Talk:Mastermind (board game)

Untitled

IMAGE PROBLEM: did anyone look at the fourth guess and see how it was scored? —Preceding unsigned comment added by 76.110.165.21 (talk) 03:01, 14 August 2008 (UTC)

Contradiction: So exactly how old is Bulls and Cows? Compare top mention with later mention. Was Master Mind "invented" or "designed"? Surely a plastic rendering of a classic pencil and paper game is "innovation" at best, not invention. Master Mind was no more invented than a plastic rendering of "battleships" ever was/is!! —Preceding unsigned comment added by 76.110.165.21 (talk) 02:56, 14 August 2008 (UTC)

I'm sure this is needlessly pedantic, but ... the picture on this page shows red and white pegs used to communicate the results of guesses, whereas the text talks about black and white pegs. Which is the original / the most common? Should the text or the picture be changed?

Pedantry is good! I changed "black" to "colored" in the text. (Speaking of pedantry, it is helpful when making comments in Talk pages to include a signature with ~~~~ (four tildes), because it includes the date and time stamp. That way, if somebody comes across this page in a month or a year, they'll know that it's an old comment that doesn't need to be immediately addressed) DavidWBrooks 16:38, 21 Jun 2005 (UTC)

I always played this game using five pegs rather than four. Presumably this was a mark II version. The rules given in the article refer consistently to four pegs and I don't know when the five peg version came about, so I'm not sure how to edit it in order to include this. Shantavira 07:24, 22 July 2005 (UTC)

Game time about 20 minutes? Last two games I played each were over 2 hours!!!!! Lochok 00:02, 9 January 2006 (UTC)

The first comment, "Image Problem", was trying to say that some guesses in the image were scored incorrectly. This could be confusing if a reader looks at the picture for scoring examples. Someone should find a new image. 50.168.5.188 (talk) 08:32, 4 June 2017 (UTC)

Algorithm

The algorithm provided is really extremely unhelpful and does not specifically relate to Mastermind in any way. Removing. -Fuzzy (Sorry... forgot to sign it a few edits back)

I prefer the Super Mastermind, and still do it in less than 10 minutes. A more challenging game is played with the 5 holes, using a blank hole as a "color" for a total of 9 colors, and allowing doubles. - 163.238.45.107

Piker! I play Super-Extra-Special Mastermind, with 127 colors including two in the ultraviolet spectrum, and do it in less time than it takes to say "ultraviolet spectrum." - DavidWBrooks 20:02, 8 November 2006 (UTC)

count_removals

What does count_removals() do? Can somebody clarify this? --Peni (talk) 16:47, 9 August 2008 (UTC)

Name and variants

Why does the article give "Mastermind" only as one word? In the Invicta editions at least, it was always "Master Mind", and this suggests that it was the original name. There was:

• Master Mind (code length 4, 6 colours, 10 guesses)
• Mini Master Mind (travel version, code length 4, 6 colours, 6 guesses)
• New Original Master Mind (code length 4, 8 colours, 10 (?) guesses)
• Super Master Mind (code length 5, 8 colours, 12 guesses)
• Word Master Mind (code length 4, 26 letters, 10 guesses)
• Number Master Mind (code length 4, 6 digits, 10 guesses)
• Grand Master Mind (which I've never seen)
• Master Mind for the Blind (which I've never seen, nor experienced by whichever sense that game relies on :-) )

And I just noticed "Duplicates are allowed, empty allowed". Allowing empty holes has never been part of the standard game IMX, although the rulebook for Super Master Mind suggests it as a more challenging variation. -- Smjg 11:01, 27 February 2006 (UTC)

But wait—there's more, at least according to a search of boardgamegeek.com:

• Supersonic Electronic Mastermind (no clue what this is)
• Mastermind for Kids (code length 3, 6 colors)
• Mastermind Secret Search (sounds similar to Word Mastermind but with up/down instead of correct/incorrect location)
• Royale Mastermind (code length 3, 5 colors × 5 shapes)
• Zoom Street: Mastermind Junior (code length 4, 6 colors)
• Mastermind44 (code length 4?, 6 colors, 4 players)

Okay, I admit I've played none of those variants—or even heard of them until just now (but I have played about three or four from Smjg's list). Still, what do people think about adding a list of variants to the Mastermind page? Good idea? Bad idea? I see there's already a Variations section with not much content in it; that's probably a decent place for such a list. Spakin (talk) 04:25, 13 October 2009 (UTC)

Heck, I just went ahead and added a table of variants taken from the above lists. I generally excluded variants that merely replace colors with automobiles, animals, etc. unless they also alter the number of colors, peg positions, or some other aspect of game play. Spakin (talk) 21:32, 18 October 2009 (UTC)

and another...

