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Wednesday, December 19, 2012

A pioneering woman in mathematics

Born December 16, 1932, Grace Alele-Williams is now 80 years old.
Prof. Grace Alele-Williams
She has a brilliant reputation as a pioneering educationist, being
  • the first Nigerian woman to receive a doctorate degree (University of Chicago, 1963) 
  • the first female professor of mathematics education in Nigeria
  • the first female Vice Chancellor of a Nigerian university  (University of Benin, 1985-1992). 
    me and Dr. Williams at the ball (Sept 30, 2011)
 References: 
Women mathematicians at agnesscott.edu: A biography of Grace Alele-Williams
Punch Newspaper: Grace Alele-Williams hits 80
Wikipedia: Grace Alele-Williams 
YNaija: Photos from the TW Phoenix Gala Celebrating Matriachs and Protegées
Bellanaija: About the Phoenix Gala by TW (Today's Woman) Magazine, with photos  
AMU-CHMA: African Mathematical Union - Commission on the History of Mathematics in Africa

Monday, December 3, 2012

Carnival of Mathematics 93

Welcome to the 93rd edition of the Carnival of Mathematics.

Here's the roundup:

Mr Honner verifies that this is NOT a trig. function
Look closely: is this really a trigonometric function?

John D. Cook shows that the Probability of Long Runs is greater than we think. 
E-Painting: Eye - Iris, by Tosin Otitoju

Nithesh at Sententia adores this book and wrote a review.
The Music of the Primes by Marcus du Sautoy "is about the history of the several attempts made to solve the long standing problem in Number theory called the “Riemann Hypothesis”. It also describes the larger picture about the lives of mathematicians, their idiosyncrasies, insecurities and their passion for the subject." 
Book cover: the music of the primes

Ed at Learn To Fish demonstrates how to draw regular polygons.
How to draw a regular pentagon

White Group Mathematics features advice for examination candidates at the A-levels: Focus on what comes next.
E-painting: Let's Fly, by Tosin Otitoju
Pat B constructs antiparallels, recommending the topic for high school geometry
Dragon, by Joan Martines, Messine, 1583

If you want more pictures, see The Golden Age of Maps/Charts online or at the French National Library till next month

If you want some physics, the Foundational Questions Institute has announced winners of this year's essay contest.

Gracias + Te amo: Cora Sadosky passed away exactly two years ago.   She was the best math professor, ever. 

See Carnival 92 at White Group Mathematics.
Carnival 94 will be hosted in January 2013 by Paul at The Aperiodical

Sunday, November 25, 2012

An unexpected power law that relates site traffic to ranking by site traffic

How easy is it to estimate your number of site visits from site ranking and vice-versa?
Very easy: double the visits to halve the ranking.
I just blogged at upnaira.blogspot.com about finding the connection, and how rewarding to end up with such a neat graph:
Relationship between Alexa rank and monthly visitors
Here's the data I used:
Site %Traffic Reach Est. Monthly Visitors* Alexa rank
yahoo  20 1000000000 4
craigslist  1.5 75000000 42
meetup 0.2 10000000 465
nairaland 0.08 4000000 1385
jobberman 0.02 1000000 4653
cp-africa 0.004 200000 44206
wemabank  0.00028 14000 557445

*The monthly visitors numbers are estimated by assuming jobberman has 1million visitors per month (I think that corresponds to a ranking around 5k) and that the traffic reach percentage (data given by alexa for each site) is simply number of visitors for this site / a fixed number corresponding to all traffic.  That is, take the traffic to be proportional to the traffic reach percentage.

Well, who wants to do this experiment on a large scale?
Plot Global rank against Traffic-reach % or Traffic-Reach-estimate-of-Monthly-Visitors and see how well the data fit this law.
Alexa.com ranks at least 10million sites, so you could test with that many datapoints. 

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Saturday, November 24, 2012

Can you guess the movie titles?

You need to know a little math to figure these out!
Mathematical film titles: check below for some answers
I found another version at spikedmath:
Movie math Quiz: another version
Enjoy!
Do you have more?

