Six Degrees of Wikipedia

Well that was quick. One of my Scrabble friends pointed out “Six Degrees of Wikipedia” is a thing and therefore it is relatively straightforward to find a path from Philosophy to Spider Solitaire. Although my friend thinks it is cheating, he certainly demonstrated knowledge of something I wasn’t aware of. Therefore I am happy to grant my friend the title of Great Grand Master of Spider Solitaire – except I just realised I should change the title to “Doctor of Spider Solitaire” which is a brilliant pun on “Doctor of Philosophy” 🙂

Unless somebody can find a path from Philosophy to Spider Solitaire without the explicit use of Six Degrees of Wikipedia within the next two weeks, my Scrabble friend will earn the title of S. S. D. Potential SSD candidates also have to explain how they got there and prove it wasn’t dumb luck.

For reference below is a screenshot of Six Degrees of Wikipedia. Good luck!

From Spider Solitaire to Philosophy – and Back Again

And now for something completely different:

Let us try the following experiment. We start with the Wikipedia page on Spider Solitaire and then do the following:

  • click the first link of the “main text” (but ignoring anything in parentheses).
  • Rinse
  • Repeat

From the screenshot below, step 1 says should click on the word “patience”

After a few iterations we reach a closed loop of the form Philosophy > Existence > Ontological > Philosophy.

The interesting phenomenon is that the starting point is almost always irrelevant: if you pick a random page then it is heavy odds on you reach the same closed loop involving “philosophy”. Not surprisingly, Wikipedia itself has a page on this phenomenon and it is estimated (as of February 2016) that 97% of all articles in Wikipedia lead to Philosophy. The remaining articles either lead to “sinks” (no outgoing wikilinks), non-existent pages or closed loops other than Philosophy. This phenomenon was pointed out to me by someone from Adelaide University on the 4th of March.

Just for the record, here is the chain that starts with Spider Solitaire. I will not discuss this chain in detail – the reader is invited to draw his or her own conclusions:

  • Spider (solitaire)
  • Patience
  • Card games
  • Game
  • Play
  • Intrinsically motivated
  • Desire
  • Emotion
  • Biological
  • Natural science
  • Branch of science
  • Sciences
  • Knowledge
  • Facts
  • Reality
  • Imaginary
  • Object
  • Modern Philosophy
  • Philosophy  > existence > ontological > philosophy

Being a self-proclaimed Grand Master of Spider Solitaire, I am more interested in the reverse process. Starting from the Wikipedia page on Philosophy, is it possible for me to choose any outgoing links of my choice (not necessarily the first) and eventually land on the Spider Solitaire page? I don’t have a definitive answer. All I know is the random link algorithm proposed by my good friend Ninja Monkey doesn’t work so well!

If anybody can find a path from Philosophy to Spider Solitaire I will be happy to grant said person the title of Great Grand Master of Spider Solitaire. Challenge accepted anyone?


So apparently my work colleague did not have time to read Steve N Brown’s book Spider Solitaire Winning Strategies at all even though I took the trouble to bring the book to work and lend it to her. I have retrieved the book from her, and still haven’t had a chance to watch her play. Another 1 of life’s disappointments!

Blowing out someone else’s candle won’t make yours burn any brighter

Just found this on LinkedIn today. Names have been withheld to protect the guilty. Short version is: (1) the Project Manager described in my previous short story ain’t the only person who plays Spider Solitaire at work (2) Not every person you see on LinkedIn is an Awesome Person

My impression is that O.M.G.S.I.72,65,87,84 thinks she is better than she really is, and she didn’t mention (or more probably doesn’t understand) the real reason she was released from her job. But of course I am not in a position to jump to conclusions. What I do know however is that she cannot even spell the name of the game correctly, and usually that is not a good sign.

I will let the reader study the image below and judge for zirself (*)

(*) Every man dog and millipede on the planet knows by now that ZE is valid in Scrabble, being the gender-neutral pronoun equivalent of he or she, but none of my Scrabble friends can work out why ZIR* (equivalent to HIS or HER) has not been added to the dictionary. But that is outside the scope of this post.



Move over Siraj Raval, Peter Denahy is my new hero!

Looks like Siraj Raval isn’t my hero after all. Yes, he is the founder of School of AI, and if they handed out titles for rap songs instead of Chess he would surely be a GM. Unfortunately Siraj has also been exposed as a fraud, organising a 83,72,73,84 Machine Learning course, borrowing software from GitHub without acknowledging the source, having no 70,85,67,75,73,78,71 clue about how the code actually works, and adding a refund policy as an “after-thought”. And the less said about that Neural Qubit paper, the better. Why anybody would go from hero to zero (terrible cliché I know) like that is a mystery, but it seems some people are worse than the Silly Goose as per described in my previous post.

