Klondike Solitaire with a Twist: A New Approach to an Old Game
Origins
The game of Solitaire, also known as Patience, has an indeterminate origin. The entry for “Solitaire” on the Britannica website suggests that a group of card solitaire games originated in the Baltic region of Europe, possibly as a form of fortune telling, sometime in the late-18th century.1
The first recorded mention of solitaire comes from France, as the French name for the game — Patience — implies. Spreading through Europe and the UK, the game of solitaire had many, perhaps hundreds of variants.
The North American version of solitaire that is best know is called Klondike, or Klondike Solitaire, thought to have originated in the Klondike region of Canada during the Klondike Gold Rush (1896–1899). This, for me, has always conjured up an image of solitary prospectors stuck in primitive miner’s cabins during fierce winters, playing solitaire in what little light was available, but the sources suggest otherwise. The game seems more likely to have evolved as a gambling game to be played in the gambling establishments in Dawson City, Yukon. It was also popular in the gambling spots in Skagway, Alaska, where fortune hunters arrived from and departed for the gold fields.2
As a parlour card game, Klondike has been a pastime for thousands, possibly millions, of card-playing North Americans.
But Klondike Solitaire received its greatest boost in popularity when Microsoft included it in Windows 3.0 (released in May, 1990) as a way to train users new to graphical user interfaces how to drag and drop selected items with a mouse. The impact of this was significant because it became one of the most-used Windows programs and it spread the game as a pastime to millions of computer users.3
Later, it generated another gold rush of sorts when software developers vied for creating the most popular Solitaire app for the iPad, iPhone, and other mobile devices. Computer versions of Solitaire, along with Sudoku, crossword puzzles, jigsaw puzzles, and other such games remain highly popular with users. I find solace in Solitaire when sitting in the waiting room for a medical appointment and the doctor is running far behind schedule. (The Solitaire app I use most of the time is Real Solitaire, produced by EdgeRift, Inc. because I like its design and interface. Microsoft Solitaire is also excellent.)
The Twist
The variant of Solitaire I always play is 3-card Klondike. I find it satisfactorily challenging, but I found I seldom won, despite the source that that puts the upward odds of winning at 3-card Klondike at 82%.4 However, a different study came up with the more realistic odds of 43% of winning.5 By this standard you should win at a nearly 50% rate.
The problem is that this just isn’t so. I may not be a great solitaire player, but I’m not bad, and my actual winning percentage was much lower (6%). This is so much lower that I came up with a twist to make the game more enjoyable. I decided to set a winning number (according to the traditional scoring rules) based on points. After some experimentation, I found what, for me, was the Goldilocks number: 150.
So, if my score reaches 150, that’s a win. If I attain what is a traditional win, I call that a “sweep.”
A simple twist, but it made the game much more equitable.
I’ve now played 3-card Klondike with this twist for a few years and it occurred to me that it would be interesting to keep track of my scores over several weeks and then take a look at the numbers.
Because none of my Solitaire apps is set up to record each game’s score, I used QuickNotes on my iPad to manually enter each game’s score in a comma-separated file. Every Sunday I would transfer this file to my laptop, then erase the contents of QuickNotes to prepare for the next week’s numbers. On my laptop I wrote a Bash script to concatenate the weekly files into a long working dataset that I could then analyze with a few Python scripts.
For this experiment I collected 14 weeks of game scores, from October 1st to December 31st, 2023.
The Results
First, the overall stats:
Items in full_list: 5854
Items in short_list: 5529
Items in sweep_list: 325
Items in win_list: 2553
Win percentage: 49 %
Sweep percentage: 6 %
In 14 weeks of playing Solitaire, I played 5854 games and recorded their scores. Of those 325 games resulted in “sweeps,” which is “wins” in traditional scoring. This means that, in traditional scoring, I won 6% of my games. No wonder I needed a new target for winning. When I add all my new “win” stats — 150 or better–I have a 49% chance of winning, though as we shall see, this is a bit misleading due to the high scores of a sweep.
The numbers came out like this:
{0: 14, 5: 24, 10: 48, 15: 41, 20: 60, 25: 64, 30: 70, 35: 77, 40: 96, 45: 101, 50: 110, 55: 119, 60: 140, 65: 133, 70: 145, 75: 152, 80: 163, 85: 137, 90: 149, 95: 146, 100: 153, 105: 144, 110: 141, 115: 159, 120: 132, 125: 121, 130: 124, 135: 110, 140: 113, 145: 115, 150: 134, 155: 170, 160: 147, 165: 114, 170: 131, 175: 96, 180: 91, 185: 74, 190: 68, 195: 97, 200: 79, 205: 72, 210: 57, 215: 60, 220: 61, 225: 59, 230: 52, 235: 64, 240: 36, 245: 62, 250: 32, 255: 38, 260: 32, 265: 23, 270: 20, 275: 37, 280: 22, 285: 21, 290: 20, 295: 17, 300: 27, 305: 15, 310: 18, 315: 19, 320: 15, 325: 14, 330: 13, 335: 8, 340: 10, 345: 10, 350: 11, 355: 8, 360: 5, 365: 10, 370: 4, 375: 8, 380: 3, 385: 9, 390: 2, 395: 4, 405: 3, 410: 5, 415: 2, 420: 2, 425: 1, 430: 3, 435: 3, 440: 3, 470: 1, 485: 2, 490: 1, 495: 1, 505: 1, 550: 1, 615: 1, 635: 1, 650: 4, 655: 1, 660: 3, 665: 3, 670: 6, 675: 12, 680: 14, 685: 17, 690: 31, 695: 47, 700: 49, 705: 47, 710: 38, 715: 23, 720: 15, 725: 2, 730: 7, 735: 4}
I got totally skunked (score: 0) 14 times, I scored 5 points 24 times, and I scored 10 points 48 times.