Monday, November 5, 2012

A Summary of Mathematics

A lecture recently given at the University of Lagos was almost-verbatim published in The Guardian*.

In the paper titled Abstract Mathematics: Exploring the Universe through imaginative science , Prof. J.O. Olaleru gave a comprehensive layman's explanation of what mathematics and mathematicians care about these days - from number theory and topology to logic and even professional rewards: publications, prizes...
He said a bit about his own work and his beliefs as well.
Johnson Olajire Olaleru, PhD
Kindly download and read the paper:  Abstract Mathematics: Exploring the Universe through imaginative science .  It's a laudable example of maths in the public sphere.
Comments?

* ngrguardiannews.com , Part 1, Part 2

Saturday, September 29, 2012

Not maths per se, just a little physics

Foundational Questions www.fqxi.org is a fun place to hang out.  On their latest essay contest, I look forward to reading a few responses:
Reductionist Doubts, by Julian Barbour.  Because the name of the author - winner of the first contest - excites me.
Revising the Topology of the Earth, by Peter Wamai Wanjohi.  Because it's the only recognizably African (it's Kenyan) author name I found among the hundred-or-so submissions.

The biographies are interesting too.   
This is Barbour's: "After completing a PhD in theoretical physics, I became an independent researcher to avoid the publish-or-perish syndrome. For 45 years I have worked on the nature of time, motion, and the quantum theory of the universe. I am the author of two books: The Discovery of Dynamics and The End of Time, in which I argue that time is an illusion. Details of my research work are given at my website platonia.com. Since 2008 I have been a Visiting Professor at the University of Oxford."

And this is Wanjohi's: "did advanced level physics but is a health professional specializing in community health and development .Works with the government and development partners. As a freelance physicist, he is a published researcher. His wish is top see a public well knowledgeable of their physical, biological and chemical environments." 

The contrast is typical; there isn't a market for "advanced-level physics" in Nigeria.

Drawing by physicist Setthivoine You

In addition to the essays by Barbour and Wanjohi, I'll try to read the top-four essays so ranked by reviewers (the public):
Black holes or anything else? by Christian Corda
Nature has no faithful mathematical representation by Roger Schlafly
On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus
Patterns in the Fabric of Nature by Steven Weinstein

Anyway, here are the past top essays, I've studied all three.  One of them - Stardrives and Spinoza - is so exciting that I may write a short-story inspired by its future-world soon.
2011 - Is Reality Digital or Analog? by Jarmo Makela
2009 - Stardrives and Spinoza by Louis Crane, answering the question: What's Ultimately Possible in Physics?
2008 - The Nature of Time by Julian Barbour

One day, maybe I'll explain the joys and cares of "hyperspecialization and the money to build stuff" in the West, versus "low infrastructure levels, and the freedom to build stuff" out here in the tropics.
Well, it looks like I have already written several research-related posts on my personal blog.  The story starts in 2005 with "The California Institute of Science: I am despondent.  In the past years, I have observed - science, research, and the labours thereof. I have discovered no new science. I have built no new machine. I'm more than two-thirds of the way to my PhD.  However, I can now give an expert report on how scientists do what they do." to this year with "There's no i in research."  I now have a math blog even (you're on it.)  Full circle?

Thursday, September 27, 2012

How is Mahjong Titans scored?

Classical Mahjonng games score different suites (types of tiles) differently and even award extra points for special patterns e.g. three of a kind*[1].  This made me curious as to how Mahjong Titans is scored.

Clearly, you can't match triplets in our pairing game (especially since there are four of each tile design.)
But this is still a valid question: do you score extra for two consecutive pairings of the same design?  Absolutely yes.  I got the hint here months ago, and I've subsequently used it to raise my score**[2] over the months. 

