Unfinished Business: Solitaire Edition

When I was evacuated from Senegal in March, there were still quite a lot of things I wanted to do before returning to the US. In addition to my work and spending with time my host family, I had a few personal projects that I was working on. I had a list of books that I wanted to get through before my service was over, a sewing project, some biking goals, and a project born out of my curiosity about winning percentages in various forms of solitaire. 

During my down time for the first 9 months of my service, I either read a book, napped, called another volunteer, listened to music, or listened to a podcast. Those were just about the only forms of entertainment I had in my hut for the hot afternoons. Then, one day, I "discovered" a "new" form of entertainment: solitaire! After just a few days of playing, I decided to make a project out of this and record how many games I won or lost each day on my calendar. Then, after playing 100 games or so I would have a general idea of what my winning percentage was. I decided to record my wins and losses for three types of solitaire: Klondike, Freecell, and "Rob" solitaire. I will present the win-loss records then explain the rules and my analysis for each game.

Klondike (aka Yukon, "regular" solitaire) 

This is the kind of solitaire that most people know from playing on the computer. Seven piles of cards on the table, red-black-red-black, stack up each suit A through K above the piles, etc. There are some variations in rules, so I will illuminate which rules I chose to play by. I flipped 3 cards from the deck at a time and allowed unlimited runs through the deck. A game usually takes 5-15 minutes, depending on how the cards fall.

After playing 122 games of Klondike solitaire, I have concluded that luck played the largest role in whether I won or lost a given game. The deal is far more important than the choices that the player makes while playing. A beginner "strategy" for Klondike solitaire might be immediately playing every card that is possible to play. While I found a few things to add to this style of play, there are not very many decisions that the player can make throughout the game. The most important strategy I found to increase the probability of winning is to count how many cards I play each time through the deck to ensure that each cycle shows me new cards. Cards from the start of the deck are generally the most important to play because they will have the greatest downstream impact on which cards appear during the next flip through the deck. This sometimes requires not playing certain cards when it is possible to do so.

Though there are some subtle strategies, the player does not have to make these strategic decisions very often. Most decisions in Klondike are fairly obvious: play the card or do not play the card. I played a total of 122 games of Klondike solitaire, which seems like a reasonable number to get an accurate winning percentage from. My winning percentage improved significantly after September 2019. This could be statistical variation, but I think that this first month of focused play allowed me to hone my strategy. My percentage was fairly consistent (make sure to look at the number of total games played each month to not get fooled by the 100% month) over all of the other months I played. Overall, a good version of solitaire, but not great. Not enough strategy to make the game interesting if you are looking for a challenge.

Freecell

This version of solitaire is also a classic from the old Windows solitaire set, but not as widely played as Klondike. In Freecell, all 52 cards are laid out face up in seven columns. Four columns have eight cards and four have seven cards. The player has the same objective as in Klondike: to stack each suit in order from A-K. The player stacks cards red-black-red-black just like Klondike, but one major difference is that all of the cards are face-up at the start of the game. Cards can be moved one at a time directly on top of another card or to one of the four free cells. When the four free cells are full and there are no more possible moves, the player loses. A game takes around 10-15 minutes.

In theory, virtually every game of Freecell is winnable. There are on the order of 10^64 possible games, of which according to Wikipedia approximately 99.999% are solvable. I did not undo any of my moves once I had made them, so it is almost surely my fault (not bad luck of the cards) that I lost 4 games out of the 64 I played. Some deals are definitely more difficult to solve than others, and I would like to think that the games I lost were on the harder end.

Freecell is a fun puzzle, but once I got the hang of the patterns in the game it became pretty easy to win. Occasionally I unexpectedly lose a game by making an early mistake and filling up the free cells too fast, but generally I am able to look ahead far enough to see that I will not get stuck. The ease of winning changed my mindset from trying to solve a difficult puzzle into trying not to lose a relatively easy puzzle. This change in mindset did not encourage me to continue playing endlessly; winning did not deliver much satisfaction, but losing was disheartening. Freecell is a good game to play every now and then, but unless my goal is to build up a huge streak of wins, I will probably not play this many games again at one time.