• Mattel Mind Boggler / Memoquiz (5 digits) http://www.handheldmuseum.com/Mattel/Mind.htm Dcsutherland (talk) 04:59, 23 May 2014 (UTC)

Moo

I moved the "moo" reference to the bottom, and I'm not sure it belongs at all. We can't just imply that Mastermind was somehow influenced by moo, as we did - we need to supply some backing evidence. - DavidWBrooks 18:04, 7 May 2006 (UTC)

Magnus Magnuson/John Humphries?

I have a mastermind box somewhere with who I think are the presenters of Mastermind on the BBC. It is a fairly old box, during the Magnus era, but the man on the front looks like Humphries, but he has an assisstant. Can anyone shed any light on this, as to whether the man on the front is Magnusson, Humphries or just an archetypal mastermind evil villain? ~~Lazyguythewerewolf . Rawr. 10:22, 20 October 2007 (UTC)

Knuth algorithm

The first line of the pseudo code for the Knuth algorighm contains an error. Furthermore, IMHO, some of the chosen identifiers are not very clear (eg. maximumGuessScore is not a score but a number of removals). I suggest the following changes:

while coloredScore != 4
   if numberOfTries == 0
       guess("aabb")
   else
       maximumNumberOfRemovals = 0
       maximumGuess = ""
       foreach possibleGuess
           minimumNumberOfRemovals = 9999
           foreach possibleScore
               numberOfRemovals = count_removals(possibleGuess, possibleScore)
               minimumNumberOfRemovals = min(numberOfRemovals, minimumNumberOfRemovals)
           if minimumNumberOfRemovals > maximumNumberOfRemovals
               maximumNumberOfRemovals = minimumNumberOfRemovals
               maximumGuess = possibleGuess
       guess(maximumGuess)  —Preceding unsigned comment added by 80.101.196.183 (talk) 14:12, 17 November 2010 (UTC) 

The first line "correction" above is incorrect. Pricklypeach (talk) 06:42, 15 January 2011 (UTC)

As i've been spending the past long while trying to parse the text given for the Knuth algorithm, i think i can say with confidence that it is supremely nonsensical. Can somebody who understands how the algorithm works better explain? Dreamer.redeemer 06:12, 13 November 2007 (UTC)

It is saying that after the first guess of aabb, you should always pick a guess that will, with the least helpful possible (accurate) response from your opponent, let you eliminate the most possible answers from your current list of possible answers. It is not assuming that you should skip considering obviously incorrect guesses. (This seems like the best strategy for always winning within a certain number of moves, but not the best strategy for winning in the lowest average number of moves over time.) 72.155.97.123 (talk) 21:03, 6 September 2008 (UTC)

It is not necessarily "the best strategy for always winning within a certain number of moves". Pricklypeach (talk) 06:42, 15 January 2011 (UTC)

In the description of Knuth's algorithm, step 3 starts with "For each possible guess (not necessarily one of the remaining possibilities) [...]". I think that the text in parenthesis is wrong, since step 2 removed all possible guesses that could not be remaining possibilities. Can anyone confirm this ? Thanks 82.121.75.8 (talk) 21:13, 6 January 2009 (UTC)chromanin

The point is that you may be able to eliminate more possibilities by guessing an obviously incorrect guess than you would eliminate by guessing a guess that is still possibly accurate. At the beginning of the game, the number of possible guesses you can make and the number of possibly correct answers are the same. As play progresses, the number of possibly correct answers decreases, but the number of possible guesses you can guess remains the same. (E.G., you know there are not four blue pegs--still yet, you are free to guess four blue pegs!) Each time you guess, Knuth says, consider each possible guess, not just the "remaining possibilities"--that is, not just the guesses that could still actually be correct answers. That is because an obviously incorrect guess may help you narrow things down more than a possibly correct guess would. For example: you know after guess #3 that the correct answer is CCC?, with the fourth peg being either E, F, or another C. You could try each of the remaining possibilities in turn, and win in either four, five, or six total guesses, depending on luck. Or, you could make an obviously incorrect guess on your fourth guess and guarantee a win on guess #5. Explanation: Guess #4: EEEF. If the response is one dark peg, then the correct answer is CCCF. If the response is one light peg, then the correct answer is CCCE. If the response is no pegs, then the correct answer is CCCC.Simple314 (talk) 05:04, 24 January 2009 (UTC)

Fair use rationale for Image:Codebreaker widget won.png

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Ambiguity about white pegs feedback info

I feel that the role of white pegs as was described:

a white peg indicates the existence of a correct color peg placed in the wrong position

is not really helpful. For example, if the secret code is RBBB and the guess is GRRR, clearly the 2nd, 3rd and 4th R pegs are exaclty in the same situation: there exists a R peg in the secret code, but in another position. But we do not give as feedback 3 white pegs, but one, if I am not wrong. So, I think the role of white pegs should be rephrased, as something like: "The number of white pegs is the extra number of black pegs that it is possible to get using exactly the pegs in your guess". What do you think? User:zeycus 11:34, March 29th, 2008 (UTC)