For those unfamiliar with Siraj Raval see this link.

Fortunately I discovered a great new song about someone who spends way too much time with his phone, indulging in many activities including playing Solitaire. Okay, he didn’t explicitly mention Spider Solitaire, but given my immense disappointment with Siraj, I’m counting it!

BTW If you know any other great songs mentioning the word Solitaire please leave a comment 😊

Okay so what is this Solitaire Cube thingy all about?

Solitaire Cube

It would be nice if the Solitaire Cube combined my talents of playing Spider Solitaire well and solving Rubik’s Cube (and if there is no cool music I can always play piano at the same time) but apparently they have tournaments where you can play for money. We’re not talking small amounts of virtual money plus a small percentage of dot com stock options indexed to inflation but real money.

Solitaire Cube is your regular i-Phone app with the usual eye candy, cool music and/or sound effects – and best of all it takes the tedium out of shuffling the cards. It was developed by Tether Studios and powered by Skillz, an eSports platform that manages the $$$$

Players are matched with opponents with similar skills in real-time and world-wide. You are scored according to certain rules (which will not be discussed in detail), so even if you can’t win you are still rewarded for partial achievements, such as exposing most of the cards. If you score more than your opponent, then you win the $$$$.

There is also a 5-minute timer, so the game ends as soon as you run out of time. Or you can quit early, cut your losses and take the bonus for time remaining. There is a practice mode where you have virtual currency (Z coins, minus the dot com stock options as described above). Once you are comfortable with practice mode then you can go to the Pro League.

There is something similar for Spider Solitaire Cube, but I described Solitaire Cube first because that seems way more popular (Klondike is much better known than Spider). Besides I would expect former and latter to have much in common.

So that’s the theory, but don’t give up your day job just yet

If I got word of mouth from a trusted work colleague then I might seriously consider wanting in on this. But I heard about Solitaire Cube only because I play way too much match-three games on my mobile and can’t be bothered getting rid of the ads.

There seems to be a growing scourge of low-quality games that are designed to cheat. For instance, a game might be advertised as free-to-play but in reality it is pay-to-win. Or the gameplay itself is lame. Or there is false advertising (think Evony). And don’t get me started on Hero Wars. Solitaire Cube seems to be no different: a simple search (hint: name the largest subsidiary of Alphabet Inc.) reveals a lot of negative reviews. Without going into detail here is a list of complaints:

  • Player’s score is less than it should be
  • Practice hands are much easier than Real money hands (sound familiar?)
  • Frequently crashes
  • Lousy customer service
  • Don’t know if opponents are humans or bots (or if they are same skill level as you)
  • Can’t review opponent’s video ergo don’t know if he legit won. Don’t even know if they play the same hands.
  • The vigorish is worse than Las Vegas
  • You have to deposit $10 into Paypal account, then they ask you for your location to see if you’re eligible for tournaments (wrong location -> no entry).
  • Fake positive reviews.


I’m not sure how many of these complaints are legit. For example, players are more apt to remember the time when the game crashed when they were doing well, but not remember the 10 times the game crashed and they were doing badly. But there are some undisputable facts. If you are betting 25 cents to win 42 cents then the vigorish is 16%, which is worse than Las Vegas. Nobody can argue with the math. And there are things that don’t pass the sniff test, because IMNSHO game developers should not only be doing the right thing but be seen to be doing the right thing. I won’t go into exhaustive detail; I will let the reader draw his own conclusions.

Let’s test this software … or let’s not.

If you read this blog regularly, you will know how to test the Random Number Generator. But I believe it is not worth my time to do the same experiment, mainly because I need to set up a PayPal account. There are other issues, but the PayPal issue alone is enough to turn me off. I leave this as the proverbial exercise for the reader 😊

Spider GM wins Connect Four!

Spider GM is off to a good start in Connect Four. He has won the first four games for a flawless victory (to borrow from the Street Fighter vernacular). His friend Ninja Monkey says three out of four games were ridiculously easy with a estimated equity 0.96 or better, but game 2 was a strange exception. The last ten cards from the stock were K2248K9264 which might explain a lot 🙂

Spider GM will continue to record results for the remainder of this month in order to settle a bet with a friend concerning the biasedness (or lack thereof) of i-Phone Spider Solitaire. For further details, please see earlier posts and references therein.