What exactly is the way to increase your score by matching consecutive pairs:
"If you get a matched pair of one class and your next pair is of the same class, you get a bonus. If the next pair is the same number and the same class, the bonus is bigger. If your second pair after that is of the same class again, your bonus is even bigger. You also get bonuses for clearing both pairs of flower or season tiles in a row."
So there you have it, from the horse's mouth (MS Windows - how to play MT)

Of course, all this assumes you know what a class/type/suite is, lol.
The basic thing is there are circles (from 1-9), bamboo sticks (from 1-9, the 1 of bamboo has a bird on it), characters (1-9, look like tally counts), winds (North, South, East, West), dragons (red, green, and black/white).  Each Mahjong layout has four of each of these tiles for a total of (9+9+9+4+3) x 4 = 34 x 4 = 136.  In addition, there are single tiles: four seasons and four flowers.  Grand total 136 + 8 = 144 tiles.

Naming the tiles in Mahjong

Things that raise your score
So you can raise your score by knocking out all four of one type in two consecutive pairs.  The next best thing is to do a sequence of pairs from the same suite.  Cool!  

Things that lower your score

When I first started planning consecutive pairs, my scores went up.  The time taken to complete each game also went up into four digits (in seconds).  I suspect the final score factors in time (higher score for quicker time.)  In fact, I'm learning that the Mahjong score is not a simple or linear thing. You have the option to undo one move or a sequence of moves even up to the start of the game.  You lose some points for reversing a move, but sometimes it's worth it.

Things that are suspected to raise your score

Can you gain higher points by targeting the rare types - flowers and seasons for instance?  For some solitaire games, but probably not for Mahjong Titans, the rules say yes, pair these earlier***[3].

NOTES
- Don't worry about raising your score until you have learned how to win in the first place.  

***[3] - This yahoo games site on Mahjong Solitaire rules gives a number value to each suit (characters get the score written on the tile, circles double them, bamboos triple, winds get four, and a basic score of 5,6, 7 for a dragon, flower, or season respectively.)   This is NOT the scoring system for Mahjong Titans.  Here are three discrepancies that make me certain of it:
1. "Granted three shuffles?" - I hadn't noticed the option to shuffle.  
2. "Move on to the next round?"  I hadn't noticed any rounds.  
3. "...multiplied by the total number of pairs left"  But the points would be too big.  My first two pairs in the last game I played were 2 and 2 (nothing near 72) and seemed to increase as game play continued, not decrease with fewer tiles.  Total scores in the hundreds, not in the thousands as their system would predict.

 **[2] - Further to the April 2012 post about improving all round, I have strong data to show marked improvement in all six configurations.  We'll come back to that later.

 *[1] - See Mahjong, Singaporean Mahjong scoring rules, on Wikipedia.


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Monday, September 24, 2012

Tanya Khovanova reviews a book: Taking Sudoku Seriously

Taking Sudoku Seriously: Why do I like this post?

I agree that sudoku is math is fun: "the goal of the book is to establish a bridge from Sudoku to math. And the book does a superb job of it."

I've also pondered: "methods to solve Sudoku, how to count the number of different Sudoku puzzles, and how to find the smallest number of clues that are needed for a unique puzzle."

Something new: "Sudoku with a twist" like this:
Taking Sudoku Seriously Puzzle 91
Elsewhere on Tanya Khovanova's blog, she discusses a geometric measure, my boy Perelman, and other mathy-things that I actually care about. Could she be my long-lost (math) blog sister?

Wednesday, July 25, 2012

All you need to know to win Mahjong Titans: The Blast Zone

I'm finally doing turtle right (once again?)
Won 10 of the last 14 games I've played. [*1]
That is a 70% win rate, up from a very consistent 35% win rate.  
Increasing win percentage in Mahjong Solitaire

[*1]
Games won in the past two months: 44 - 34 = 10 
 divided by 
Games played in the last two months: 111 - 97 = 14

All you need to know to win at this most popular configuration of Mahjong Solitaire? 
THE BLAST ZONE
Blast Zone: How to Win Mahjong Titans

Essentially, ignore all I said about turtle feet (see here
Just blast through the entire line that runs from head to tail (see the blast zone in the picture.)
Blast through horizontally, and blast through depth-wise (vertically) as well.  

