May I Have a Wordle With You...

Everybody seems to be doin' it, thinking about it, or just seein' and wonderin' about it!  Longish piece from The Aperiodical on the latest online viral hit game, "Wordle":

https://aperiodical.com/2022/02/a-mathematicians-guide-to-wordle/

Though, like many, they compare it to the classic game "Mastermind," for at least a few of us oldsters it is even more reminiscent of "Jotto," my favorite (word) game growing up in the 50's and 60's, and still available in online versions (in fact, I find it a bit ironic and funny that some guy has suddenly made a ton of $$$ with Wordle, when Jotto has been quietly around for... well, a verrrry much longer time!)

As to "best" starting words for Wordle (a much discussed/theorized topic) I'm surprised that more people haven't settled on my two starters: "ADIEU" or "AUDIO" -- with these starters I rarely require more than 4 entries to get the target word, and probably at least 20% of the time 3 entries suffice (...but then I'm a pretty good guesser once I get it down to 4 or fewer word possibilities).

The 2nd word choice obviously is also very key to this game, but it is highly dependent on the results of the first word choice. Most often though, my second word will derive from these letters: r, s, t, y, either o or e, and one of the letters pinpointed by the 1st word guess; however, c, h, l, or n, may end up subbing for one of those choices in some instances; and the exact results of the first word choice may, more rarely, lead to still other letter choices for guess #2.

Now, with the NY Times purchasing Wordle for a tidy little sum, not certain what its future will be, for the game or its millions of addicts for whom Wordle is as much a start of the day as is coffee.

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ADDENDUM  (2/6/22):

Having read a number of articles now touting various "best" starting words, pointing to the sort I used to use based upon letter frequency, I went back and tried that approach again, fairly successfully. Then I started trying unlikely starting words (zebra, radar, oozes, queen, excel, etc.), and what I'm largely discovering is that I can most often solve Wordles within 4 guesses by the careful, thoughtful selection of the 2nd and if needed 3rd guess, REGARDLESS of the first word choice! 'Rules' for the selection of the 2nd & 3rd word choice are what really need to be spelled out, though they are difficult because they are so dependent upon the the highly variable results of first word choice. Anyway, it all says something interesting about the redundancy and patterning of language.

Who Doesn't Love Games...

 Well, look who has a new book on the way (it could even be a game-changer... so to speak):

https://mathwithbaddrawings.com/2022/01/19/math-games-with-bad-drawings-2/

When Losing Is Winning

Jim Propp’s fertile posts or tweets often get me thinking about tangential things… 

Yesterday in a tweet he whimsically mentioned wanting to lose quickly at Monopoly when he plays against his kid.

Which got me immediately thinking about game variants where the object is to lose (you WIN by losing!). The only thing I could find, quickly googling around, was this somewhat technical piece on a checkers variant, sometimes called “suicidal checkers” with the object to lose: 

https://arxiv.org/pdf/1806.05657.pdf

Seems to me over the years I’ve read other such game variations, but a quick search didn’t turn much up (there are plenty of common game variants, just not where losing becomes the goal).

I did find this year+ old Scam School video showing a similar fun variation for Tic-Tac-Toe (the main description beginning ~2:16 mark) -- this is essentially a version of what's been called "misere tic-tac-toe," reverse or anti tic-tac-toe, or even "eot-cat-cit," where whoever gets 3 in-a-row first loses:

Presh Talwalkar did a nice, more expansive analysis of this game a couple years back at his Mind Your Decisions blog:
https://mindyourdecisions.com/blog/2016/11/01/the-best-first-move-in-misere-tic-tac-toe-3-in-a-row-is-losing-game-theory-tuesdays/

If anyone can point to other such win-by-losing variations of well-known games let us know.

Staying In The Middle...

Been some discussion around math-Web this week about the “Median Game.” It got started with this Gil Kalai posting:

https://gilkalai.wordpress.com/2017/01/14/the-median-game/

A quick, simple game (requires exactly 3 people to play, and just a pad-and-pencil), intriguing because of its recursive nature, and the resultant strategizing required.

The game actually shares origins with games called “Hruska” or “Mediocrity,” created by ever-inventive Doug Hofstadter, and described in Chapter 28 of his fantastic volume, “Metamagical Themas.”

Mike Lawler took the plunge and played Median with his boys recently and they quickly picked up on some of the nuances of the game:

https://mikesmathpage.wordpress.com/2017/01/15/gil-kalais-median-game/

As has been done with other games, would be interesting to have AI people write programs to compete at Median and hold an all-computer tournament to see which program (strategy) works best (…or perhaps this has already been done?)

Anyway, check it out at Gil’s site, and if you can, get 3 folks together to wile away some time playing it.

