#019 - Solitaire Checker Puzzle: Digital Peg Solitaire

Release Date: June 25, 1973

Platform: Mainframe

Genre: Puzzle

Developer(s): David H. Ahl

Publisher(s): Digital Equipment Corporation

Solitaire Checker Puzzle, or One Check as it's called in the 1978 edition of BASIC Computer Games, actually originates from the original edition of that very same book. It was created by the book's author, David Ahl. I'm going to refer to it as One Check through this article simply because it's less characters I have to type.

I'm not sure where Ahl's idea for the game came from, as there's no information online I can find explaining the origin. His writeup for the game in the book doesn't give much info, either. In fact, it's identical across both editions of the book. 

Apparently playing this game turns you into a wizard.

From what I can observe, the game concept itself bears a lot of resemblance to those peg boards that I used to see around my parents' and grandparents' houses. Peg Solitaire is what it's called. It has the exact same concept of leapfrogging pieces to remove them, only in physical form and with different patterns. My suspicion is that's what Ahl may have been referencing with One Check. This Peg Solitaire rabbit hole goes a lot deeper than you might expect, as we'll soon discover...

Presented for comparison.

The key difference with those, compared to One Check, is that you could leapfrog from any cardinal direction. Left, right, up or down. You can't do that in this game - it only allows diagonal moves, as in regular Checkers. That makes things a bit more tricky. There's a total of 48 checkers on the standard-size Checkers board (64 squares), with the claimed maximum possibility of removing 47 of them. According to Ahl, removing over 40 is a challenge. Challenge accepted.

The game doesn't even bother asking this time - the instructions are slammed right in front of your face straight up. It tells you that each tile of the board is keyed to a number, starting with 1 in the top left and counting up left-to right, top-to-bottom.

No questions asked.

What's great is that you get to see the full 64x64 board, which is represented in binary. 1s represent counters, and 0s represent empty spaces. The board is re-drawn every time you make a move. It's kind of a pain to have to keep scrolling back up to the reference board each time. No way am I memorising the numbers.

The opening state of play.

I managed a respectable 42 counters on my first attempt, which I was fairly pleased with. The strategy I went with was to take all the counters off the border first. What ended up happening is that I cleared out the top-left and bottom-right corners, with all the counters congregating in the opposite corners. Progressing from this point was actually a rather delicate process, with not many moves being available, but all having a significant impact on how the rest of the game would progress. I realised that this might not have been the best strategy to go with.

Nice diagonal symmetry.

Pressing on, I fumbled around, trying to figure things out as I went along. Turns out the strategy you start with makes a huge impact on the rest of the game. I was, at one stage, left with some scattered clumps of counters in the top-right area that I realised I couldn't completely remove. There goes the 47 counter dream for now.

That top right section gave me fits.

I had to make the most of the situation, which resulted in solitary counters spread across the board at the end of the game.

A somewhat disappointing finish.

42's not a bad score, but I'm not fully satisfied with it. Back to the strategy drawing board for this one. I noticed for One Check, that games take much longer to complete than most of the previous games I've played. Part of that, I think, is down to having to constantly reference the numerical board every time I want to make a move. There's also quite a bit of thinking to do. This first game took me about 20 minutes to complete.

So what's my revised strategy? My first thought was to move all the corner pieces. They have no other place to go, so it seemed they were the logical first moves to make. Having done that, I thought that moving in all border pieces from the corners would help further. Turns out I was mistaken on this second point. I ended up with a nice symmetrical pattern, but nothing I could do with it.

Looks nice, but is completely useless.

I tried a few different ideas after this, but the best count I got was 44. This result came from the idea of aiming to take out one corner of counters at a time. I think it was working reasonably well, up until the end where it fell apart.

Best result so far.

I had to take a little step back to reconsider my strategy; reconsider what I actually needed to do to get those 47 counters. I swiftly realised what I needed to do. What needed to be done at endgame was create a situation where you only need two counters to remove the final trail, but one of those two needs to consume the other. Say what you will about the simplistic look of the game - the strategy appears to run deep; it's something I can stick my teeth into, which is a good thing.

