- Pretty Good Solitaire

Odds Are??

Hello all - I've been playing Goodsol games for at least 10 years, and my all time favorite has been Geoffrey. However I've often wondered about the actual mathematical/statistical odds of overall win/loss of a particular game. I know there's a category here to look up a games' winability, but I'm talking about how close to the `real world' are these games. I can honestly say with Geoffrey, I have been so close to 30% but somehow it seems the game turns on me and my % goes slowly down and down and down, then up etc. It feels like the programming has some set limit based on (?) where the overall win/loss record is never allowed to go beyond a certain point.

This all got me thinking about where there are actual statistics that are available that were used to come up with these settings. And having this line of thinking going, it also made me wonder if it was possible within the app to stipulate as a general setting the difficulty level of the solutions, or have programming that allows you to graduate to the next harder level.

Anyway maybe this defeats the simplicity of the solitaire concept. I just wish that someone could tell me why I can't hit 30%...


  • Don't go the conspiracy theory route, enjoy your game play as your ability allows. If you save games, Richard and others can review your losers for possible conversion to wins.

  • edited May 2021

    Thanks for your input Larry. 😊 I totally agree.

    Welcome to our little group/madhouse. You have to be careful about taking statistics posted online as gospel. People who cheat have corrupted them to the degree that some of them are hilarious. Those played in Climb Mode are 100% reliable though. In practically every deal of a game there are numerous moves that you can make, and the permutations of them grows with each move. The butterfly effect. Massive computers have been developed for working out the best moves for Chess which has just 16 pieces. Some of Goodsol's games have as many as 208 cards. A mind-blowing number of possible permutations are possible. Solvers exist that can work out whether any deal of Freecell is winnable or not. It is a relatively simple game with all 52 cards dealt face up. The rules are pretty straightforward too, even then a huge amount of work must have gone into its creation. Despite that, you'd have to input each game number manually to discover the actual winnable percentage. You'd just scratch the surface in a lifetime attempting that.

    By and large, the win rates you see in the rules for each game are just educated guesses. Some are fairly accurate but some are very wide of the mark. People like myself play thousands of games in numerical order. We may play 5000 of one particular game before moving onto another type. Larry and myself are currently approaching 2000 Coronas. Our win rates are honest, but even with teamwork we may let the occasional winnable one slip through.

    Don't fret about your win rate for Geoffrey. It could be 100% accurate. However, before giving up on a particular deal, just post the number here and see if anyone in our group can win it. If we can, we will assist you in doing likewise. I presume that you are aware that you can cherry-pick the deals that you play. As long as you don't make a move you can flick through as many as you like.

    Have fun,


  • Thanks guys - I was myself going to use the `conspiracy' word in my original post but I as expected I got outed on that pretty quickly lol

    I am going to look into that option to cherry-pick the deal. Is that the same as the Game #?

    Amazing what some people will do to `win' or otherwise screw with something just because....

    Thanks again!


  • Welcome to the forum, Dan!

    I can address the internal workings a bit, but you may be disappointed at the answers. 🙂

    >I just wish that someone could tell me why I can't hit 30%...

    Pure coincidence. 🤷‍♂️

    >It feels like the programming has some set limit based on (?) where the overall win/loss record is never allowed to go beyond a certain point.

    It may feel that way, but I can absolutely assure you that is not the case. I could write a dissertation on this topic, but the simple answer is that the human brain is evolved to seek patterns, and as an extension of this, seek extraordinary explanations where simple randomness is at work. (I mean, at a deeper level, this is an inaccurate use of "randomness", and in your example, 30% is just an arbitrary number, but I digress...)

    A related (and, to me, frustrating) inclination is for people to think that random deal numbers make shuffles more random; they don't. From a practical standpoint, playing the deal numbers in order is every bit as random, it just means that (like with the solving groups in this forum) players are playing the same games, so the statistics are comparable. This is why I created Climb Mode (not available on PGS Windows). If we take away the ability to play random game numbers, though (as I did via bug recently), we really hear about it.

