Last week we asked the following:

Is it possible to determine the identity of the next unknown card for all columns containing at least one face-down card?

The answer is no. I can get columns 4,5,6,9,10 but not 1,3, or 8.

The problem with column 8 is we need to build off-suit with 3-2 to get the empty column, but then there is no Four or Three to shift that off-suit 3-2. One empty column is not enough. I will not discuss columns 1 and 3. That has already been covered last week with Bart and Schistocerca Americana’s (SA) excellent comments. Well done again to Bart and SA. I guess the next step is to take the easy turnovers and take it from there.

BTW Thanks also to Sebastian for liking one of my recent posts. I hope to hear more from him.

We reach the following position (both the current game state according to Microsoft Spider Solitaire and our cheat sheet) with the five newly turned over cards highlighted:

Let’s just say these are not the most helpful cards. At least this can partly explain why I lost this game rather convincingly without undo. It seems to be hard enough to win, even with the undo Awesome Superpower.

I guess we can take some freebies in column 4 at the expense of dumping a King into an empty column. This leads to the following:

And now we reach a dead-end. There are no more easy turnovers and we have to make some choices. If we think about long-term planning (rather than short-term gains) then there are three basic choices to consider:

• Go back to the very beginning and look for more turnovers without dealing anything from the stock
• Go back to the first position of this post(score = 141) and try to arrange matters so that the next deal of J-6-2-5-4-A-3-8-8-K is as helpful as possible
• Look for ways to remove at least one suit to the foundations, given the information we already know

Stepping back for a minute, we can observe a problem with Fours and Nines. Despite turning over more than half the cards in the tableau we didn’t find a single Nine. We know six of these are in the stock. We only managed to find two Fours at the expense of dumping a King into an empty column.

Over to you. How would you continue here?

A small reminder: Microsoft Spider Solitaire will not allow a player to deal a row of cards if there is at least one empty column.

In the last week I asked the following question: how many rows do we need to deal from the stock to be sure of procuring an empty column (assuming the worst possible permutation of unseen cards)?

First let us clear up the Captain-Obvious stuff: Column 2 is the only column with no unknown cards so we must focus on that. Also, there is not a single Nine anywhere until the second deal so the answer must be at least 2. By that time, two Sixes will appear in Column 2 so we need to find enough Sevens to take care of these Sixes.

Schistocerca Americana gave a correct answer of three rows. I say correct because the Grand Faster mucked up by not asking for the minimum number of deals. I should have asked what is the minimum number of rows we need to deal from the stock to be sure of procuring an empty column?

Bart gave another correct answer of two rows. Starting from the game state from last time:

The following moves do the trick:

Before deal: dj,aj
After deal 1 (J6254A388K) : db,ad,ba,ge
After deal 2 (562259AJ8Q): gc,bg,bf

Note that the first move dj is a typical tesuji (link) when playing with undo. This can only be explained by prior knowledge of cards in the stock – it is inconceivable an expert player can find some miniscule advantage of dj over “doing nothing” if playing without undo. Also observe that we got lucky with ba after deal 1: the Five and Six are the same suit, hence the move is indeed legal.

Of course, it will be desirable to achieve an empty column without dealing any rows from the stock. We can guarantee at least three turnovers in columns 1,6 and 7. On a good day, we will get an empty column without any of the shenanigans described above. The worst-case scenario says we are forced to deal two rows, take the empty column and proceed from there.

Our luck is in: the final hidden card is the Queen of Spades which can immediately go onto the King of Hearts in column 5. So now we know it is possible to get an empty column without dealing any of the shenanigans described above.

Our cheat sheet now looks like the following:

The power of an empty column should be pretty clear. For most of the columns it is easy to determine the next face-down card, then undo to recover the empty column.

It is time for a new question: Is it possible to determine the identity of the next unknown card for all columns containing at least one face-down card?

Assume we are allowed to restart from the very beginning, but cannot deal any cards from the stock.

Thanks to Bart Wright and Schistocerca Americana for once again reminding me of my lack of cultural knowledge (e.g. Kung Fu). There is only so much one can do with my favourite animal types from Phil Hellmuth’s book Play Poker Like The Pros 😊

Last week I asked the following questions:

• Which suits have all 13 cards appearing at least once?
• Assuming you answered “more than zero”, can we actually remove a suit (regardless of identity of face-down cards)?

Bart Wright had some vague intuition that it might be possible. Judging from his writing, I think he would have some valuable management skills to contribute to any company who is interested in hiring. Unfortunately, he failed the “specific/measurable/achievable/relevant/time-bound” test. Schistocerca Americana has found a solution: Diamonds is the only suit with each card appearing at least once. His solution is as follows:

Deal – Do Nothing

1st Draw – ed

2nd Draw – hj, hf, dh, da, eb

3rd Draw – fb, hf, cg, eg, ig

4th Draw – ja, ji, ji, jd, fj, eg, fg, ei, gi, ga, ch

5th Draw – da, ad, ab, ib, ab, jb, af, aj, aj, ij, fj, hd, hj

The result is shown below. Using cut-n-paste in Excel proves this solution is indeed valid with no illegal moves, sloppy explanations or typos.