From previous experimentation SpiderGM expects the equity to be between 50% and 100% for each game, since each game is supposed to be winnable (each daily-challenge deal has the option of “show me how to win”, so users would be 80,73,83,83,69,68 off if a game turned out to be unwinnable). The average would be much lower if the games were random. Spider GM will also expect to accumulate plenty of red in the latter half of the month. Fortunately the game of Connect Four is considered won as soon as one side achieves 4 in a row, even if the opponent “goes perfect” during the remainder of the month


Bring it on

One of my friends has challenged me to repeat my Ninja Monkey experiment for September 2019. Those who follow my Facebook page will know the good goss, but here it is in a nutshell:

  • I have Spider Solitaire on my i-phone.
  • This software comes with “daily challenges” where a fresh deal is provided for every day, akin to a random number generator – thus if you enter the same “seed” of e.g. 15 August 2019 fifty times you will play the same hand fifty times etc. NB: Players are restricted to any day between 1st of previous month and today.
  • However, I believe the RNG is not uniform and if we choose any month then games corresponding to later days are harder than games corresponding to earlier days
  • This can be done via statistics: choose 2 days of the same month at random and let Ninja Monkey compute the “equity” of games corresponding to both days. The probability that the later game is harder than the earlier game should be 50%,
  • but my actual probability was significantly higher (p-value < 05) when I tested the games in July 2019.

I am now going to repeat the same experiment for September, and I am laying my friend 4:1 odds in his favour that I will not get the same result as my July data.  My friend told me that twenty 66,85,76,76,83,72,73,84 tests should give one significant result (as if I didn’t already know!). But I was definitely not cherry picking. Even if I am wrong, I will have no regrets. To put it in Poker terms, my experimental results force me to call all the way to the river and if I am beat … then I am beat. We are using happy stars as currency, so it’s not as though my credit card details are at stake.


Bring. It. On.

Time to spill the beans I guess

I guess it’s time to spill the beans (though avid readers of this blog may have gathered already):


Earlier this year, my Spider Solitaire paper was published in the excellent journal Parabola, a mathematics journal aimed primarily at high school students. In this paper I showed that a particular Spider Solitaire server is biased: If a player wins too often the cards will be stacked, making it harder to win (assuming I did not “hit” the 1 in 20 chance of incorrectly rejecting the null hypothesis). I do not know why or how the server does this, but perhaps that will be the subject of a future post 😊 What I do know is the Spider Solitaire server in question is very badly designed. The company in question does a number of card games involving the well-known Klondike, Freecell and the like. if you look past the beautiful graphics, sound and animations, the server has a number of “fundamental errors” such as not knowing almost every game in Freecell is winnable or that every tile in MahJong Solitaire should appear exactly 4 times. Once upon a time I played 24 games of Spider Solitaire after resetting my stats. I won 50%, had a longest winning streak of 8 and a longest losing streak of 1. Go figure.

I kid you not.

The key observation I made was that making random moves is sufficient to beat 1-suit solitaire without undo more than half the time. Ergo, we can estimate the difficulty or a particular hand by repeated simulation. If the game is played at 4-suit, we can still estimate the difficulty of a hand by pretending it is 1-suit. All this requires that we are able to determine the identity of every unseen card in the initial game state.

In my experiment, I bought a new computer (to remove the possibility that the computer already knows I am an experienced player). I played 40 games, because that provides a reasonable amount of data without being too onerous (I definitely want my experiment to be replicable for less experienced players). I deliberately used undo to ensure that every game was won (and also to record the identity of every unseen card). To test whether games get harder, I computed the probability that of two randomly chosen games the latter would be more difficult than the former. I found the result to be statistically significant at the alpha = 0.05 level.

I highly recommend Parabola for the serious mathematicians among you. The feature articles are very well written. The problems are somewhat beneath my dignity (but what do you expect given I competed in the 1995 International Mathematics Olympiad and composed my own problem for 2016?) but I can see how they are intended to make high school students enjoy mathematics. High school teachers will definitely want in on this. Yes, I thought that Square Root of Negative Pun and 2Z or Not 2Z are a bit weak (at least with Bad Chess Puns you get to sharpen your tactics), but overall I think Parabola has much to recommend it.


For me, the most pleasing aspect of this paper was how I was able to combine various “elements” such as statistics, random walks, basic Spider Solitaire strategy etc and combine them into a harmonious whole, resulting in something more awesome than my Flappy Bird cover of the Wintergatan Marble Machine. In closing, I will leave the final word to Thomas Britz, editor of Parabola: “In each their way, these items remind me of some of the many reasons for why I love mathematics: maths is elegantly useful and usefully elegant; it is beautifully surprising and surprisingly beautiful; and it provides insights into connections and connections between insights. It challenges; it entertains and it provokes much humour.”