    The truth is that it is far easier to simply write an honest game with no deal manipulation, and that's what we have done. There is no code in the program to adjust difficulty of deals based on results nor any other factor. The only deviation, if you might call it that, from the straightforward Goodsol card shuffle is that we use a different shuffle for certain FreeCell games so the deal numbers match the well-studied deals from the game that shipped with Windows.

    As pointed out above, the effort to calculate whether a particular deal is winnable or not is substantial and time-consuming, and the aforementioned ability to select random deals means that there are more than 2.2 TRILLION potential shuffles over the (currently) 1040 games. It would not be vaguely practical to either store expected results nor calculate them on the fly. (If we could calculate results at the rate of 1000/second, which is far beyond our capabilities, it would take more than 70 years to get all the results.)

    Of course, the simple proof of this is that deal #1234 is exactly the same for me as for you, regardless of our statistics. 😉

    >This all got me thinking about where there are actual statistics that are available that were used to come up with these settings.

    Spoiler: prepare for disappointment...

    Thomas chooses the initial winnability percentages when a game is released; I am not sure his exact method but I am confident that "guess" fairly adequately describes it. During beta testing, he gets some feedback from me and other testers and makes adjustments, and again, after the game is out long enough for significant statistics to have been reported, he may adjust them again. The method is not mathematically rigorous; in fact, I am not sure that there is even a clear understanding of what the percentages actually mean. I think that they are intended to be a guideline based on a generally skilled player. (For example, Lower 48 is listed at "80%"; I have rigorously played and won every one of the first 5000 deals, which means absolute winnability is better than 99.9%, but a less determined player could easily be closer to 80%.)

    >And having this line of thinking going, it also made me wonder if it was possible within the app to stipulate as a general setting the difficulty level of the solutions, or have programming that allows you to graduate to the next harder level.

    It is not currently possible to do this, but it is theoretically possible to do so, with the addition of new programming and new constraints to make it achievable. The simplest manifestation of this would be a "winnable" setting that assured that any deal for a particular game was winnable. It would be non-trivial, but possible, to then add calculations to attempt to classify a solution as easy/medium/hard/incredible.

    However, the biggest constraint is that we support more than 1000 games, and while doing these things for a single game is fathomable, generalizing it to support all of the games, many of which have vastly different goals and priorities, would be a huge undertaking. Actually, Thomas and I have had long discussions about this, and we disagree on whether this (a general solution) is even possible at all. From a business perspective, for a tiny company, the question is whether it makes sense to pursue features that directly benefit players (e.g., more games on the Mac Edition) or these intellectually fascinating diversions that, honestly, would not be noticed by most of our players.

    Interestingly, this all ties in together, as if we were able to solve the games, I have an idea of how we could mathematically define the percentages, not only of winning percentage, but also the skill/luck ratio (so, for example, Lower 48 could be 99.9% winnable, 90% skill, say, and 'Medium' rather than 'Easy' because it is difficult to achieve the ultimate percentage).

    Note that I also wrote a commercial backgammon program many, many years ago, and these same issues were much more pronounced there, with players claiming (incorrectly, yet vociferously) that the program cheated. (Same deal, though: it is harder to cheat than play fair, and there is no benefit to the developers to have a program that cheats.)

    I guess I did write a bit of a dissertation. 😀 I hope you have your answers but, obviously, I enjoy this topic, so if you have more questions or want to discuss further, please feel free.

    Gregg 🐵

  • edited May 2021

    My footnote to all of the above would be that almost every time we play any of our games we are entering into virgin territory where no man/woman has gone before. NOT knowing in advance whether it is winnable is what drives me to play them in the first place. We know that some games have previously been won from the input of fellow players in this forum and in Gregg's Climb Mode. Stats appearing online shall we say, do not display the actual deal numbers, and consequently cannot be verified. It takes more than a pinch of salt to accept their integrity, even a truckload on occasion.😊

    Dan ...... By cherry-picking we mean that we can click on new game as often as we like and only actually tackle the best looking of the ones that appear. For example, in Gregory you could look for deals where you already have uncovered aces. No guarantee that such deals would be winnable though because there are face-down cards. It would just tilt the odds a little in your favour. We don't class this as cheating.

