Yet Another Digression: DJDJDDJKDK is the new COVFEFE

So here I am, innocently literature-reviewing something that is work-related. Spider Solitaire is the last thing on my mind. Someone has written an interesting Ph. D., titled “An Analytical Framework for Soft and Hard Data Fusion: A Dempster-Shafer Belief Theoretic Approach”. I’ve been there many years ago, so anyone who has something to show after three years of solid research has my respect. The author successfully navigates the first hurdle by not spelling Dempster with a ‘u’ (GIYF). After 16 pages it’s all looking good and the dude seems to know what he’s talking ab– rot13(JUNG GUR NPGHNY SYLVAT SHPX) JUST HAPPENED?!?!?!?

“Decision-level fusion: Here, each sensor makes a preliminary estimation of an entity’s identity in terms location, attributes, or any other DJDJDDJKDK.”

Yes, you read that right.


All capitals.

Ten consonants in a row.

Don’t bother looking it up in Scrabble. Even if it happened to be legit, there are not enough D’s J’s K’s and blanks in the bag to spell that word without violating the laws of physics.

Yes, rot13(jung gur shpx) indeed.

I mean, this word beats “covfefe” hands down. At least the latter has only seven letters and some of them are vowels. I could understand ASDFASDSDF if somebody was too lazy to type “Lorem Ipsum” as place-holder text. But D and J/K are separated by three letters on a standard keyboard last time I checked, so button-mashing doesn’t seem a very plausible explanation of DJDJDDJKDK.

I did what any self-respecting research scientist would do: I googled the thing. Nothing, zilch, nada, zippo, duck’s egg. Buckleys plus Buckleys squared. Worse-than-Anton-Smirnov-getting-smashed-with-the-white-pieces-against-Duda-in-26-moves. With nothing to go on, it looks like I have to invent my own definition.

Not. Even. Close.

Let us say that a DJDJDDJKDK is a special cheevo that occurs whenever you deal ten cards from the stock, such that the first card is any diamond, the second card is any Jack, followed by another Diamond, another Jack and so on. That’s a total of five diamonds, three Jacks and two Kings. Probably a lousy deal unless some of the diamonds happen to be Queens or Tens, or you have strong chances of completing a suit of Diamonds.

Assuming cards are drawn with replacement it’s easy to compute the probability of a DJDJDDJKDK. Every diamond occurs with probability 1/4 and every Jack or King occurs with probability 1/13. The overall probability is obtained by multiplying (1/4)^5 * (1/13)^5. Of course, the cards are not drawn with replacement but it’s a reasonable approximation to say the chances of achieving DJDJDDJKDK are not exactly great. We can improve our chances a bit by allowing any permutation of DJDJDDJKDK. Also, the Jack (King) of diamonds can count as a J(K) or a D. But If I were the author of a Ph. D. mentioning the words “decision-level fusion” I wouldn’t be betting my Ph. D. to a brick on the elusive DJDJDDJKDK given those odds. The above image is a randomly generated 4-suit hand, and clearly, we are not even close to a DJDJDDJKDK. We only need one “bad card” i.e. not a Jack, King or Diamond to disprove a set of ten cards achieves DJDJDDJKDK. But if it ever does happen in my Spider Solitaire career, I would definitely let the whole world know 😊

Well, that’s enough digression for today. How would you explain someone choosing DJDJDDJKDK as a Ph. D topic? And more importantly, how would you define DJDJDDJKDK?

April Fool’s Joke Explained

IM Bart has reminded me via email I haven’t yet explained the joke on 1st of April.

It turns out if you click the last link with words “please click this link” you do not get the video of Never Gonna Give You Up. Instead you reach my Spider Solitaire paper in the UNSW high school Parabola (which doesn’t involve any Rick-Roll at all).

Oh of course

I’m Seeing The Same Scam Ads Again And Again

Well, not much luck with my efforts to get more readers into Spider Solitaire. I’m sure IM Bart and IM Bug will appreciate someone else stepping up to share the load.