Why is this is a better strategy than the multi-focus one I proposed earlier?  
Think about the hardest-to-reach tile on the foot row - it's only six tiles away from the outermost tile.  But the hardest-to-reach tile in the entire game is likely nestled layers under the cap of the turtle shell (five layers down) and seven tiles from the outermost one.  It is very hard to reach that buried tile, so focus on getting close.  Ignore the pursuit of foot tiles, since that is half as hard.  Did that make sense? 

I have previously given solid advice for playing all the other configurations very well.  Been getting amazing improvements in many of the other configurations.  For example, I just won a game of dragon that I thought was hopeless (was about to quit, but said, no, I've never quit before).  Hung in there and it ended up my top score EVER in Dragon.  Crazy.

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Sunday, April 29, 2012

Becoming Charlie

Poincaré died one hundred years ago, in July 1912. He was a French mathematician who also wrote essays on the nature of mathematics.  I happened to visit his Wikipedia page today, which would be his 158th birthday anniversary.  In the days before Wikipedia, this was a leading source for Poincaré's biography online in English. Also try this.

I wonder how many mathematicians there are in the world.
If "a mathematician is a person with an extensive knowledge of mathematics, a field that has been informally defined as being concerned with numbers, data, collection, quantity, structure, space, and change" (source) then I suspect that the number of people that I would consider to be mathematicians is 100,000 - 200,000.

You could think about membership of the American Mathematical Society (about 30,000)
Multiply by 3 (for counterparts in Europe/former SovietUnion and Other) = 90,000.
Double that number to reflect those outside pure mathematics but close enough = 180,000.

I also like this estimate of 150,000 people.

Other fun data: SIAM, Society for Industrial and Applied Mathematics has ~13,000 members, while Association of Women in Mathematics has ~2000 members

These days I'm watching season 5 of NUMB3RS again.  Charlie is a fictional math genius who teaches at CalSci but often assists his crime-busting brother at the FBI.  This TV show features imaginative and engaging stories of math life.  I find it inspiring.  

Sunday, April 15, 2012

Improving all around in Mahjong Titans

Raising the score:
Two days ago I resumed playing Mahjong Titans.  I started applying my new knowledge of the rules: that you score bonus points for matching two pairs at once.  (You see, I don't even know the rules, I'd rather learn as I play.)  This is yielding higher scores (when I win) :
#1 top score in Spider (14th April; won 2 of 4 new games played since the 13th),
#1 (14th April) and #3 (13th April) in Crab (won 2 of 3 new games played)
and #3 in Fortress (this is 1 of 1 new game played, 13th April, possibly without the new rule.)
I expect that all, not just most of, my new wins will displace the old wins at the top, as soon as I've won about five more games in each.  

How to win at Turtle, modified: 
Then again, my previous posts were about winning at the game (which is not the same thing as scoring high, but related.)  I learned a new idea about winning at turtle too: ignore the two long rows (which I'd named "the feet") at the top and bottom of the layout.  Focus heavily on the middle (head, shell-top, to tail) since there are so many more tiles packed in this region than at the feet (even if the feet have long rows.)  I think it's working.  When I've tested it a bit more, I'll officially modify my rule book.

Improved or not?  Two more tests.
Criticizing Method One: 
In the previous post, I glanced at the plots of top 5 scores for each layout and declared that those that were going up and to the right were "improving" and so on.  I concluded that Turtle and Crab had a weak outlook, Cat and Spider were possibly stagnant, while Dragon and Fortress were strongly improving. But this was a messy and inconsistent measure.  Turtle was up and down and up again, making the slope rather meaningless.  Spider may have pointed down, not improving, but with such a slight slope (and small range; all the top five scores packed into three months)  that it's hard to tell. And so on.  Like I said, messy and inconsistent.