I theorised how I could accomplish this "snaking" strategy, as I'm calling it, and came up with a diagram of a theoretical 47 counter situation:

It looks like a random assortment of colours, so allow me to explain what all this means. The yellow squares are the "active" counters. These are the counters being moved. The red squares are the counters the active counters remove. The orange square is where the changeover happens. The first active counter in the top-left moves until it gets to the orange square, then the second active counter takes over, removing the rest of the red counters until it lands on the embossed red square, as the final remaining counter. The lines are there to show the path of travel of the active counters. This probably represents one of a dozen similar scenarios, it just happens to be the one I came up with. Obviously, this is just the endgame - I still have to try and get the game into this scenario, if possible.

So I tried this, and no result. Frustrated at my lack of progress, I decided to do the one very thing that's an unspoken rule of mine: look up a guide. What I discovered truly shocked me: David Ahl's "substantial feat" is actually impossible. 

I also discovered that there's quite a lot of game theory research that's been done on Peg Solitaire over the years. There's far more to it than I realised, and many varieties of boards and setups that are available. A key piece of theory I learned is that there are essentially two types of Solitaire boards: null-class and non null-class. What's the difference between the two? Null-class boards are solvable, while (in most instances), non null-class boards are not. It turns out that the 8x8 board here is not a null-class board, therefore meaning that having a single counter remaining on the board is impossible to achieve. If you want to read more about this, you can get a fuller explanation here.

Unfortunately, that particular site didn't deal with this specific, diagonal setup. There were a few sites that very briefly discussed the diagonal variant of Peg Solitaire, but not with the particular setup, or the detail, that I looking for. Eventually, I came across a page that gave me the exact answers that I was looking for. It calls this variant "8x8 Diagonal Solitaire." It even directly references Ahl's digital rendition! It declares that Ahl's highest tier of 45 - 47 counters is impossible to achieve. The major problem is that the counters will never leave their colour - red stays red, and black stays black, no crossover, meaning that there would have to be at least two counters left. In practice, it actually turns out that the minimum amount of leftover counters is four, for a maximum removable total of 44. I'm actually quite chuffed about that, seeing as I was able to achieve that total without any external assistance. The Zillions of Games site provides a sample solution, which I'll provide in the game video.

Well, this article went in a very different direction to what I was expecting. I found scoring a little bit of a challenge also. It's always tricky with these digital renditions of real-life board games. Do I rate the game based on its source material, or the implementation of it?

Time Played: 2 hours

Difficulty: 6/10 (Challenging)

It requires a lot of thought and planning to get the 44 counters.

Gameplay: 7

I'm somewhat blending the ideas of scoring based off the source, and the implementation thereof. It's a fun game, to be sure, but the implementation has its problems. Constantly having to scroll up and down the screen to reference the number key is a pain.

Controls: 5

Like usual, it's a standard input system. I imagine it could've been a whole lot worse if Ahl chose to use co-ordinates, for example.

Visual: 5

It does what it should. While the formatting is good and all, I'm not going to give brownie points for doing what's expected. That what the 5/10 score is about - doing what's expected, but not going beyond.

Functionality: 5

No issues.

Accessibility: 3

It can be a somewhat intimidating game to learn, but is rewarding once understood. It also helps that, for a text game, it doesn't require a whole lot of reading.

Fun Factor: 8

I found it enjoyable and mentally engaging. If not for the discovery that more than 44 counters was impossible, I'd still be playing, trying to devise new strategies. It really put a damper on my enthusiasm knowing what I now know.

So, Solitaire Checker Puzzle does better than you might think - a score of 33, and a place in the D-tier, just above the original Lunar Lander as the 9th game overall currently. It's a good time, for what it is.

Back to the arcade next time. Going to be racing through space.

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