sense. But maybe it should be deleted entirely as it is insufficiently important in most of the contexts discussed on the MC page (there is still a link to the main "Applied Information Economics" page). --Rinconsoleao 16:09, 16 July 2007 (UTC)

If you thought it would be more appropriate further down the article, you were free to move it, or reduce its length if necessary. But sinse I've actually trained quite a few Monte Carlo experts in methods for improving their tool, I felt it was relevant. I'm perfectly willing to limit my contribution on this to the discussion page. I might concede that much of what is said here about AIE is probably more appropriate within the AIE page itself.Hubbardaie 03:03, 17 July 2007 (UTC)
I think this section should go. OliAtlason (talk) 00:38, 12 February 2008 (UTC)

Inverse Problem citations by Author of citations[edit]

Most of this section was removed because it was argued that, since the person who originally posted the supporting citations was, in fact, the author of the citations, it violated NOR. I don't see how this follows and I undid the edit. There may be a COI argument but if the sources are published in some reliable source then it is, by definition, not OR. Even a COI objection would be irrelevant if the citations are verifiable and there for all to judge for themselves. I think if wikipedia starts saying that the only people who can't edit an article are the very people most qualified to edit it (i.e. published researchers in the field) then you would be setting bad precident. The only action should be that the COI should be a flag for others to examine the citations in detail. If they are valid, then leave them alone.Hubbardaie 15:26, 26 August 2007 (UTC)

Battleships diagram[edit]

What is the point of the battleships diagram? It has no caption, and I have literally no idea what it could possibly mean. I've skimmed the article and it has nothing about Battleships. What is it meant to be proving or explaining? I am baffled by it. —Preceding unsigned comment added by Edbrims (talkcontribs) 23:52, 19 October 2007 (UTC)

I agree, I really don't find it illuminating at all, and there is no "battleship" example in the text. Furthermore, as a student of these things, i've never heard of a battleship example, nor do I follow where it's going. If an effort was made to make a pedagogical laymans example out of Battleship then great. Otherwise Buffons needle, random walk optimization of TSP, ray tracing, etc. are all better examples that could easily be coupled to an illustrative figure. Right now I fear the figure is doing more harm than good. Thoughts? jugander (t) 19:03, 23 October 2007 (UTC)
How about: a) a random sampling is taken showing one 'hit'; b) an algorithm is run which suggests two possibilities; c) one of those possibilities is chosen. It illustrates the method by the fact that more samples, or game rounds, would provide more hit/miss data points and thus improve the accuracy of the prediction. 21:01, 23 October 2007 (UTC)
Oh wait, the 'c' image shows that an additional game round has been played which absolutely determines the position of the ship -- isn't that the Las Vegas algorithm instead? 21:07, 23 October 2007 (UTC)
Hmm. What exactly are we trying to calculate by Monte Carlo? The probability distribution of the opponents ship placement/orientation? In that case it's a bad example, because if we're playing many games to infer the opponents strategy, then in fact each *game* would be a draw from the underlying distribution, observed at the end, and then we estimate the strategy based on those draws. It seems like a poor exmaple since the probability collapses at the end of the game. Unless the illustration is trying to say something about estimating th placement distribution online. But then we have problems with game theory, dual control. et al. Somehow this seems like a messy example, compared to a clear presentation of how to estimate pi by MC integration. Or I've once again mis-/not understood the figure... jugander (t) 17:49, 24 October 2007 (UTC)
I think you've nailed all of the problems with that diagram 17:11, 29 October 2007 (UTC)
Then why is the diagram still there? — Preceding unsigned comment added by (talk) 07:34, 14 June 2011 (UTC)

Cootie, Candyland or Chutes and Ladders: Solving a Parent's Dilemma with Monte Carlo Simulation[edit]

A tongue-in-cheek but scientific study was done by a fellow named "Barry M. Wise, PhD, Father" (as he put it) to show that the Monte Carlo Method could be used to solve real-world (as in everyday) problems - in this case selecting a pre-school game that won't have the parent's tearing their hair out over its length when the parents have to play with their pre-schooler.

He says in his introduction: "Monte Carlo simulation is used to determine the distribution of game lengths in number of moves for three popular children's games: Cootie, Candyland and Chutes and Ladders. The effect of modifications to the existing rules are investigated. Recommendations are made for preserving the sanity of parents who must participate in the games."

While this study hardly fits into the "high-flutin'" things in this article, it is a good example of a more common use the Method could be put.