Method Two, are the wins recent or early? 
Think about what it means that only three of the top five scores in Turtle came in or after Oct 2011, with the other two long time ago in Dec 2010 and Jan 2011.  That means nearly all the winning scores in Turtle (28-3 of them) came in Sept 2010 - Aug 2011, the early period, while only 3 were in Sept 2011 - Jan 2012.  That is a lot of early wins; remember that I played more and won more Turtle than any other layout.
In fact, let's try to see a new win/early win breakdown for each layout.  Put September 2011 as the cut-off. 
WINS        New   +    Early      New % (of total wins)
Turtle         3        +        25           11%
Cat             4        +        9            31%
Crab           4       +       9          31%
Fortress      3       +      10          23%
Spider       5+       +      9-           36% or higher
Dragon       4       +       9            31%

This makes the point I wish to make better:  If play was for 16 months of which 11 are termed "early", then wins spread randomly will give 5/16 in the new period (or about 31%).    By this measure, Cat, Crab, and Dragon showed flat performance, a win distribution consistent with no improvement / no degradation.  Spider showed improvement, while performance in Fortress got poorer.  Turtle showed a marked degradation in performance.

Method 3: Let's look at this another way, when did the top 5 scores occur, on average?
Top 5 (Average of the dates in which the top five scores were attained in each layout)
Turtle 7/8/2011
Cat 8/7/2011

Fortress 9/23/2011
Crab 9/25/2011

Dragon 11/2/2011
Spider 12/5/2011

ALL : 9/21/2011

Answer: Early in Turtle and Cat, same as random in Fortress and Crab, recently in Dragon and Spider.
This suggests Turtle and Cat performance worsened, while Dragon and Spider improved.

TO SUMMARIZE an analysis of my progress in different layouts of Mahjong over 200 games, 6 layouts, and 1 1/2 years:
Above are linear regression lines for the top five scores in each layout.  The average date at top 5, or midpoint of the line, is more important than the slope of the line.  From bottom (early) to top (new) along the 3 mark, that gives clearly Turtle, Cat, Crab/Fortress , then Dragon, then Spider.  To decide the near-tie between Crab and Fortress, consider that Crab points down (degrading performance) while Fortress clearly points up (improving).  Hence Turtle, Cat, Crab, Fortress, Dragon, Spider
That's my answer and I'm sticking with it!

Coming up: An introduction to topology, a proof that women cheat, and more games, particularly my unsolvable computer solitaire.  Meanwhile, try Mahjong Titans and tell me your results.

Friday, April 6, 2012

Worsening performance in Turtle

I told you months ago about the sense I had that while I learned the tricks to play the most structured layouts in Mahjonng Titans e.g. Fortress, I seemed to lose the ability to win at Turtle as naturally as before.  Let me show you in numbers (the few numbers I have):
I think the scores are for about 18 months of play, from my first game in late 2010 to the last in January or February.
As you might expect, my best result is in 2012, with another two top-fives just the month before.  Basically my recent games won are good compared with my old games won.  This implies improvement.

Comment on using proxy measures: 
Of course the real data I would have liked to use is my wins and losses over time, to see if I won more (percentage wise) more recently than in the past.
I couldn't find such records in my game, but I found top-five "High Scores" with dates, which I am using as an alternative measure of performance trend over time.  Make sense? 

Now check out my scores for the other layouts:

Fortress seems to show a similar trend: top score in 2012, another two top-fives in Oct/Nov 2011.
Spider shows all five top scores come in Oct 2011 or later.  That is, better than what I played earlier --> improvement too.
Crab is somewhat similar; three top-fives since Oct 2011, just like Fortress.
Cat has four of the top scores in Sept-Oct 2011, and notably the number 2 top score from all the way in 2010.  Not as clear a picture of improvement with the Cat configuration.

Now look at the Turtle scores: of 28 games won in 16 months from say Oct 2010 to Jan 2012, two of the top five are in the early days: December 2010 and January 2011.  The remaining are in late 2011.  Compared to the other configurations, my top Turtle scores are not clustered in the most recent past. 

Or you could look at this picture I made by plotting the top 5 dates for each configuration in MS Excel:
Strongly improving: Fortress and Dragon
From rank 5 (or imagine the lowest rank wins in the blank space to the left of the chart) up to the top rank, the Purple Fortress appears to be marching up (improving).  To look at the best three scores in fortress and dragon, the message seems to be "the best is yet to come."  