Maybe I need to take a leaf from Facebook’s book (yes I know!) and start thinking of creative ways to encourage more participation in the Royal Game. What would Zuckerberg do?

What Would Zuckerberg Do?

Happy April Fool’s Day

In this document I will discuss April Fool’s Day and various other pranks. Your mission, which you must choose to accept, is to figure out what all this has to do with Spider Solitaire.

As is well known, April the 1st is the day for pulling off pranks against people who were not born with the awesome gene. When I was in High School, my Geography teacher once wrote the date as 29th of October which wasn’t even close to the correct date. At least one student fell for it. Fast forward to the last decade and I once boasted about scoring over 600 in a single game of Scrabble, but I failed to produce any evidence the game was real. There was no mention of my actual score, plenty of phonies such as ETEARIO* instead of ETAERIO and OT* (a very common two-letter phony when someone isn’t paying attention!). The best giveaway was FOOLISHLY on a triple word with only the “Y” connected to the rest of the board. Therefore, this play is mathematically impossible unless someone had eight letters on their rack without opponent noticing – not to mention FOOLISHLY is an appropriate word for any prank involving today’s date.

What makes an April 1st prank successful? I can think of the following criteria:

In my Scrabble example, a switched-on person may notice the board has an abnormally large number of questionable decisions, indicating at least one player is deliberately playing below is true strength. But if the person is switched-off then that’s hardly gonna impact his Key Performance Indicators in the workplace.

We should also remind ourselves that all pranks have a use-by-date and April Fool pranks are no exception. After the initial laughs, we need some ingenuity to keep things fresh. A good analogy would be Rick-Rolling. It was “grudgingly-accepted-funny” the first time around and perhaps the second and third, but I can’t imagine any self-respecting comedian of today attempting a Rick-Roll without putting “a new twist on the theme”. One well-known example is the atrociously written high-school essay on Niels Bohr but my favourite Rick-Roll occurs in Grant Woolard’s Classical Music Mashup III, which you would have to google for yourself. Actually that was only my second-favourite. If you really really really really really really need to see my Absolute Favourite Rick Roll Of All Time then please click this link.

Happy pranking everyone!

The Ideal Game of Spider Solitaire Among Us

You and five friends wake up on a deserted island. Luckily you have brought two decks of cards and all your friends are fanatics of Among Us and Spider Solitaire. How would you design the rule-set for a Spider Solitaire Among-Us mashup?

I came up with the following:

  • There are four cool mates and two impostors. Both impostors know the identity of the other impostor.
  • Cool mates win by removing eight suits or by ejecting both impostors.
  • Impostors win by stalemate (i.e. eight suits are never removed) or ejecting enough cool mates to achieve numerical parity.
  • At each “turn” all players discuss what is the best move or sequence of moves (it is not necessary to turnover one or more cards). Cards can only be moved after unanimous agreement by all remaining players.
  • Any player can call an ejection(*) if they believe someone is acting stupid.
  • You can call ejections as many times as you want! Beware that calling too many ejections without purpose will likely result in yourself “winning” an ejection
  • If an ejection is called, all active players have a minute to vote to eject any player of their choice or pass. The player with most votes gets ejected. Ties mean nobody gets ejected.

(*) We all know it should be “emergency meeting” but I can’t resist the bad pun!

Sanity Checking

To verify these rules are reasonable one can observe the following:

  • If the game is “guaranteed winnable” regardless of the distribution of unseen cards then the cool mates can force a win (unless the impostors already have numerical parity). All they have to do is agree on the same winning move and eject anybody who suggests a move that doesn’t guarantee a win.
  • If the impostors achieve numerical parity with cool mates then they can easily force a stalemate by always voting to move no cards and voting for the same cool mate in every ejection.

