Thin Margins

This is an example of “thin margins” in this month’s game of Connect Four. Recall that I am playing Random Hands, as opposed to Daily Challenges from last month.

It is not possible to turnover a card in column 8. The problem is after shifting the 9-8-7-6-5-4-3-2-A onto the doubled Ten, there are no “stepping stones” to handle the mid-range cards in the remainder of column 8. We need any free Seven, Eight, Nine, Ten or Jack (or the Six of Diamonds on top of any Seven to enable a ‘swap’ operation) yet none of these exist. This problem occurs when the exposed cards in all ten columns are not distributed evenly (they are 2-K-A-2-Q-?-5-A-6-A leaving a huge chasm between the Six and Queen). Failing column 8, the best we can do is get a tenuous 12-suit in Clubs, with every card except the Four in column three.

For what it’s worth the last ten cards in the stock were A-9-5-9-A-J-4-J-K-9. Winnable with rot13(haqb) but not guessable sans rot13(haqb). Thin margins indeed. My stats say I am up to Level 46. I have won 84, lost 59 and my percentage is 58.74%.

Here is the current position in Connect Four. Team Red has taken the important squares labelled 16 and 17, setting up threats on the y=6x+4 diagonal, the WHAT column and the 15<x<20 horizontal. I think Team Yellow would need several Uno Reverse Cards to escape from this one.

Do you have a Spider Solitaire that upgrades your level after sufficiently many wins? If so, what level are you up to? Please let me know in the comments!

Connect Four May 2023 Update

With almost half the month gone, it’s time to assess the board situation in Connect Four. I have used Yellow and Red for games won and lost respectively.

The first question is whether the pieces should fall to the bottom or rise to the top. Gravity suggests the former, but last month’s daily challenge suggests the latter. In any case, I have gone with the latter.

Red has the numerical superiority but Yellow seems to have better control of the centre. If we count vertical and diagonal threats of Connect Four then we see three possible threats for Red (all going through 10) and four for Yellow.

In other news, I have verified with a work colleague that two different players indeed get the same starting hands for the 4-suit daily challenges, even though solutions are not available. To be honest, this is what I expected – but I was still willing to ask the question due to the “low effort high reward” factor. Imagine what would have happened had my work colleague got a different hand …

FWIW, here is today’s loss. After dealing the final row, most of the movable cards are covering Aces.

Connect Four May 2023 Update

It’s been an eventful game of connect 4. It’s certainly tougher than the daily challenges when I could safely assume each hand was solvable with sufficient use of rot13(haqb).

I won on the first day of the month, then had a string of three losses. Games 2 and 4 were perhaps close, but game 3 was a walkover to the bad guys. Game 5 was a crunch moment – a loss would mean four Reds in a row horizontally and the rest of the month to stew. Indeed, I had a rough middlegame after dealing the first row of cards – and somehow I managed to rescue one of the strangest “almost-losses” I have ever seen. A true display of rot13(junggurshpxrel) from an app I do not entirely trust.

As for why I consider this one of my “strangest almost-losses”, that’s something you have to figure out for yourself (Incidentally figuring out how to proceed is a good test of your analytical skill).

Having avoided an early defeat, it seems we are headed for a long war of attrition as both sides jockey for position. The fourth week is where things get spicy as possibilities of diagonal and vertical connect fours come into play.

I saw my connect 4 and raised myself to connect 7

It’s the last day of the month. The game officialty ended on the 13th of April, but I decided to keep playing until the not-so-bitter end  – and it turns out I would still have won if I were playing Connect 7 instead of Connect 4.

My only losses were 2,4,6,8,9 – giving me below 50% for the first and only time – followed by a connect-5 from 18,19,20,21,22 and every other game was won.

Indeed I would have won the game of connect-N where N is an integer between 1 and 7 inclusive. Next month will be Connect Four but playing Random Hands instead of the Daily Challenge. I expect this to be significantly harder, but I will have more to say in a future post.