Possibly stagnant: Spider and Cat
The performance in Spider is mildly falling, with best performances around October 2011 not looking likely to improve.  Cat is the same, if you ignore that the #2 performance in 2010.  Not getting better.

Weak outlook: Crab and Turtle
The green crab is almost certainly falling down, better past than future.  And the turtle?  It's a bit haphazard, but it's also sweeping down. 

It's not just my imagination, I used to play better Turtle before I learned all those specific tricks. 

Thursday, March 22, 2012

Play to win: Mahjong Titans

1. The major constraint is that you can not see the lower tiles until you have peeled away the upper tiles. You can't move these 'covered' tiles.
2. There is an important secondary constraint: you can not move a tile when it is hemmed in on both sides by other tiles.  Think of these tiles as 'covered' from the side.

What should you do:
Of course, because of (1), you must try to get to the lowest level of tiles and eventually remove all the tiles. Dig vertically. 
Also, be strategic because of (2): when you see a long row of tiles with strong dependencies, focus on that row. Dig/Chisel/Peel horizontally too. 
Course of attack in Mahjong Titans
For example, in the Fortress layout, you will lose the game unless you focus almost absolutely on the two long rows of tiles.  If instead, you just pair tiles as they come, you will end up with several unpaired chunks/layers at the end of the game (i.e. loss of game).  Rule (2) is utterly important in Fortress.

I think it is also of the utmost importance in Spider, which has two super-long rows (focus on these), and then one other long row (the thin red arrow above the other two) where you should source for free tiles before considering other (largely freestanding) tiles.

(2) is also very important in Dragon, which is crowned with a super-long row of tiles.  You must focus on that row, and then also the two tricky bottom rows.  Secondarily, consider the two short half-rows.  Avoid the free-standing tiles as much as possible.

(2) is less important in the other layouts:

To solve Turtle: You can see why it's called a turtle: it has a hard shell on top - attack that, circled in red, very early or you may never win the game because the heart of the layout is buried layers deep.  It has a head and tail sticking out, cut those off early too.  First thing you should do in Mahjong Turtle, try to pair the top tile (circled), the and the three other tiles blocking progress (at the head and yansh).  There are also two long rows at top and bottom that you must peel back.  Turtle is a balancing act.  It was the first layout I played (previously I had a computer that had just this layout, back in the day).  I just matched tiles more-or-less randomly, although I noted the top two layers on the shell as well as the edge tiles.  I don't recall how much I won then. (Note: NEW Strategy for Turtle here, with very high win rate guaranteed) 

To solve Cat or Crab, it takes some Turtle skills (balance width with depth) and some rule (2) skills (don't leave long rows).  However, these are so easy that you could win without thinking about strategy.  Truly.

Anyhow,  in Crab, focus on two important long rows and the big belly, you should not focus on the small sections. Cat has a big region and a small region, so focus on the big region to some extent.  

I want to talk about other rules but they are less important and can wait till next time.  I am also dying to tell you why I think getting smarter at playing the "hard" layouts made me dumber at playing Turtle.
Footnote:  In a way, the gross strategy for playing a given game is to follow the rules of the game i.e. start pairing tiles in Mahjong. The finer strategy, then, is to discover what makes it nearly unsolvable (or nearly lost) and then combat that.  
For another example, I recently started playing chess: gross strategy - move in the allowed patterns, take hostages preferably big ones, take the king's head;  finer strategy (think what happens late in the game) : the queen is a vicious bitch so get your opponent's out, pawn promotion by your opponent is bad for you so frustrate the frisky pawns, etc.

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Tuesday, February 28, 2012

Minor News Headline

2012 is Mathematics Year in Nigeria.
 I wonder what that means - time to be more mathematical?
No problem.

CATCH UP ALERT!!! This is the FEBRUARY 2012 post.

Friday, February 17, 2012

Next time there'll be some tricks but you should try the game first

Although you can play Mahjonng on your computer, the game was played even before electronics.
You can watch some actors play real Mahjonng in this video.