Rob Solitaire

I do not know the actual name of this type of solitaire, so I have named it after the family friend, Rob, who taught it to my dad and me over a decade ago. Cards are dealt face up in four rows of thirteen. The aces are then removed, leaving four blank spots. The objective is to line up each suit in order left-to-right from 2-K in the four rows, leaving all four blank spots at the far right end of the area. 

A card can only be moved directly to the right of the card one lower than it in the same suit. For example, if there is a blank spot to the right of the 5H, the 6H can be moved from its current position (regardless of where it lies on the board) to occupy the blank space. This will open up a new vacancy were the 6H was residing. If the 8S is to the left of this new blank space, the 9S can be moved into the vacancy. If the new blank space opened up by the move of the 9S is to the right of a K of any suit, nothing can be moved into that space because no card in this game is one higher than a K. If a blank space is opened up on the left-most column, any 2 can be moved to fill the space. Once a 2 is in place in the left column, it must stay there for the remainder of the game. When no more moves are possible (all four blank spaces end up to the right of kings), any cards that are not permanently in place are gathered up. Any 2 in the leftmost column and any cards in the correct order to the right of it are left in place. For example, if the first row is 2D 3D 4D 5D 8S 2C 8D 10S... the 2-5 would be kept in place while all other cards would be gathered into the deck. Even thought the 8D is in the "correct" position, it is not preceded by the 6D and 7D. The aces are added to the deck and cards are dealt again to fill out the four rows of thirteen. This process is repeated one more time for a total of three "deals." If all cards are not in perfect order at the end of the third deal, the player loses. A game takes 30-60 minutes, depending on how much time is spent deliberating all possible combinations of moves.

This game is the pinnacle of solitaires. It is difficult, has multiple possible strategies, and requires looking far ahead into combinations of potential moves. The four open spaces on the board mean that there are up to four potential moves that could be made at any time; after making a move, there are again up to four potential moves. The order in which the player makes moves is absolutely critical because the available moves change as the cards shift. If the player is not paying attention, he can lose the chance to make a helpful move. I have made this mistake many times, prompting me to study the possible sequences of moves even longer during the next game. Choosing which 2 to put into an empty space in the left column is also very important. Not only does the new blank space opened up by moving the 2 need to be considered, but the potential to place its respective 3 and 4 (and 5 and 6...). With a multitude of decisions to make, all of which will affect future decisions, this version of solitaire is both the most engaging and the most fun.

I won 13 out of 77 games over my time in Senegal. As with Klondike, my winning percentage improved significantly after the first 1-2 months of playing. My strategies became more sound and I became more adept at seeing exactly what I needed to look ahead for when calculating possible moves. My win percentage was such that I was encouraged when I won but not discouraged when I lost. I have no idea what percentage of deals are winnable and what percentage are not, but there are certainly many deals that cannot be won. As all cards are face-up and there are a limited number of moves, a computer could in theory calculate the best possible sequence of moves for any given deal. This is of course impossible for a human, but the challenge of trying to do so as best I can is worth the mental effort that it takes. If you are looking to get into playing more solitaire, I highly recommend Rob solitaire.

Conclusion

This project was born out of a curiosity and a copious number of hot afternoon hours. As fun as it was to do this experiment with solitaire, I will not do it again. The goal of solitaire for me is to have an engaging game to play when I have a little time to fill. I still of course enjoy playing a few games of solitaire now and then, but the game has its limits. Is it healthier than looking at my phone? Almost surely. Is it engaging my brain more than reading? Probably not. Regardless of its level of brain engagement, it will always be a great way to pass some time.

tl;dr: In addition to reading lots of books in Senegal, I played lots of solitaire.