Some time ago I wrote that DJDJDDJKDK was the new COVFEFE with good reason – someone actually managed to invent a new word with ten consonants in a row for his Ph. D. titled “An Analytical Framework for Soft and Hard Data Fusion: A Dempster-Shafer Belief Theoretic Approach”. A ground-breaking discovery if ever there was one. Unfortunately, I have no idea what the author intended so I had to invent my own definition. Luckily for me, I noticed that D/J/K are initials for Diamond/Jack/King. I also remembered there are exactly 10 columns in the Royal Game and the rest, if you pardon the cliché, is history.

And that’s where the story ended – or rather that was where it was supposed to end.

Then along came the World Chess Championship between Ding Liren and Ian Nepomniachtchi. Round 11 ended in a quick draw in the Ruy Lopez. Chess celebrity Levy Rozman (a.k.a. GothamChess) did a recap of that game. Click this link and Quad Erat Demonstrandum. ASDFASDFASDLFKHASDF is officially the new DJDJDDJKDK. Personally, I would have chosen TAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKESTAKES because the game contained no less than 15 consecutive captures but for some reason Levy chose ASDFASDFASDLFKHASDF.

So now my next task is to somehow figure out what ASDFASDFASDLFKHASDF means in the Royal Game. I know all these letters are on the middle row of a standard keyboard but unfortunately the middle row contains only 9 letters not 10, so I can’t define a natural 1-1 correspondence between letters and columns. Of course reader suggestions are more than welcome!

Trevor vs The Barber

And on a slightly sadder note, I lost a game of Spider Solitaire against a barber situated near where I work. He’s a great guy who loves to engage with his customers and I reckon I know a thing or two about negotiating my way to a quick haircut 😊 I can’t give away too much information since there is no reason to risk “de-anonymising” said barber.

I had an ‘informal bet’ that I could complete a game of 4-suit Spider Solitaire without undoing any moves before the barber completed my “hair job” (if you pardon the poor choice of words), assuming we both started at the same time. As you can see below, it wasn’t even close. I guess the moral of the story is 4-suit Spider Solitaire isn’t exactly designed for “speed-solving” and is more suitable for players who like deep strategic thinking and less reflexes.

Last time I had a haircut there, I think I was playing Toy Blast instead of the Royal Game, but unfortunately, I recently decided Toy Blast had a biased random number generator so I am no longer playing that game.

At least I managed to win this hand after finishing my work for today. So until next time, happy Spider Solitaire playing 😊

Connect Four – Victory is Mine!

I have now achieved victory in my game of Connect Four with the MobilityWare Spider Solitaire app. After a balanced start things looked bleak – removing two suits was not enough on the ninth hand, giving me a win ratio of less than 50%. But I pulled myself together to take four wins in as many days, thus ending proceedings then and there.

Probably my favourite hand was Game 12. The critical position is shown in the diagram below (left).

I spent two empty columns to get one turnover + a “twelve-suit”. I like this kind of “pig play”, sacrificing the possibility of turning over (at least) two cards in column ‘d’ and hoping to complete Clubs on the next deal. Of course, don’t forget that the software app could also make a pig play of its own and make you look stupid. I turned over a disappointing Ace of Spades to reach the diagram below (right) but managed to scrape home after dealing the last row.

Turning two cards in column ‘d’ feels short-sighted to me and likely to lead to serious problems once the stock is empty. I might have more to say about this in a future post.

In any case, well played Me and the SpiderSolitaire app has the rest of the month to stew 😉

Connect Four progress

Having made it to the seventh day of the month – and also the start of the Easter long weekend – I think now is a good time to review my progress in Connect Four.

A brief refresher of the rules: on each day of the month I either win or lose a game of Spider Solitaire. Wins and Losses are marked on the calendar month. In the MobilityWare app, wins are indicated by crowns and losses by the absence of crowns respectively. The Orange cells numbered 8-14 indicate I can play the daily challenges up to one week in the future, if I am willing to “go premium”. In this case, I have managed to alternate wins and losses although that was not my intention!

Neither side has managed to gain a clear upper hand. Threats of winning are starting to percolate on the 1-7-13-19 diagonal but there’s always a chance that some horizontal connect-four for either side will terminate the game prematurely before we reach that point.

