A Closer Look at Maslow’s Hierarchy of Wants

Maslow’s Hierarchy of Wants

Okay, so I goofed. The eagle-eyed among you may have spotted an embarrassing typo or two in my last post. Mainly because I made a last-minute decision to change “hierarchy of needs” into “hierarchy of wants” which led to inevitable consequences. This should be fixed now. Lesson learnt!

The basic idea of MHoW is that given our current game state we should assess how well or badly we stand with respect to each layer. Then we have some idea of which part of the game to focus on. Sure, there may be some trivial decisions such as making a reversible move to build in-suit but inevitably there are critical points in a game where the right or wrong decision can decide your fate.

I should point out the Hierarchy of Wants is not necessarily linear. Either two items should be swapped or you could work on them simultaneously. As an extreme example, you might be able to remove a complete suit without obtaining an empty column at any stage of the game – which would be a cheevo in itself! There is certainly no law forbidding you from doing so, if the card gods were kind enough to allow it. But for most hands I would expect the above pyramid to be a good approximation of how an expert player would plan to win. In any case, you should feel free to tweak this pyramid as you gain experience.

Let’s look at an example or two:

Example 1

If Simon Anthony from Cracking the Cryptic were playing, he might be waxing lyrical about some promising signs: a suit of Spades has been removed, we have plenty of in-suit builds and excellent potential for obtaining empty columns (most columns have no face-down cards). Meanwhile Captain Obvious is yelling at the Screen, vainly trying to convince Simon the winning chances are exactly zero. With MHoW we immediately see the problem: we have failed at the lowest layer of the pyramid – and everything above this layer is rendered useless.

Okay, this was admittedly a trivial example but I only mentioned it because most losses are conceded before the player actually reaches a game state with no legal moves (and therefore “at least one legal move” is something we take for granted). So, this is something to bear in mind.

Now look at a second example:

Example 2

We have plenty of turnovers already and no problem finding legal moves. Although we cannot turn over extra cards before the final deal, we don’t really need them. We have one empty column – and hence some flexibility – and some promising in-suit builds. Clearly, we need to work on removing suits. For instance, we can immediately see a long run of Clubs in column 4 so one possible plan is to look for the remaining clubs (K-Q-J and 2-A).

Third example:

Example 3

Things look fairly promising. We immediately see two empty columns in four moves and further analysis shows we can actually clear at least one suit of Diamonds. With only six face-down cards remaining, either the game is mathematically won or the odds are very much in our favour. Therefore, we can jump to the top of the pyramid and start thinking about cheevos.

This example demonstrates another important lesson: don’t be intimidated by the sheer number of face-up cards in the tableau: It may turn out your position is very strong without realising it.

As a final word: it may be tempting to monitor the number of cards left in the stock to help decide which layer of the pyramid you should be working on, but that only works “on average”. I’ve had games where I could only ascend to the second level with only 10 cards remaining in the stock – yet still managed to win. Conversely, I’ve seen things go sour after a promising start. Use your common sense, and if something in the tableau screams “not an average hand” then listen to your gut and watch your results improve.

Until next time, happy Spider Solitaire playing 😊 May all your builds be in-suit and may all your long-term plans come to fruition!

Awesomeness has been achieved!

I have finally achieved awesomeness! My Spider Solitaire Sudoku puzzle has been featured on Cracking the Cryptic.

For those who are interested in the puzzle only, here is the grid: if you’ve played any Spider Solitaire the rules should be guessable – and if you get a unique solution then you know you’ve guessed correctly 😊 But if you’re interested in the back-story then please read on.

If you follow this blog regularly, you are probably aware of a paper I published some time in 2019. I showed that a particular Spider Solitaire server was biased: if you win too many games then future games will have the cards stacked against you – and one could “prove” this using Statistics.

I use quote marks because the nature of Statistical testing always implies some degree of uncertainty. For instance if you are 95% confident of a hypothesis, then there is a 5% chance you made an error. But it is commonly accepted practice. If your experiment is sound and you get a sufficiently small p-value then go ahead and publish it anyway. You may be wrong, but – to put it in Poker terms – your results pretty much force you to call all the way to the river. If you are beat then you are beat.

Of course, getting the results you want is only the first step. We all know the academic publishing model is broken. The peer review model is hopelessly flawed. At best, peer review is based on good intentions and met the demands of research scientists 30 years ago – but certainly not today. It already takes long enough to get accepted into a mediocre journal, or even the dreaded arXiv. If you’re that desperate you might be willing to spell arXiv backwards. And don’t get me started on predatory journals. I won’t describe the ills of academic publishing in all its gory detail. Someone else can probably explain it much better than I can. In my case I ended up publishing into a high school journal. Parabola from UNSW to be exact.

But at the end of the day, publishing is essentially “a way to prove or showcase your research skills”. Once you complete your thesis (or minor thesis, 3-month vacation employment, etc) and may or may not be a major component of your career depending on your employment. (It is true that my Spider Solitaire paper is not relevant to my job, but that has nothing to do with the Fundamental Theorem of Calculus.)

