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).

5 thoughts on “Game Off (13 February 2021)

  1. Really interesting!

    Some quick notes.. more to follow.

    You say the “Game over” doesn’t let you see the deal, but it actually does let you see 7 of the cards — they are there in plain view on the grayed-out board. The others are under the message box. And there are no legal moves involving those 7, meaning it is consistent with your first hypothesis.

    I followed your set of moves, but it’s not complete. Somehow the jack of hearts in column 2 moved, but there is no “b” anywhere in your list of moves. I can at least analyze your final state, which must be more reliable than your list of moves, and it’s good enough.

    It’s nice you were able to have done stuff with column 1 and still leave 4 atomic piles. You’ve done good cleaning up. However, you have 3s in two of those atomic piles. There is only one 4 left undealt, so your chances of regaining a space — or 2 spaces — are much reduced. If we can get 2 spaces and have the nearly-complete club suit to use as “lubricant”, amazing things are possible. Are they likely? I don’t know. But over the years I have tended more and more to take a “wait and see” attitude — there are things you can do right now, which are tempting because you can see them, but maybe more things you can do later if you wait. Earlier I took “wait and see” and you had a more direct approach, and I could immediately see that yours was better. I think “wait and see” is more appealing later in the game.

    Your analysis here could very well be better. Maybe all the folks with a black belt in “Supaidero” would agree. Mine is dramatically different. But my hunch is still that it’s better.

    I absolutely hate the “game over” message. I hate it with a passion. It does show up in my online version sometimes. I feel I can figure out when the game is lost for myself, thanks. I don’t need it to tell me the bad news. If they HAVE to make use of their clever AI, they could put a little tiny note off to the side somewhere saying roughly, “our AI thinks you can no longer win” but let you keep trying. You suggest that the Microsoft AI is even more aggressive than my program’s. You can easily imagine a good AI sometimes being able to tell you you’ve lost well before you’ve made your 5th deal! And that’s surely no fun!

    More notes to follow, I’m sure.


  2. Second (and last) set of comments on this:

    So, I did two computer simulations. It turns out that with the unknown cards we had, dealing 10, the chances are 1.5 out of 1000 that we would fail — .15 percent. Pretty darn low. A number that low makes you look out for a bug. But I looked pretty hard. The other possibility is a bug in Microsoft’s program, but I guess that’s unlikely. But did I see somewhere a setting where you can call for better or worse luck?

    However, as noted before, I spotted 7 gray cards of the final deal that we can see. Given those cards, the chances that the other 3 with those 7 will allow no move are 9.5%. So it’s still not likely that we’d get no literal moves, but at least at a reasonable level. I did NOT check for a card landing on an in-suit match with the card above, but that’s quite rare.

    Further thoughts on the difference in grand plans. I don’t think mine has much of an advantage in retrieving one space, but I think it has a big advantage in retrieving TWO spaces. After shuffling things around, I’m very likely to be able to put that ace back on one of the available 2s. The “breathing room” of your plan seems notably less. Your plan moves a 3 from column 1 into the space, irreversibly. You get a bit of cleanup. Mine moves an ace in instead, with two 2s preserved to get it back.

    It’s possible that counting moves would favor your choice — I can’t say.

    It also occurred to me that the decision to remove the clubs or not is independent of what we choose to put in the space.

    “Can you compute all the possible game states given the screen dump above?”
    If we do anything beyond a superficial analysis, this is a LOT of work, isn’t it?

    “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.”

    That confuses me. I see those two aces in my grayed cards, but… if you saw those you wouldn’t say “we didn’t even get a chance to examine what the last ten cards were”, would you? Since we can see 7 of them?

    Footnote: You had said that no literal moves comes from all even or all odd cards, but it can also come with gaps of 3 or 4. As part of my debugging I printed out some failure cases (this is 0-based, so ace is 0 and king is 12).

    11 9 4 1 1 9 11 6 9 9
    9 0 9 9 11 3 5 9 0 11
    9 0 5 5 9 3 0 5 11 9
    11 9 9 1 1 6 9 3 9 6
    6 11 1 6 11 4 9 9 1 9
    9 9 11 9 5 1 11 1 9 5
    11 9 11 0 9 4 0 6 6 9
    11 11 0 5 9 5 0 3 0 9
    5 9 11 9 0 0 9 0 5 5


    1. Hi Bart,

      Yes the noble Spider GM has goofed re the Jack of Hearts in column 2. I actually realised my error, but cut-n-pasted the wrong thing during the final editing phase. Good thing I screen-dumped the final state before dealing the last row! Actually I never claimed my option was better than yours. The game is sufficiently complex such that even an expert cannot definitely claim that one move is better than another.

      I also agree the game over message stinks. The vast majority of losses occur by resignation, not when there are no legal moves. This consideration alone implies the message should be scrapped. Q.E.D.

      For your second comment: yes, Microsoft gives you a setting where you can ask for better or worse “luck” or difficulty. I addressed this in an earlier post (“choose your difficulty”). For what it’s worth, the last ten cards were AT6TQT64TA.

      Re your footnote, you correctly point out no legal moves can occur without “all odds or all evens”. That’s why I specifically said the last ten cards BE LIKE all odds or all evens 😊

      Finally, well done to you and George for excellent contributions throughout the game. Next challenge of course is to get more people reading this blog!


  3. Well that was fun, we be oh-n-won.

    Many thanks to Master T and Esteemed Scholar B for sharing their ideas.

    I think that this is an excellent venue to improve one’s W-L record, especially if used as I have. I do not read other’s comments before posting. This is sometimes difficult because it exposes you to saying something incredibly incorrect, but those are the lessons most remembered and not repeated. Also I do all the moves in cerebral, write them down and then post them……afterwards I play them out on my Ancient Excel CheeterSheeter to see if the sequence was possible.

    I encourage any lurkers to join the conversation in the next hand.

    Master T one thing I like is that you always let at least four days pass before continuing. I could under stand if this is annoying to most people but it helps me as I plod along behind the quick and clear thinkers.

    Esteemed Scholar B I like your vision of bringing this into a realm parallel to Duplicate Bridge: Multiple players playing the exact same hand at the same time. Only then could we appraise as to where we are at in the hierarchy of the peer group.

    As a snapshot on where I am in all this let me share that I think my game play should be up to about 200 hands now. I lost all data on my play in “Win7 games for Win10” version of SS in the recent ‘puter meltdown. But the reload of Win10 brought me the MS Solitaire Collection which I think Master T is using. I decided to play 25 hands at each level and record results. At the Expert level I went 16-8 and found many hands so easy that I feared developing bad habits. I am working on the Master level.

    And lastly the main thing that brought me here is the play san ZeeKee.


  4. Thanks for your comments. Personally I think Win10 MS Solitaire Collection ticks a large number of boxes. Players can aim for different goals such as (i) improving their play on difficult hands (ii) estimating their win rate with random deals or even (iii) perfecting technique on easy hands e.g. they may expect to beat 2-suit random 100% of the time, not 98% or 99% etc.


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