I have also included a brief description of how each game went. For instance, game 2 was a really bad loss when I only managed my first empty column after the stock was empty, whereas game 3 was extremely easy with the entire tableau face up before dealing any cards from the stock. Game 5 was noteworthy, with the rare scenario of removing four suits that are not “one-of-each”. It is quite rare for a player to remove both suits of Hearts before removing a single suit of Clubs (and WLOG we can replace Hearts/Clubs with any other suits), assuming we only play to win and ignore the possibility of “achieving the cheevo” if the hand is too easy! Game 6 saw a narrow loss when “one card would have made all the difference”. Of course I can’t be 100% certain since losing implies I did not discover the identity of all face-down cards, but my experience tells me I would probably have won if I could replace the “critical bad card” with the one I wanted.

On Day 4, I struggled from the very beginning and the only thing that prevented an early surrender was the software not having a Backgammon Doubling Cube. But the software did have an annoying pop-up message asking me if I wanted to see the solution for this hand (which I found insulting).

Of course, this does not guarantee that two players playing the hand corresponding to the 4th of April will get the same starting hand since the solution is not publicly available.

Finally, I should mention there was no effort to prove or disprove if the hands are biased via recording the starting configuration and applying the Ninja Monkey’s algorithm. I think that dead horse finally deserves some rest and no more flogging is required.

MobilityWare App

If you want to play the same Connect Four game, the MobilityWare software can be downloaded here

It can also be found on the App Store (search MobilityWare Spider Solitaire). Note that my version says “update” instead of “get” because I already have this app!

The instructions for playing a 4-Suit Spider Solitaire hand corresponding to a particular day of the month should be fairly self-explanatory.

To delete the app, press “some empty area” on your mobile phone and each app will have a minus-sign icon appearing the upper left corner. The apps will start trembling, as if saying “don’t pick me don’t pick me …”. Of course once you do click the minus sign icon there is no turning back!

Connect Four – Bring It On!

Okay, I’ve submitted to temptation and finally downloaded the MobilityWare Spider Solitaire app even though it’s probably rigged – but only because I wanna try the daily challenges.

A daily challenge is a certain starting configuration that is guaranteed winnable. MobilityWare has several games (not just Spider) and solutions can be found by googling. Games include Freecell, Solitaire Draw 1, Solitaire Draw 3, Spider Suite 1, Spider Suite 2, Spider Suite 3, Crown, Tripeaks, Addiction. That’s quite a lot of variety, and I will admit I don’t even know the rules for some of these games. Although I thought the “Suite N” part was weird because it clearly should be “N suits” where N = 1,2,3 … no wait, there’s no solution for N=4?!?!?!?

If a solution is given, it means two players can play the hand corresponding to the same day and same game (e.g. Tripeaks, 5th of February) and they are presumably guaranteed to get the same starting hand. If they didn’t get the same hand and wish to check the solution, at least one player would complain very quickly! However, since I can’t find a solution for any 4-suit Spider hand, it is mathematically possible (though unlikely) that two players can play DIFFERENT 4-suit Spider hands corresponding to the same day and they would be none the wiser unless one of ‘em specifically asks the other if they get matching hands.

NOTE: in some cases only partial solutions are given (because some games take longer than others) and you have to pay some $$$$ to get the full solution. But a partial solution is more than enough to confirm two players indeed get the same hands.

Assuming two different players do get the same 4-suit Spider hands, I can play these hands with reasonable expectations they would not be ridic hard – since I can’t see a game developer with rot13(fznyy qvpx flaqebzr) punishing random novices with insanely difficult hands if my win rate is too high, even if he or she works at Zynga (or an equivalent company).

I think a fun challenge would be Connect-Four. On every day of the month I either win or lose the hand corresponding to that day. Four wins/losses in a row, horizontally vertically or diagonally means I win/lose. For instance, if I remove all eight suits on days 5-13-21-29 then I achieve a winning Connect Four, unless I also achieve a losing Connect Four earlier (such as 9-10-11-12). The downside of playing Connect Four of course is if the game ends after 6 days, then I might have to wait a while before the next month! The screen shot below is for April 2023, coming soon to a place near u.

Ultimately, I am interested in playing all the daily challenges in April 2023. Can I expect to win most hands? Also, do hands get tougher as we approach the end of the month or is it roughly uniform difficulty?