Still, the Parabola publication still wasn’t entirely satisfactory. My paper wasn’t truly a publication. It was a story. I wanted to tell a story about how a certain Spider Solitaire was broken. There is nothing intrinsically wrong with Parabola (with the possible exception of some really lame comics and puns), but try telling that to the average Joe Bloggs with an average job, has little aptitude for mathematical puzzles and swears by Nova FM. In fact, telling this story was the original motivation for me starting this blog in the first place.

Scientists don’t have a way of getting their work recognised. They have no way of “controlling the narrative” if you will. I can publish a paper in some journal. Or I can post something on a blog and have all the scientific evidence to back it up. But how many people are going to read it, let alone believe it?

Enter Cracking the Cryptic.

You may have already guessed I am a fan of CtC (not necessarily because of this blog!). I was vaguely aware of it last year. It seemed to be massive in the UK.  I tried one of the harder puzzles. Solving it was beneath my dignity – after all I scored a silver medal in the 1995 International Mathematical Olympiad. Okay I get it. There’s a pandemic going on. People are struggling in the UK. Some viewers have even commented on YouTube how watching episodes of two people solving Sudoku puzzles helped their mental health issues. I’m living in Australia not the UK. Australia really is the lucky country, so who am I to judge?

I then stumbled on this puzzle by Lucy Audrin.

This is a “Sandwich Sudoku with a twist”. Before solving the puzzle Mark briefly mentions Lucy’s website and eventually finishes the puzzle in just over 15 minutes.

You read that right. Lucy wanted to draw attention to her website. All she had to do is submit a half-decent puzzle to CtC and Mark will take care of the rest. To be fair her puzzle is more than half-decent and a good illustration of how one can keep the puzzles fresh by tweaking various rulesets (such as thermometer, anti-Knight, XV, arrows etc). If Simon and Mark only did classic Sudoku every day of the week, CtC would have finished long ago. I should also mention that Lucy can write much better stories than I can!

Great – if Lucy can draw attention to her website then perhaps I can do the exact same thing with Spider Solitaire.

This was much harder than anticipated.

It would surprise nobody if I claimed I could construct a correct Sudoku puzzle with a unique solution and Spider Solitaire theme. There was one obvious hurdle: if I submit my puzzle and it gets rejected – then good luck trying to resubmit the same puzzle a second time. I decided to play it safe by first submitting “test puzzles”.

It was a long process. Essentially I needed to “play the networking game” and gradually build up reputation. I spent a significant amount of time testing puzzles by other setters, joining the Discord server and chatting, signing up for Patreon, creating my own puzzles, etc. I submitted the above Spider Solitaire paper to the Discord a few months ago, but eventually realised that was not the same as submitting directly to CtC (submitting to Discord only means CtC have permission to do it, if it gets nominated). Yes, networking really did make things a lot easier in the long run. If you play nice and do all the right things then eventually people will help you when you need them to. If Sudoku is your thing then I heartily recommend you join the discord server. Great people, great puzzles, great jokes and cultural references. Occasionally somebody may attempt to pull off a rick-roll. What’s not to like? 😊

I emailed CtC my puzzle earlier this week and finally my luck was in.

So there you have it. If you follow my blog regularly, then I hope you enjoyed the journey as much as I did. Until next time, happy Spider Solitairing 😊

Spider has made it on CTC!

Spider has finally appeared on Cracking The Cryptic! Unfortunately it’s not the right type of spider we know and love. We all know how many words a picture is worth so I’ll just do a screen dump and let you judge for yourself.

I believe every man dog and millipede on the planet must have heard of CTC by now. If you’re not familiar with CTC there’s always Google Search. If you’re not familiar with Google Search you can apply recursion and do a google search on Google Search. Bad jokes aside, this is easily one of the best Sudoku puzzles I have ever come across –

Yes, it’s a Sudoku. With no given digits. Not one. Just a bunch of lines that look like a spider. Plus a black dot between row 9 column 4 and row 9 column 5.

Lucy Audrin has set a number of puzzles for CTC and she also has many interests outside of Sudoku. She is definitely one of the Awesome People, and the world could do with a few more of those!

Oh yes, I should probably mention the rules: Normal Sudoku rules apply. Digits on a “thermometer” must strictly increase starting from the bulb (for example 13678). Some thermos share a common bulb. The black dot indicates two numbers in a ratio of 1:2 but you don’t know which cell is twice the other. It turns out this is enough to enforce a unique solution.

HINT: for those unfamiliar with Thermometer Sudoku, one of the thermometers is length 9, allowing you to enter nine digits immediately.

If you know your Kropki Sudoku, this puzzle has no “negative constraint” i.e. some cells can have consecutive digits or digits in 1:2 ratio despite the absence of a black or white dot.

Let me know if you enjoyed this Sudoku 😊