I would recommend adding at least a mention of it in the article. Dr. Wise's study may be found in its entirety at this website: 04:34, 15 November 2007 (UTC)

Renaming the article[edit]

I suggest the article be swapped with Monte Carlo algorithm to comply with other articles with similar names, e.g. Las Vegas algorithm. Stimpy 16:17, 5 November 2006 (UTC)

But Monte Carlo is a whole class of methods, not just a single algorithm. So the page name seems appropriate as it stands. --Rinconsoleao 16:13, 16 July 2007 (UTC)
I propose therefore that we simply pluralize it.--Adoniscik (talk) 00:36, 10 January 2008 (UTC)

Randomized algorithm and Monte Carlo[edit]

Isn't this article far more informative than the Randomized algorithm article, of which this is a subclass? should some of this be merged into that article? Paulcd2000 (talk) 16:19, 19 May 2008 (UTC)

"JIANG BANG"[edit]

Hi. Am I the only one who sees this strange phrase showed on thisscreenshot? There's no such text in the page source. The template doesn't have anything like that either. How can this be explained? --Nevknown (talk) 13:33, 16 December 2009 (UTC)

One of the templates used to make the page was vandalized here. It's fixed now. Thanks for the screenshot; made it easier to track down. Kuru talk 00:36, 17 December 2009 (UTC)

Broken Links[edit]

The link in external links to 'Introduction to Monte Carlo simulation' is broken. (talk) 09:55, 28 June 2010 (UTC)

Fixed, thanks for pointing it out. Qwfp (talk) 10:27, 28 June 2010 (UTC)


The definitions section has 3 examples, and - maybe I'm a bit dim - there doesn't seem to be any difference between example 1 and example 3. It there is, it is very subtle and needs to be made clearer. Fmph (talk) 07:09, 25 April 2011 (UTC)


hot line paradigm: a monte carlo technique that knows that interest comes from border line n tries to take account of that (talk) 21:24, 16 September 2012 (UTC)

using just as that necessary mem (O(log)) to compute correctly a digit, n using doubling precision on one iterration might b able to produce much more than 10^15-th decimal for PI

ok, USA, m sorry if i interrupting anything like some civilisation all long sleep around ... i think PI might b computed liniarely by a technique used by analog to digital converters n Monte Carlo techniques... try a simulated numeric analyse n u might b beating by far world record for pi nth decimal or binary digit Florin Matei,Romania — Preceding unsigned comment added by (talk) 11:03, 25 November 2011 (UTC)

ok, in this technique, for example to estimate PI aiding a circle that is sourunded by a square, u might use the actual set of random generated coordinates to make a fuzzy math numeric style new.... terms added to... amount already made for the two numeric values that form the probability... Florin Matei,Romania — Preceding unsigned comment added by (talk) 10:42, 25 November 2011 (UTC)

"Monte Carlo method applied to approximating the value of π. After placing 30000 random points, the estimate for π is within 0.07% of the actual value. This happens with an approximate probability of 20%." 20% ?? Shouldn't it instead of 0.07% be given a percentage that can be ashieved in MORE than 50% of trials, instead of just 20%? - Maybe 80% is the correct figure and it should read: "... with an approximate probability of 20% OF FAILURE." ? (talk) 06:18, 15 January 2013 (UTC)

simple program means sometimes simplistic, 2 simplistic... they sometimes use to say g in g out but dont worry, im a poor encoder too, no offense, i hope :) — Preceding unsigned comment added by (talk) 16:06, 16 February 2013 (UTC)

Games sub-section[edit]

The only reference on that section is a non-published pdf. I searched Web of Knowledge and that paper does not exist in the database, and the authors don't show in keywords "Topic=(Monte-Carlo Large POMDPs)". If no one opposes, I'm going to delete that sub-section: it does not fulfill either nobility requirement neither proper citing references.Jorgecarleitao (talk) 08:57, 15 January 2013 (UTC)

I readded this section, edited it heavily, and added references. Monte Carlo Tree Search has been used for many games and there are many published papers about it, so I certainly think it qualifies as notable! Mattj2 (talk) 06:49, 15 May 2013 (UTC)
Now I agree more on the notability and referencing. Thanks for working it out!Jorgecarleitao (talk) 07:40, 15 May 2013 (UTC)
You're welcome. (And you were right to delete it before when it had no references. :) Mattj2 (talk) 08:02, 15 May 2013 (UTC)

Monte Carlo method[edit]

This method is not about who used it and when. All text of such type shall be removed for not having any value.--Michelle Ridomi (talk) 13:43, 12 February 2015 (UTC)

External links moved from article[edit]

Given the state of the article, I think we're well beyond having most if any of these in the articles except perhaps as references: --Ronz (talk) 19:26, 26 June 2015 (UTC)