Game Off (13 February 2021)

Here is the game state from last time

We were in the unhappy position of not being able to turn over any cards despite having one empty column (or more precisely the ability to procure one). At least there is the option of removing clubs.

George suggested the following moves: (dj, fj, ed, ge, ae, ag, aj, jc, jg, jf,)

We can improve that slightly: the Two of Hearts can be placed in column 6 instead of column 5. This allows to built in-suit with the 43 of Diamonds. George is hoping to reveal more cards in column 10 which is a reasonable plan.

Bart gives some detailed analysis but doesn’t offer a precise sequence of moves. He suggests something completely different to George: first it is not necessary to remove the Club suit now, since if we deal the “other” King or Ace of that suit then things might improve. He also wants to shift the Jack of Hearts in column 2 to the KQ of Spades. Since there are four Tens unseen, it is highly advantageous to free the 98 of Spades in preparation of the last round.

I actually want to focus on the left-most column because we have all the Hearts exposed. If we can reach the Four of Hearts from under the King then we will have an excellent chance to clear Hearts. Therefore we don’t need to expose any more cards since we already have what we need (I’m hoping that once we clear Hearts and Clubs, the face-down cards will take care of themselves). Yes, this has the disadvantage of exposing an extra Ace, but I’m willing to take the risk.

My preferred sequence is: dj, fj, gd, ad, eg ae, aj, af, da <deal>

Note that the clever gd saves a move because we want to build in-suit with 32 of Hearts. If the third move was the more obvious gf, we would need an extra move! Now surely this attention to detail deserves to win the game, or there would be no justice…

Before going through the usual routine of computing guaranteed turnovers, in-suit builds, empty columns, removing full suits, making coffee etc, a careful examination of the board state reveals a rather unpleasant message saying that we have lost the game. This one is particularly rude since we didn’t even get a chance to examine what the last ten cards were!

As far as I know, there are three fundamentally different scenarios where the “No More Moves” message occurs:

  • We deal 10 cards and they be like ten odd numbers (counting J/K as 11/13) or ten evens. Unless we get lucky with at least one card falling in-suit then there are literally no legal moves.
  • Our position is hopeless, but we still have some legal (but irrelevant) moves. We know the game is mathematically lost but OCD compels us to make as many in-suit builds as possible. At least the No More Moves message doesn’t come as a surprise.
  • The game is actually not over. I’ve had this happen but can’t remember if Microsoft Windows was the culprit. The game state does look pretty bad, but with some clever manouevering one can actually make progress despite the lack of an empty column. Essentially you are playing the Tower of Hanoi without any free spaces, but you have the right “stepping stones” that achieve the same effect as an empty column. But it is difficult for the software to detect this.

A fun exercise for the reader: recall that we didn’t even get to see what the last 10 cards were. Can you compute all the possible game states given the screen dump above? For instance, we know no column can contain an exposed Two of any suit, otherwise we could shift an Ace in column 1 or 10, and the message would not have appeared. If you’re really obsessed with improving your game, try playing out this position with two physical decks of playing cards and see if we had good winning chances or not.

For ease of reference here is the position before the fateful last round (the Score should be 447 but I had to undo after dealing the last round, since I wasn’t expecting this to happen).

Game on (21 January 2021)

This is the position from last time

We asked the following questions:

  • What is the longest “straight-flush” we can obtain if we weren’t allowed to turn over any more face-down cards? (for instance 7-6-5-4-3-2 of Hearts would be of length six).
  • Can we guarantee three empty columns if we weren’t allowed to turn over any more face-down cards? Obviously these would be columns 2,4,6.
  • What is the minimum number of guaranteed turnovers?
  • What is the minimum number of guaranteed in-suit builds? Of course, if we get enough in-suit builds then completed suits might suddenly materialise by weight of sheer numbers 😉 More often than not, players have to earn them especially at the Four-suit level.

Let’s start with the easy one. Three empty columns is indeed achievable. We can clear columns 4,6 with five moves. We can then shift the Eight of Spades onto the Nine of Hearts and rearrange the 9-J-T-8 onto the Queen of Spades.

Minimum guaranteed turnovers is also easy: just take our three empty columns and then drill down column 3 like a madman.

Now we come to the more difficult question of longest straight flush. I believe there are some “professional” Spider Solitaire programs that do “card tracking” automatically, but the Microsoft Windows version ain’t one of them: Let’s take all four suits and thirteen ranks and record whether it appears face-up at least once in the tableau.

Assuming the noble Spider GM hasn’t goofed, I get the following:

We can immediately tell a run of 12 cards is available in Clubs. Unfortunately the cards are scattered in many columns and I believe it is not possible to obtain a run from King to Deuce, even if we were willing to trash our game state in every way possible. Yes, we get three empty columns, but it will cost two of ‘em just to shift the Eight and Two in column 5.

I can get a run of J-T-9-8-7-6-5-4-3-2 in Clubs, but no better. If you do see a way please give me a heads up 😊

What this does mean is it ain’t necessary to consider other suits. From the tile-tracking above no suit other than Clubs can beat a run of ten, even if we were allowed to yank them from underneath the Kings.

If you’re one of the Awesome People you may remember we had a beautiful run of Clubs much earlier in the game, but for some reason that got scrambled up as we were desperately fishing for our first empty column. Now we have no problems with three empty columns, but the run of clubs is gone. Oh well, them’s the breaks. Perhaps we did not play optimally in previous rounds. That’s water under the bridge if you excuse the numerous cliches.

Finally we look at in-suit builds. An experienced player can tell that column 8 offers many possibilities for  tidying up: 8-9 of Hearts, 8-9 of Diamonds, J-T of Clubs and so on. Column 5 doesn’t offer many in-suit builds. There’s 9-8 of Clubs, but K-Q of Clubs isn’t actually possible. The only real benefit of digging Column 5 is two Victory Points for the longest straight-flush. And there are other ways to achieve VP. For instance, largest army or building lots of cities and settlements – no wait, I’m getting mixed up with Die Siedler von Catan. My bad. In any case we can improve our chances by keeping all options in mind and resist going all-or-nothing on the Clubs.

I won’t compute the maximum number of guaranteed in-suit builds here. If your OCD is worse than mine then you are more than welcome to compute this in your own spare time, but for now let’s focus on winning the game 😉

The observant player may have noticed I did not ask for the best play last time. This is because it took quite a bit of effort to evaluate this game state. Now that we have done some analysis, it is time to decide on the best play.

(I noted that Bart has already thought about the best play from a previous post. The above may prompt him to change his mind … or not)

How would you continue here?