In this hand I wanna set the task of winning a game with undo. Normally I would view undoing moves as a cardinal sin – equivalent to Mark Goodliffe’s infamous bifurcation strategy when live-solving Sudoku. but I will allow myself this luxury for an important reason: I needed undo to get my paper published when proving that a certain Spider Solitaire was biased (or at least there was good reason to believe so). Therefore, the U-bomb will not be considered a rude four-letter word and there will be no attempt to encrypt it with a rot-13 cypher.
Our goal is to win the following deal with the luxury of undo. I will not attempt to optimise my score. Also, there will be no cheevo considerations. Note that Microsoft Windows does not offer the player of explicitly restarting a hand: the best we can do is repeatedly press undo until we reach the start (Some folk have complained about this, but I have seen much worse bugs from other servers. Hence, I will avoid the Microsoft-bashing bandwagon for now). At least Microsoft allows undo of every move, including removing a suit or dealing a new row. Other programs may be less luxurious in that regard.
You may have recognised this deal from my previous blog posts. I deliberately did this since a random deal should be easily won with the undo superpower – but since I lost rather badly without undo I would expect this particular deal would not be a walkover.
When playing with undo I assume we have the luxury of card-tracking (this is equivalent to tile-tracking for serious Scrabble players). A card-tracking sheet will indicate the identity of known cards in the starting position. This would look something like the following:
I will use four different colours green/blue/red/black for C/D/H/S respectively. This colour scheme is often used in poker.
SANITY CHECK: the cards in the first four columns are all different suits. If this colour scheme is inconvenient (e.g. for people with red-green colour blindness) please let me know in the comments!
We will start with a warm-up question: 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?
NOTE: For purposes of this exercise, we will pretend we have conveniently forgotten about my previous blog posts. This means e.g. the answer is not X, where X is the number of face-up cards when I conceded the game in my previous post.
Edifying Thoughts of a Spider Solitaire Addict 
Using “undo” is totally new to me, so this will be interesting. Back in the 1970s, when I played Spider with real cards, I experimented once or twice with just dealing all the face-down cards face-up (careful not to honor any in-suit sequences). My conclusion then was that there was just too much information for my limited brain to process. I didn’t even get to inspecting the cards in the deals. If the game is in fact unwinnable, this is more information than you could get with Undo, but it still doesn’t affect the outcome. I should think that if playing with “Undo” is an accepted and popular thing, one of the Spider platforms should simply give you a mode to do this — tell you the identities of all the cards, so you can do the same logical analysis without tedious use of that Z key. Does that sound right to you, the reader(s) of this blog? That they are equivalent?
You as Spider GM could also just do this yourself. Deal a hand with real cards and transfer the values into a spreadsheet. Five rows for the hidden cards, one for the initial cards that show, and five rows for the redeals. Of course, without a spider program it would be tedious to show the different steps as the game progresses.
Back in the 1970s I also experimented with, say, having twelve piles instead of ten, to make the game easier. With real cards, there are far fewer limits on how to arrange the game, of course.
The simple answer to the warm-up question seems to be “6”. The two kings, the 3 and the 6 don’t have any place to move to, but the other six cards (10s, Js, Q) all have something to receive them. Because of Undo we can move all three tens even though there are only two jacks, and similarly both jacks even though there is only one queen. There could be aces under all 6 of those cards, in which case there would be no further turnovers from any of them beyond the one card.
If I was struggling to extend the problem, I could take this to include the fact that we have five more deals to make. Could those deals guarantee any other turnovers? I am almost positive the answer is they do not and the same “6” is the answer since it shouldn’t be hard to arrange the deals so that none of them allow moving a single card. When we see this “in the wild” it’s typically because there are all A, 3, 5, 7, 9 in one deal, all 2, 4, 6, 8 in the next, etc. But since we stack the deck completely, there should be no problem. For instance, if there are indeed only aces under the 6 guaranteed turnovers and the first deal is the 8 8s and two kings, no further turnovers are possible that round.
So I take the simple answer to be the right answer: six.
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Hi Bart – (FYI) I’ve just found out Microsoft Spider Solitaire allows the player the option of single-click to move cards (goto Settings) 🙂
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Yay! Thanks so much for the tip. I also figured out how to navigate back to a game from the desktop in just 2 or 3 clicks. I could see how to turn the timer off, but not the score. I can live with that. Somehow my “notify me of new comments” thing didn’t work on this, so I’m just seeing the other comments on this thread now.
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I now have played six games with this new program. I have won four! 66% wins? This is notably better than what I did with either of the earlier programs: the Tree Card Games (TCG) version you proved was biased (26 out of 137 won), the one I’ve been using recently, and the version shipped with Windows XP, which is the one I have used most. (368 out of 1134 games won, over 10 years on my home machine — no, I’m not an addict, though not exactly a casual player either). Six games is a small sample size, almost certainly not statistically significantly different from the other results. I imagine the lower win percentage on the TCG version might be partly due to bias, but more likely to my being stupider and less motivated as I get older.