But fair warning, it can quickly play havoc with your brain! ;)

Who Knew?... Of Scammers and Scrabblers

from WikimediaCommons

Turns out (to my surprise, and I assume others) that the country which harbors perhaps the greatest reservoir of ludicrous, over-the-top email scammers, Nigeria, also is home to a bevy of championship-level Scrabble players! Further surprising, they have developed their own contrarian strategy on how to winningly play the long-popular game. And that strategy is both linguistically and mathematically interesting.

Previous commonplace play revolved around using as many letters (out of 7) as possible on each turn to spell out words as long as possible. Nay, nay, say the Nigerians... who prefer instead to employ 4-5 letter words, saving some of their best tiles for future planned use. Five letters, properly played, can capture a couple of bonus-scoring spaces, while also denying opponents access to key spaces. In the long run, more words, and more and easier scoring takes place with shorter words, and also doesn't open up as many possibilities to your opponent.

Most may have heard this story from the Wall Street Journal, but here is another piece about the approach:

http://www.11points.com/Games/Analytics_Have_Found_the_Ultimate_Scrabble_Strategy,_and_It_Is_Not_What_We_Thought

And the Nigerians DON'T even need to be fluent in English to win: "Rather than using robust vocabularies to win at Scrabble, many of them just memorized the combinations of letters that made up words -- without knowing or caring what those words meant." (from the article)

All of this got me wondering if there was currently computer software capable of playing championship-level Scrabble (the WSJ article briefly mentions it). With the success of chess and Go-playing programs, one would think it possible, but the only related information I found in a quick search was this Wikipedia article:
https://en.wikipedia.org/wiki/Maven_%28Scrabble%29
Anyone know any further or updated info?

One last thing: despite all this seeming ingeniousness, Nigeria... I'm still not opening your damn emails.

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ADDENDUM:  Thanks to "Jared" (in the comments) for passing along an extended Slate piece offering more context to the spin of other popular links to this story. Try to find time to read it for a more-nuanced, less-hyped view:
http://tinyurl.com/zg4zuwd

Elliptical Pool!

via ClipArt etc.

So far as I know, the game of pool hasn't changed much in a long time... until NOW! Alex Bellos has created a fun, new version of pool (he calls "LOOP") based on an ellipse. How cool is that! Take a look:

http://tinyurl.com/p8g5236

Fun and Games (and oh yeah Math)

"The Innovation Factory" is promoting its "Magic Cube" product (a Rubik's Cube on steroids) with a contest to see who can be first to find the correct solution out of the 140,000,000,000,000,000,000,000+ possible solutions:

http://if-chicago.com/portfolio/the-magic-cube/

In exciting news from Keith Devlin, his company InnerTube Games is finally out with its "Wuzzit Trouble" app game for young people (currently available for iOS platforms as a free download). Great interview with Dr. Devlin in this Forbes article:

http://tinyurl.com/nhqkovr

This older American Scientist piece by Keith gives more of the principles behind 'Wuzzit' (with an analogy to music):

http://www.americanscientist.org/issues/pub/the-music-of-math-games/1

And finally, Keith also gives an introduction to the game in this video:

http://vimeo.com/73095116

More generally, one may also want to read about MMO games (if not already familiar with them) and their possible future in education:

http://en.wikipedia.org/wiki/Massively_multiplayer_online_game

And Dr. Devlin wrote a whole book on the general topic:

http://www.amazon.com/Mathematics-Education-New-Era-Learning/dp/1568814313

Wax On, Wax Off...

Another great post (with many good links) from Keith Devlin, on the use of video games for math education, with specific reference to the game "DragonBox" and 'algebraic learning':

http://devlinsangle.blogspot.com/2013/07/it-only-takes-about-42-minutes-to-learn.html

(I feel like he's over-reacting a bit at the start to a magazine headline -- such looseness of language is pretty darn common in the press, generally, and headlines in particular -- but once you get past that part, a lot of interesting food for thought.)

Moreover, I have to love any post that works the original "Karate Kid" (one of my favorite movies), into a discussion of math education!! (via the topic of 'transfer learning').

Tic-Tac-Toe… on Steroids

Just an interesting post on a simple way to turn tic-tac-toe into a more challenging, strategic game:

http://mathwithbaddrawings.com/2013/06/16/ultimate-tic-tac-toe/

Rock-Paper-Scissors Fans

On the heels of IBM's Watson's victory on 'Jeopardy,' you can play "Rock-Paper-Scissors" against a computer online via this NY Times piece:

http://tinyurl.com/6fk9us8

Have at it! (...do try to get some work done today as well, though)

A Few Number Games/Puzzles

Ken-Ken on the Web here:

http://www.kenken.com/

Shikaku (and some other games) here:

http://www.puzzle-shikaku.com/