No feedback in two weeks, so I am going to be bold and make the change in the article. User:zeycus 14:04, April 13th, 2008 (UTC)

First of all, on the early 1970s Super Mastermind game, there are 8 colored "pegs",red blue green black yellow white brown gold & using a blank or empty peg hole/space acting like a 9th color. These are the "coding pegs", such as the "code pegs" under the cover. Then there are the black & white "decoding sticks" that are placed on the left side to help you work your way to the final matching code. There are 4 methods of play that I know of to solve the code. When I purchased the game, there were no rules of play or instructions in the box. On the 12 row by 5 column Super Mastermind game, you should be able to solve the code by the 6th or 7th or 8th or 10th row (employing all 8 colored pegs and the blank space), depending on the chosen method of play. Beware of "pulling" or non-congruency of sticks to pegs, from the other player who is not properly matching the number and/or proper color of the decoding sticks to the coding pegs.(Edited Aug 4, 08) —Preceding unsigned comment added by 65.184.163.219 (talk) 02:11, 5 August 2008 (UTC)

Technical confusion

In the article, it says there are 10 rows, but in the picture, there are 12. I'm going to change it to 12, but if it really is 10, please provide a picture that has 10 rows of spaces in it. ZtObOr 03:31, 4 October 2008 (UTC)

• It's either 10 or 12. I was playing today on a 10-row set, which we've had for at least a couple of decades. Perhaps the 12-row sets are newer. 91.105.22.251 (talk) 20:00, 2 January 2009 (UTC)

Kenji Koyama

was one of those ... subsequent mathematicians ... finding various algorithms...in 1993. The entry linked to this name is about a football player born in 1972, hence an 11 year old pupil. Are you sure, the two are the same person? Note that the cited source names Mami Koyama. ( --217.231.44.120 (talk) 22:21, 25 November 2008 (UTC)

Computer Version

A superb freeware version of Mastermind called Absolute Mastermind by By Peter & Sven Nordstrom exists and can be found here: http://w1.435.telia.com/~u43509647/ DJParker39 (talk) 03:16, 19 December 2008 (UTC)

Variant currently without ref

there is a version of mastermind that I don't yet have a reference for used in competition in the past (late 80s? early 90s). It translates as "absolute mastermind". The code setter never actually marks the code and play continues as normal. Each time the code setter has to give a valid score or else they lose. Play continues until the code is cracked or that the guesser makes a challenge. If a challenge is made then if the setter can make a valid code they win otherwise they lose.Tetron76 (talk) 12:31, 29 April 2011 (UTC)

Numerical error in article

The article reports that "Koyama and Lai found a method that required an average of 5625/1296 = 4.340 turns..." and that "The minimax value in the sense of game theory is 5600/1296 = 4.341". But 5625>5600 and 4.340<4.341. The origin of this mistake is probably in another result of Koyama and Lai from that paper [1]. At any rate the correct minimax value should be ascertained as reported properly. עוזי ו. (talk) 19:11, 8 December 2013 (UTC)

Both numbers are correct. The second number is bigger because it is based also on the strategy of the codemaker. To get the first number (the average) it is assumed that the codemaker is choosing each code with the same probability 1/1296.--Lefschetz (talk) 16:46, 11 December 2013 (UTC)

Clarifying the Knuth Algorithm description

Fresh off implementing it after reading Knuth's paper (thanks to someone for the reference and whoever put Knuth's paper online in .pdf) I have attempted to clean up the description here to the point that someone else might be able to program it without referring to the paper but without rendering it as code or pseudo-code. I also retained the term "guess" whiles Knuth uses the term "test pattern" and "codeword" in the paper. In particular Knuth states that the next guess should be from the current "set S" (a "valid" pattern, as Knuth writes it) whenever possible which gives the best chance of winning on the next turn while still assuring the win in five or less. That detail was omitted in the prior version. He then gives an example (that I will not spoil here as he leaves it as an exercise for the reader) showing a fourth guess (Knuth describes it as "really a brilliant stroke") that cannot win because it is not in S but is the only guess that nails down a win on the next turn. I used the numbers 1..6 as Knuth does in the paper, where he also refers to black and white pegs. I have used "colored" in deference to the picture and the earlier talk. I found the term "possible guess" vague. What is an impossible guess? It seems that every code except those already used are the set of possible guesses (codes previously used will not add any information, and will be eliminated by the minimax process in any case). I did not go into detail about how to calculate how many possibilities would be eliminated for each "possible colored/white peg score" nor did Knuth. The easiest thing seems to be to run each trial guess against every member of S and count the scores that result. This certainly gets all the "possible scores" very directly. The count indicates the size of the new set S for a given colored/white score thus the maximum count will be the minimum removed and equivalent to the score mentioned in the article. Knuth expresses his result in "Fig.1" a concise (considering the number of cases it deals with) but challenging to read expression in a notation he develops earlier in the paper that completely characterizes the result of applying the minimax process described here to all 1296 codes. It is an good example of why we have references rather than republishing in these articles. I would like to add more detail about how the "worst case 6 with lowest average" methods work but I have not been able to obtain those references. Jszigeti (talk) 00:27, 23 January 2014 (UTC)