It’s interesting that the interpretation of “move cards with a single click” is different in the TCG version and the Microsoft version. In TCG, when you click on a card, its top priority is to make it an in-suit move, the next priority is a legal move onto a pile, and as a last resort it will put it in a space. Each priority is evaluated left to right for the first match. Microsoft also works from left to right, but it will put a card in a space even if there is a legal receiving rank in a pile to the right of that. I haven’t mapped it out completely. On that difference, I like TCG better.
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Now it’s gone up to 8 wins out of 10 games. Not using Undo. I don’t recall the details of your proof about bias. But it sure looks to me like there is some bias in the Microsoft version. Encouraging new players to get them hooked on their gaming collection? Might be difficult to detect/prove if it only applies to new players.
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I wish to reply to Esteemed Scholar Bart and his going 8 ‘n 2 in his latest playing. Sans ZKey
Is this the Microsoft Solitaire Collection? If so, does it have four levels in the Four Suit Division? Expert, Master, Grandmaster, and Random? Lots of ads and the occasional request for saleable data, in typical MS fashion? Of course you can opt out of the ads for a fee; we use to call that extortion.
I will proceed as if the answers are yes.
I wonder if we are playing the same version. It appears that Master T is using the Random Level on this Blog.
This is where I have been playing for the past months, also Sans ZKey. I just got finished with game 200, 50 in in each category. I play 25 games at each level then move to the next. So I have made two loops. My win percentages by level, in order are 64% 26% 8% 24%
I totally concur that MS has stacked a lot of easy games in the Expert Level. And a lot of hard games in the Grandmaster Level.
The expert Level is where I was Playing when I made the comment it was too easy and I was fearful of developing bad habits.
And I think that one of my comments to myself sums up Grandmaster perfectly: “another absolute disaster…at least they don’t take long to play”
Anyhoo, I hope we are playing the same game and that we will continue to post our status / progress from time to time.
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Esteemed Scholar B your idea of dealing out all 104 cards face up and not using the Z Key leaves me terrified. You should collaborate with Steven King. I see myself sitting, staring at this for weeks and weeks before being able to precede, a film of dust coating my bald head.
I can see perhaps 10 moves into the future with accuracy. I believe Master T can easily do twice that. But this would take the ability to see 100 or more moves ahead. TMI – Too Much Information.
But I like it !!!
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I wasn’t trying to suggest not using the Z key and figuring it all out in advance. I’ve never tried using the Z key in earnest, yet. I imagine I would use Z a lot even if all the cards were exposed. You can always ignore the extra information (easier said than done, often). But it just gives you an opportunity sometimes to look ahead and say, “There’s nothing good under that pile anyway”. I mean, if in playing you ever get to a point where you say, “I want to see what’s under that card, let me see how to do it”, you can skip that step, and go on to the next part of your plan (or trial and error, or whatever).
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Well I was hoping that my welcome back party would be filled with brilliance but instead I first must confess my limitations at recollecting and then admit that I am confused.
Master T wishes me to forget a previous post. No problem, Sir, I am a fast study at forgetting things. And I am getting better at it as I age. Formerly when I discovered myself standing in the middle of the kitchen and not knowing why I was there I could return to the place I was before materializing amongst the pots and pans and then remember why I went to the Kitchen. Now I am having trouble remembering where I was prior to my trip into the unknown.
But I digress. Forget? Mission Accomplished!
Now my confusion is in our first homework assignment.
“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?”
Isn’t the number of guaranteed turnovers plus ten the same as the minimum number of face-up cards we are guaranteed?
I sense a trap but cannot find one. Or maybe I am not seeing what I am looking at?
We can move the Queen, one Jack and two of the tens. A total of four discoveries. I don’t see how using the zedkey or walking the dog between moves changes that. My answer is 14, we are guaranteed to be looking at a minimum of 14 cards.
Now, the number of cards we can play peek-a-boo with is greater by use of the zedkey, (zeekey for any fellow Schistocerca Americanas reading). We can look under the Queen, Both Jacks and all three tens for a total of six new entries on our CheeterSheeter.
As a veteran of two suit play-til-you-puke I can say that this can become a tree that grows branches very quickly, especially if we can create a void ( or even two voids, YIKES ) early in the game. In my two suit days I did not use a CheeterSheeter due to a set of self imposed rules: I would try for a win straight up, and upon failure regress via Ctrl+Z. Sometimes a short go-back of only one or two cards was all that was needed, sometimes the hand would stretch out for many sessions over many days. Eventually I could always win those games that offered at lest one move on the final draw.
Poo, I’ve digressed again.
I see there is one comment posted ahead of me, perhaps Esteemed Scholar B, so I will post this and then read the other.
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Thank you both for your prompt reply. Six cards is of course “correct” – but I would also have accepted the answer of 56 since you can deal 5 rows from the stock and then undo 5 times. This question was perhaps too easy, but I did say it was a warm-up 🙂
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Master T, I knew I was overlooking something totally obvious: just crank out the next 5 draws and record 50 new entries on our CheeterSheeter, then Z Key them back to their holding positions. After that we look at what the Queen et al are sitting on. I now think 56 is indeed the correct answer. Are we going to continue thusly?
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