When the numbers are sorted by frequency, they look like this:
{425: 1, 470: 1, 490: 1, 495: 1, 505: 1, 550: 1, 615: 1, 635: 1, 655: 1, 390: 2, 415: 2, 420: 2, 485: 2, 725: 2, 380: 3, 405: 3, 430: 3, 435: 3, 440: 3, 660: 3, 665: 3, 370: 4, 395: 4, 650: 4, 735: 4, 360: 5, 410: 5, 670: 6, 730: 7, 335: 8, 355: 8, 375: 8, 385: 9, 340: 10, 345: 10, 365: 10, 350: 11, 675: 12, 330: 13, 0: 14, 325: 14, 680: 14, 305: 15, 320: 15, 720: 15, 295: 17, 685: 17, 310: 18, 315: 19, 270: 20, 290: 20, 285: 21, 280: 22, 265: 23, 715: 23, 5: 24, 300: 27, 690: 31, 250: 32, 260: 32, 240: 36, 275: 37, 255: 38, 710: 38, 15: 41, 695: 47, 705: 47, 10: 48, 700: 49, 230: 52, 210: 57, 225: 59, 20: 60, 215: 60, 220: 61, 245: 62, 25: 64, 235: 64, 190: 68, 30: 70, 205: 72, 185: 74, 35: 77, 200: 79, 180: 91, 40: 96, 175: 96, 195: 97, 45: 101, 50: 110, 135: 110, 140: 113, 165: 114, 145: 115, 55: 119, 125: 121, 130: 124, 170: 131, 120: 132, 65: 133, 150: 134, 85: 137, 60: 140, 110: 141, 105: 144, 70: 145, 95: 146, 160: 147, 90: 149, 75: 152, 100: 153, 115: 159, 80: 163, 155: 170}
Here’s what a histogram of all the scores look like in terms of their frequency:
This clearly shows that the stats are imbalanced by the sweep scores which which have a much greater value than non-sweep scores. If we remove the sweeps from the data, the histogram looks like this:
You can see that the scores are clustered around the 150 mark. In terms of 150-point and above wins, excluding the rarer sweeps, the percentage of winning drops to 43%. That makes my choice of “150” as a win just right for me. You might choose to use a slightly higher score, like “200”.
More Stats
Matching Sequences
One of the oddities is that as you play, you sometimes get the same score twice or even three times in a row. It feels almost spooky, especially when the game play is very different but leads to the same score as before. I wrote another Python script to see how often this happened and if any numbers dominated.
{10: ‘o’, 25: ‘o’, 110: ‘o’, 140: ‘o’, 145: ‘o’, 170: ‘o’, 180: ‘o’, 190: ‘o’, 200: ‘o’, 210: ‘o’, 220: ‘o’, 235: ‘o’, 300: ‘o’, 20: ‘oo’, 55: ‘o|o’, 70: ‘o|o’, 85: ‘o|o’, 90: ‘o|o’, 120: ‘o|o’, 125: ‘o|o’, 135: ‘o|o’, 160: ‘o|o’, 205: ‘o|o’, 710: ‘o|o’, 115: ‘o|oo|o|o’, 40: ‘o|o|o’, 65: ‘o|o|o’, 80: ‘o|o|o’, 95: ‘o|o|o’, 100: ‘o|o|o’, 130: ‘o|o|o’, 175: ‘o|o|o’, 45: ‘o|o|o|o’, 60: ‘o|o|o|o’, 75: ‘o|o|o|o’, 150: ‘o|o|o|o|o’, 165: ‘o|o|o|o|o’, 195: ‘o|o|o|o|o|o’, 105: ‘o|o|o|o|o|o|o’, 155: ‘o|o|o|o|o|o|o’}
An “o” by itself indicates a pair of sequences back to back. A double “o” indicates where this happened three times in a row. The vertical bars (pipes) between the “o’s” indicate that it happened again, but later, in another sequence. The only triples I got were the numbers “20” and “115”. The others were all pairs, but some of the pairs happened more frequently. The number “155” paired seven times, with the number “105” happening six times. If I were superstitious I might specify those numbers in a lottery ticket, but I won’t. I know the odds are against me.
Winning Streaks and Losing Streaks
Remembering that “150” and above is a win, and “149” and down is a loss, it’s instructive to compare winning streaks and losing streaks. My definition of winning and losing streaks is the same as for many sports: “3”. Three or more wins in a row is a winning streak. Three or more losses in a row is a losing streak.
This in some ways is the heart of gambling. When you’re on a roll, you feel you can score anything. Then comes the reality.
The Winning Streaks look like this:
While the Losing Streaks look like this:
As the numbers show, I once had a 10-game winning streak, but I also once had a 16-game losing streak.
The moral of these particular stats are that even when you’re on a roll, you shouldn’t feel too confident. Losing streaks solidly outnumber winning streaks.
Bottom Line
I enjoy Solitaire. I use the game partly the way some people finger worry beads: it gives me a mental break from writing and other mental activities and I find it calming. By setting “150” as a win, the game has more immediacy for me.
Try it out yourself, if this interests you, and let me know how you fare. See if you, too, find the game more enjoyable with a better chance to win.
2 Gamblers and Dreamers: Women, Men, and Community in the Klondike, UBC Press
3 “The History of Solitaire”, Solitaire-Palace.com
5 Ibid.