Spider Solitaire Among Us in Real Life

Of course, in real life it is not really possible to get an ideal game of Spider Solitaire Among Us. I can’t pull 6 random people off the street and demand they be expert players with plenty of spare time on their hands, so during the last few weeks I had to compromise somewhat by playing multiple roles of blogger, cool mate, impostor etc. On the other hand, it should be feasible to convert any solo-player game into an Among Us mashup – particularly if the game is already popular. For instance, you can have six Chess or Backgammon friends play as a team against an AI. If you’re really mad, I guess you can have two Chess teams of six players each but with one impostor per side. You’re really only limited by your imagination. Anything goes as long as it obeys the laws of physics!

Any thoughts on how to play an ideal game of Spider Solitaire Among Us are more than welcome!

Among Us Lite – Round 3 Summary

Final position in Round 3

An eventful round. We snagged the last unseen card in Diamonds (the Three), enabling us to clear the suit – but at the expense of a turnover or two. The Kolourfull Kibitzers had some robust discussions along the way.

With one suit removed, I expect the worst is behind us (in terms of complex decision-making) but we only managed to turnover two cards this round. Still, there is plenty of play left for the good guys. An excess of even-numbered cards is still a problem, but as the endgame approaches, we have every right to expect … the odds to shift in our favour.

Yep, looks like Spider GM is still in fine form. Bring it on 😊


SA has suggested I add another move “cb” before dealing a new row of cards and Bart is happy with this decision

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


Connect Four and Spider Solitaire

Every man dog and millipede on the planet has heard of Connect Four, a well-known two-player game by Milton Bradley. The objective is to line up four pieces of your colour horizontally diagonally or vertically. Unfortunately it is not played in serious competition these days, mainly because the game has been solved. With perfect play by both sides the first player wins.

The solution was found independently by James Dow Allen and Victor Allis (independently) in October 1988. The first player must start in the middle column. If she plays adjacent to the middle column then it’s a draw. Playing anywhere else even loses. Furthermore, the first player requires all 21 discs to force a win if a perfect opponent puts up maximum resistance. For a detailed analysis of the game please check out this excellent video  by Numberphile.

However, I believe Connect Four has not been solved after all, because everybody has been playing it the wrong way.

Consider the board state below. Before reading on, can you predict where the next two discs should be played?


A cursory examination shows that Yellow threatens to win on the left-most column. Moreover, Yellow has played 8 pieces but Red has only 7. Therefore it is Red to play. Clearly Red must block the threat of vertical Connect-Four. This in turn threatens a diagonal Connect-Four so Yellow’s next move is also forced.

But if you examine the board carefully, you will notice each column is labelled with one of the seven days of the week. Moreover, only 30 cells are marked with numbers but the others are empty. Not surprisingly, the board represents the calendar month for September 2019, which is further corroborated by the text above the board.

It is not hard to guess that Spider GM is going to play a game of Four-Suit Spider Solitaire on every day of this month. Every yellow disc represents a victory, and every red represents a defeat. Spider GM is only concerned with winning the game regardless of the number of moves or time taken to complete it. Of course Spider GM will play without undo. Four in a row still wins the game (but Spider GM can continue to play the remaining days just to fill up the board and see what it looks like). The current position shows a hypothetical game state after the 15th of September.

This completely changes the dynamics of Connect Four. For instance, odd and even threats still exist but here they refer to whether the cell contains an odd or even number (instead of what row the cell lies in). Going back to the example, Spider GM has an even threat on Sunday the 22nd. Unfortunately the next game will be played on Monday the 16th. Therefore the next move will either be a Red or Yellow disc on the cell numbered 16. In other words Spider GM has to wait for a whole week before his threat of winning on the Sunday column comes into play. Of course if Spider GM does win the battle on the 22nd of September then he also wins the war, unless Daily Challenges manages to build an unlikely winning horizontal Connect Four before that date.

Well done if you correctly predicted the next two moves to be “cells 16 and 17, either red or yellow”.

It is easy to see that Connect Four is now an unsolved game again, since the colour of each cell depends on the result of a single game of Spider Solitaire, and not even the Spider GM knows the perfect strategy for the latter. This I believe is the way Connect Four should have been played all along. So if you have enough spare time on your hands to play one game of Spider Solitaire per day and wish to make Connect Four great again then you know what to do 😊 Good luck.