Can you believe that I do not play chess?  Yesterday, a colleague at work showed me to play.  (Actually I've played a few - like 5 to 10 - games in the past, I know the queen can move all these directions etc.) My teacher was really good - he really loves the game and loves teaching people to play.  You could tell that it made him happy.

Well, chess is one game of strategy.

I just watched this Chinese movie titled Battle of Wits.  This village was going to be attacked by a very large army, and guess what?  A special agent, yes - one single peace-loving warrior strayed into their village and within minutes their defeat started to become victory.  I love those Chinese historical war films - they idolize knowledge and strategy.  Check out Red Cliff, for instance.

Any more great films I should know about?

JANUARY 2012 post

Monday, February 13, 2012

Ali G- Science

Remember this Ali G favourite?
Yes, my computer can multiply two numbers.


DECEMBER 2011 post

Thursday, February 9, 2012

Easy and hard layouts in Mahjonng Titans

You can download Mahjonng Titans here, although it comes free with many Windows installations. I've played the solitaire-like game since mid-2010, with about a 50-50 win/loss average.
See my win percentages for the different layouts*:
Turtle         28 / 80       35%          
Dragon      13 / 24       54%          
 Cat           13 / 20       65%          
Fortress     13 / 24       54%         
Crab          13 / 22       59%         
Spider        14 / 30      46%         
Table: Percentage of games played that I won (All Layouts || 94/200 || 47%)  

It seems that Cat is particularly easy, and one may suppose Crab is the 2nd easiest.  I win nearly 2/3 of these games.
It seems that I find Turtle hard, winning about 1/3 only, and that I have also played it A LOT compared to the other configurations: while I played Turtle 80 times, I only played each of the other layouts 20 to 30 times. 
Crab is easy

From the winning percentages column, I can deduce this order of easiest to hardest layouts:
Cat - Crab - Dragon/Fortress (tied) - Spider - Turtle

In other news, the layouts I have played the most have the lowest percentages.  Plot total games played against win percentage and you see this.  But what does this mean?  Does this mean that I play the harder ones more - I love a challenge?  Or maybe my game gets worse as I play along?  
Negative correlation between win percentage and number of games played

How about you, which layouts do you find easy/hard?

I actually feel like the truly easy ones are Cat, Crab, and (surprise) Turtle.
I think that Dragon and Fortress and Spider are tricky, but that once I found the trick, I started playing these three layouts better while at the same becoming worse in Turtle.  Could my added knowledge actually have worsened my game in Turtle?  Does this seem ridiculous to you?

* I have given my real playing data for this software installation.  I did not plan to have the round numbers (80 games of Turtle, 200 games in total, 13 games won in each of four layouts...)  These are coincidental, believe it or not.

It is now NOVEMBER 2011 at this monthly blog.

Sunday, February 5, 2012

Match the tiles - should be easy enough

I no longer play (regular) solitaire.  Mahjonng Titans -  imagine the young prince in ancient China taking strategy lessons - is one of the games that came preinstalled on my laptop.
The popular configuration is the Turtle, then I discovered new types of Mahjonng Solitaire, and some secrets of the game.

Can you guess which shapes are the easiest to play?  Why do you think so?
Try some games first and then deduce which shapes are easy and which are hard.  I'll be back in a few days.

This is the OCTOBER 2011 post.

Thursday, February 2, 2012

NKS - A New Kind of Science, by Stephen Wolfram

A Caltech alum published a popular and very fat book in 2002 (wow, has it been that long?)
A New Kind of Science, by Stephen Wolfram
It was a big (controversial) deal.

Serious scientists said : this is rubbish (especially because the author doesn't seem humble enough about proclaiming the importance of his experiments) , while on the other hand, the book got more sales than almost anything serious scientists have written in decades. 

NKS is worth reading for how it gets you thinking in New directions about math, computation, and the natural world.  It has beautiful pictures too.  

Other reasons to get a copy - you can place it on a side-table at home, to make you seem intelligent :) 
If you just want to read/look, it's here --> the whole thing

This is only my SEPTEMBER 2011 post

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