More clarification for the Knuth Algorithm description

The algorithm description reads:

"minimum eliminated" = "count of elements in S" - (minus) "highest hit count"

However, I was wondering if it should instead read:

"minimum eliminated" = "count of elements in S" - (minus) "number of elements in S which have the highest hit count with the guess"

Solution of (7,5) Mastermind

It is not widely known that the (7,5) Mastermind. It is ALWAYS possible to solve within 6 guesses (despite that Knuth's heuristic fails to achieve this).

I post this result in the table, with a link to the demonstration and discussion on my NON-COMMERCIAL WEBPAGE from which I get zero revenue. However some vandal who refuses to identify himself removes this link repeatedly. Who's right? Jamesdowallen (talk) 13:09, 9 February 2016 (UTC)

The IP editor is right. You added your link to the "some examples of Mastermind games produced by Invicta, Parker Brothers, Pressman, Hasbro, and other game manufacturers" table, but it does not appear to be such an example. Linking to personal web pages is discouraged under WP:LINKSTOAVOID, and linking to your own website is discouraged under WP:COI. --McGeddon (talk) 13:40, 9 February 2016 (UTC)

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Remark on edit of 14 April 2019

Answer to

I found the claim that Knuth had found the minimax value at 4.321 for Mastermind odd, given that the previous sentence cites a paper titled "An Optimal Mastermind Strategy" that gives a value of 4.340. Investigating further, the Knuth paper does *not* claim the Mastermind optimal strategy is 5600/1296; this appears to be a conflation of several different numbers Knuth references ("5600/1296" does not even appear in the book).

The book states

Tom Nestor, who has continued to develop sophisticated algorithms for studying Master Mind strategies, wrote to me again in 2010, stating that his programs yield a proof that 5600/1290 is the minimum average number of guesses per game if we don’t allow the codemaker to choose xxxx—although xxxz patterns might still be guessed by the codebreaker if desired. It follows that the mixed strategy that we have discussed for (N0, N1, N2, N3) is in fact optimum.

In other words, Merrill Flood’s problem has now been resolved, and 560/129 is the true value of the guesses-per-game criterion when both codemaker and codebreaker play optimally.

The same result was, in fact, announced by Michael Wiener, in a posting to the sci.net newsgroup of Usenet on 29 November 1995, “from a program that ran for months.” Wiener had done this unpublished computation during the late 1980s.

--Lefschetz (talk) 21:32, 4 June 2020 (UTC)

Without examining beyond the quote you referenced and the existing content on the Wikipedia page, the distinction here is probably that Koyami and Wai's result (5625/1296 = 4.3403 turns) was for randomized boards (I have made an edit reflecting this), whereas the 5600/1290 result is for a strategic codemaker. Both results are probably relevant and interesting to include in the article.

The quote provided is a bit unclear, because it's missing some context. I'm not sure what Merrill Flood's problem is.

Also, I will note that this does not completely contradict my earlier edit summary; by its nature, adding a strategic code makes the average solve length longer. The previous page content suggested the solve length would somehow become shorter (probably an error of using 1296 as the denominator for the fraction instead of 1290). Retro (talk | contribs) 15:10, 5 June 2020 (UTC)

With the quote I wanted to give a base for a new version. The correct and original stated value 5600/1290 = 4.341 was faked in two steps (step 1 and step 2) to 5600/1296 = 4.321.

I think that the German WP version is much clearer.

Merrill M. Flood's paper (Mastermind strategy, Journal of Recreational Mathematics, 18, 1985-86) is only of historical interest.

Kind regards, --Lefschetz (talk) 06:28, 6 June 2020 (UTC)

Ah, I see. I must have made this edit before I learned how to perform more sophisticated blame checks for edits, otherwise I would have traced back this (that edit was made in April 2019, but my Wikipedia workflow became more sophisticated in May-July 2019 before I took the break I am in currently). It looks like the first IP editor made a mistaken assumption about what the denominator should be; I doubt the numbers were altered with the intention of making them wrong.

If you can improve the page, go ahead! I'm not fluent in German, so I can't really read the article you linked to (though I could use a translation tool), and it's been a while since I looked into Mastermind mathematics, so I have no illusions that I'm the most knowledgeable about this topic, especially at this point in time. Retro (talk | contribs) 18:04, 6 June 2020 (UTC)