Here are the hands for N-suit Spider Solitaire corresponding to 29 March, for N = 1,2,3,4. I would be interested if readers can confirm they get the same starting hands for N=1,2,3,4.

Of course the result I am really interested in is if you get the same hands for N = 1,2,3 but different hands for N=4. Then I would know something suspicious is going on!

Toy Blast – It’s A Force Delete

It’s official – I was finally forced to delete Toy Blast from my phone. Some time ago I thought this was one of the cool games, but it seems the random number generator is rigged, just like every other game. Of course, I recognise this is only my opinion, which I can’t force onto others. All I can do is turn to page 7374 of the Big Book of Clichés and say “judge for yourself”.

The problem is if you attempt to design a game with rigged RNG, it’s probably too easy to design an experiment that can expose certain issues. The culprit is level 7374 which looks like this:

It is beyond the scope of this document to explain the rules of Toy Blast in detail. The essential points are:

  • To beat this level, one of the requirements is getting at least three slices of bread. This is difficult since there is only one toaster which cannot be accessed with ordinary cubes. Power-ups are a must.
  • The basic power-ups are rotors, TNT and Rubik’s Cube. Rubik’s Cubes are always a particular color (one face is a solid colour, other faces are random).
  • Power-ups are obtained by matching 5 or more ordinary cubes of the same colour in one move.
  • Combos can be obtained by getting two or more adjacent power-ups. Adjacent means touching horizontally or vertically, but not diagonally.
  • If the player activates a Rubik’s Cube + rotor combo then every ordinary cube with matching colour turns into a rotor that can be oriented horizontally or vertically.

Let us define a “coin-flip” as follows. The player activates a Rubik’s Cube + Rotor combo when exactly one of the four cells in the top row is a matching colour. The following four images show example of coin-flips. For instance, the first diagram has Y-B-G-B in the top row and a Yellow Rubik’s Cube next to a Rotor in column 6.

Note that if more than one cell is the matching colour, we do not count it as multiple coin flips. For instance, if the top row was Y-G-G-G and we activated a Green Rubik’s Cube + Rotor combo then I do not count that as three coin-flips. It’s not even worth one coin-flip. It’s ZERO coin-flips – the same number of points you get for playing a phoney in Scrabble.

The term “coin-flip” should be self-explanatory. If (in the first diagram) every yellow cube turns into a rotor then the yellow cube in the top row will collect one bread with 50% probability. Any other yellow cube on the board cannot collect bread, even if the player were allowed to call directions for every individual rotor. As every student of probability knows, all this assumes rotors are indeed horizontal or vertical with 50% probability.

I played level 7374 multiple times with the objective of getting as many coin flips as possible (not necessarily maximising my chances of beating the level). With enough skill and luck, it’s possible to get three coin flips in a single game. After sufficiently many games I got 50 coin flips and every time the rotor was vertical instead of horizontal. I did not hit the toaster once in 50 coin flips. Yes – Every Single Time.

On one occasion, I was down to my last move (see images above) and was destined to fail the level for multiple reasons. And the software still saw fit to give me the vertical rotor in the top row.

Just out of interest, I have already beaten level 7374 (I’m up to 7377) and managed to beat all levels without spending any coins (e.g. getting 5 extra moves or strategically changing the colour of a single cube). It’s hard to avoid the conclusion that Toy Blast is trying to punish players that are playing a little too well.

It is quite possible that something untoward happened to Peak Games (e.g. acquired by another company) when I wasn’t looking – but I do not intend to discuss this in detail. I recommend the reader google search “Peak Games” and “Zynga”.

And if you happen to be a game designer – don’t even think about it. You are not fooling anybody.

Let me repeat that for the 7374th time:

You. Are. Not. Fooling. Anybody.

It goes without saying the same holds for Spider Solitaire. I believe we have reached the point if Joe Bloggs claims the game is rigged then the onus of proof should be on the game developers, not the player.

To be fair, I should point out that Toy Blast survived far longer than some other game apps on my phone. Some really awful games (both match-three and card games) basically “didn’t even try to hide it”.