To be honest, I didn’t try to solve this problem myself since I am currently working on another fun project that is unrelated to Spider Solitaire. Well done to Bart Wright and Schistocerca Americana for their excellent contribution to this blog.

Of course, we are interested in removing eight suits instead of one. Clearly it makes sense to look for easy turnovers and empty columns at the beginning of the game. But the above was not an exercise in futility. At least we know that it’s possible to remove a suit just by sheer power of information (i.e. knowing the identity of unseen cards) even without an empty column. Besides an aspiring player must (i) learn to analyse long move-sequences involving a large number of face-up cards when playing without undo (ii) learn to play the cards well even when there is no empty column 😊

Let us first focus on exposing as many turnovers as possible without dealing any cards from the stock. Experimentation shows it is easy enough to turn over many cards in the tableau, including all cards in column 2:

Further experimentation with undo leads to the following cheat sheet:

It’s time for another fun question: how many rows do we need to deal from the stock to be sure of procuring an empty column (assuming the worst possible permutation of unseen cards)?

Note that NaN may be a valid answer if this turns out to be impossible even allowing for dealing all cards from the stock.

We continue our game from last week. Last time I asked what is the minimum number of face-up cards we are guaranteed if undo is allowed and we don’t care about losing 1 point for every move or undo?

Not surprisingly Bart and George found the correct answer of six cards (it wasn’t meant to be difficult). With the help of undo we can see what’s beneath the Queen of Hearts, the two Jacks and the three Tens. One can also argue the correct answer is 56 because we get to deal all cards in the stock and then undo – or perhaps even 66 cards if we count the ten cards that are already showing.

Nitpicking aside, our card-tracking now looks like this:

It should be pretty clear we can improve on our 66 exposed cards. But given we know so much information it might be possible to complete a suit by force! Here are some questions to ponder:

• Which suits have all 13 cards appearing at least once?
• Assuming you answered “more than zero”, can we actually remove a suit (regardless of identity of face-down cards)?

As promised, we deal the final row of cards:

Yeah that does look pretty bad … if the next card in column 1 is e.g. an Ace then there will be no legal moves (ignoring breaking the in-suit build with fb). I guess the only bright spot is the Ten and Jack are the same suit which is what keeps us mathematically alive.

Right card, wrong timing. Game over, thanks for coming!

Here is the position from last week

Our latest turnovers have not been good. We started with four guaranteed turnovers and only managed to increase it to five. On the other hand we did manage to find the Queen of Clubs – which means there may be some prospect of clearing the club suit (which Bart has correctly pointed out).

If you’re wondering why the Noble Spider GM has goofed, it’s because I was no longer able to connect the J-T-9 of clubs in column 4 with the 8-7-6-5 in column 10. By trying to be too clever with delaying certain non-reversible moves, I only succeeded in losing the ability to build the massive run of clubs. So maybe I shouldn’t have extolled the virtues of procrastination as per a previous post. In any case, it’s adios to our empty column, unless we get a good card.

It’s tempting to shift the Queen of Clubs into the hole, but Bart found the Wright idea (ba-dum-tish!!!) of tidying up the 8-7-6 of Spades with the moves df,ad.

There are several reasons why this is important:

• there are three Eights unseen as opposed to one King, therefor more chances of getting back the empty column
• The move bf would duplicate Queens in columns 7 and 8, and that also means less chances of getting back the empty column
• The most important reason is that we want to correct our earlier mistake with the Grand Master’s Goof from last week. In other words, if we get the empty column back we get the additional bonus of building in-suit. Note that any Nine will not yield an empty column, but we would still be able to correct the Grand Master’s Goof.

There is another possibility to consider. We can build in-suit with the 6-5 of spades in columns 1 and 5. This also allows us to swap the Twos of Clubs/Spades in column 5/9, thus tidying up our club suit. Because we have committed to completing the clubs, it makes sense to extend the run by one card. The downside of course is we expose another Ace. But since there is only one Five unseen, the Six of Spades is expendable. If the card gods give us the case Five – then they give us the case Five. I’m not sure why poker players use the term “case five” but I digress.

My recommended move sequence is: ea,ef,eh,ih,ie,he,hi,fi,df,ad.

And sure enough we do get a Nine – so now I can sleep with a clear conscience even if we do manage to lose the game!

It is now time to deal the final row of cards, but I will wait till tomorrow – for no other reason than to build up the suspense 😊