  • You could post a screenshot of your statistics for Geoffrey.

  • Wow! Such amazing passion here! THANK YOU ALL for taking the time to address my queries; and not only explain the responses, but provide a significant amount of background and context! It means so much more when someone takes the time to elaborate on the subject. Definitely means a lot more to me now and my understanding of things under the covers is improved immensely.


  • Cheers Dan. 😊

    My favourite Scottish toast is, "Here's tae us. Wha's like us? Nane at a'. And they're a' deid". 😂

  • edited May 2021

    FASCINATING discussion, Gregg! I'm embarrassed to tell this story but YEARS ago I queried of Tom why when I play random deals, I almost always get deals of 6, 7, 8, 9, & 10 digits long and rarely see 1, 2, 3, 4, or 5 digit deals. His very polite reply was something to the effect of, "Because there's more of them". The "you dummy" was implicit.😀

    Btw, how did you & Tom first meet?

  • >Btw, how did you & Tom first meet?

    We were both part of an organization (now defunct) called the Association of Shareware Professionals, so we originally met online. There were relatively few successful game developers in that group. When I first went to an associated conference in 2000 (I think), we met in person, and over drinks in a lounge setting, I distinctly remember telling him, "No offense, but I will soon be your competition" (or words to that effect), which he took in the jovial spirit in which they were offered. (He was in no way worried. 😉)

    Later that year, Microsoft finally released a card game product my company (i.e., Rick Tumanis and I) had helped develop. When I announced it in the ASP newsgroups, Tom replied that he wished he could have artwork like that in his games, and I replied, "You can." That was the start of Rick doing a lot of the artwork you still see in PGS.

    The next year, we were struggling to land development contracts, so we started working on a puzzle game of our own. Shortly after we started concentrating all our resources on that project, with a theme of tearing down buildings, some evil bastards flew planes into the World Trade Center, which made our project immediately unpalatable, contracts and jobs essentially unattainable, and put us in a dire situation.

    In the midst of what, for me, qualifies as panic, along comes Tom. The one thing that Rick could not do for Goodsol (yet) was card set artwork, because PGS used a library for drawing cards that did not allow for card customization. Tom did not have the time to write a replacement library, whereas I had both the time and the specific expertise, so when he offered the contract, I immediately wrote a replacement library that did everything that the old library did, plus allowed for custom card images (and, later, different card sizes). That was my lifeline, so I did the bulk of the work for the first version over that weekend and delivered a useful library to Goodsol the next week. Fun fact: that library is called GDcard and still works in the Windows version of PGS to this day.

    Anyway, that project went well enough that Tom suggested a much longer project that became Pretty Good MahJongg. Despite the longer development cycle, from initial design through product release, there was essentially no friction; Goodsol is the best client we have ever had. We have been collaborating ever since, and now that he is on the mend, we have a very good chance of celebrating our 20th anniversary of working together later this year. 🙂

  • INTERESTING! Thanks...

  • I'm not sure I care for the "you dummy" comment. I am not a dummy and I am pretty sure that the responder was not being passive-aggressive in his answer. In any event, I have my answers.

  • I think Ken was referring to himself as "you dummy".

  • >I'm not sure I care for the "you dummy" comment. I am not a dummy and I am pretty sure that the responder was not being passive-aggressive in his answer. In any event, I have my answers.

    Ken was just saying that he felt silly after hearing the answer because it was obvious (in retrospect). However, Tom used to be a mathematics professor, so I suspect that he has dealt patiently with worse, and I know he has had far sillier customer support issues. 😉

  • Gregg and Larry, thanks for defending me. They are exactly right, jdanham, while you asked an intricate question that required an intricate answer from Gregg, I asked what should have been an obvious question, so I was only making fun of myself!

  • edited May 2021

    No need to make fun of yourself Ken. I'm happy to do that for you. 😃 I'm about to return to the Favourite Music thread. I wonder if you could get a mention. 😁

  • You do keep me on my toes, Richard, and that's hard for me to do with my neuropathy...🙃

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