Category Archives: Games

#44: The Feeling of Victory

This is mark Joseph “young” blog entry #44, on the subject of The Feeling of Victory.

Moments ago I finished a game of computer pinball, and it was such an exciting finish–on the final ball I finished the extra point task list, crossed the two million mark, and lost the ball, all within a second, and I couldn’t help going, yes.

Don’t get me wrong.  Two million is a paltry score, even by my standards. I have to break six or seven million just to get on my own leader board, and I think that my record score is up somewhere above fourteen.  This wasn’t a particularly well-played game overall.  It was just–

Screenshot of 3D Pinball Space Cadet (c)Microsoft

It illustrates something that every game designer and every role playing game referee needs to grasp.  It is something inherent in Multiverser, something that I tried to capture in the novels.  Some call it the “payoff”.  It’s the feeling, perhaps the “rush”, you get when you do something special.

Note that you don’t have to win.  You don’t even have to break even.  You don’t have to have reached some pre-defined goal.  At no point did I think that I wanted to reach two million–on throwaway games of pinball, I figure I did fine if I passed the million mark, and I’d done that.  Nor did I give much thought to whether I was going to “complete the mission” by hitting all the intended targets.  It was this juxtaposition, the unexpected success on both of those in-game milestones at the moment of defeat.

After all, let’s face it, you never “win” pinball.  It’s not like Solitaire, where sometimes you win and sometimes you lose and if you know enough you can improve your odds.  With pinball, you keep playing, and you keep winning, until suddenly you lose.  You can count it a win if your particularly high losing score is high enough to put you on the leader board.  Yet this unwinnable game has an appeal of its own, an appeal that comes from the small victories along the way, and particularly from the unexpected ones, the ones that come in under the wire, the ones that surprise.  It’s fine for me to lose, as long as at some point I felt like I won–even if it’s the same moment.

It’s fine to run or design a game in which people lose.  In Multiverser, player characters get killed all the time.  Ron Edwards once wrote that the game had some of the best answers to the problem of character death, because we use it to advance the plot into the next adventure.  You lost the round; get ready for the next round, because you get to keep playing, you’re just on a different board.  The game you lost isn’t lost if you won something along the way, and the sting of defeat is considerably mitigated by the thrill of a victory gained at that same moment.  People love their victories, but they also love their glorious defeats.  Icarus may have crashed and burned, but for a moment there, he was flying.

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#40: Multiverser Cover Value

This is mark Joseph “young” blog entry #40, on the subject of Multiverser Cover Value.

In a thread on Facebook on a completely different issue (an article I encountered on an effective non-lethal weapon) posters made some comments about the complexity of the Multiverser game system.  I don’t happen to think it that complex, really (to create an Original Advanced Dungeons & Dragons™ character without limiting in advance what the player might want to be, the referee needs to have access to twelve of the thirteen hard-cover volumes), but they did tackle two of the more complicated areas:  the spell system and the way to calculate cover value for armor.  I promised to provide answers, and since I no longer have the Gaming Outpost forum for such things, the answers are going to land here.  We previously addressed the issue of Multiverser magic; this entry will deal with the cover value problem.

Combat image from Multiverser: The Game: Referee's Rules, by Jim Denaxas, (c)E. R. Jones & M. Joseph Young

This part of it was raised by one of the most experienced Multiverser referees out there, my own son Kyler:

While you’re talking about complicated math in multiverser, I’m surprised no one has brought up Cover. That was one of the first things I changed when I was trying to streamline the system.

The math for Cover can get ridiculously complicated when you’re wearing layers of armor. “Add this, divide that. Take into account material density.” I abandoned it in favor of a system that focused more on where you were hit and ascribed a damage value to each piece of armor.

I’m not saying that the Multiverser system’s way of dealing with it is bad. I’m just saying that it’s needlessly complex, basically no matter what we’re trying to do.

Ouch.

Well, in my defense, the rule book does say that calculating cover is a complicated bit of math–but at the same time, that you don’t have to do it generally, as once for any piece of armor is sufficient.  Reading some of the other comments on the thread, I’ll note that if for Multiverser purposes you’ve calculated the “cover value” of five different pieces of armor, and you wear them all, your cover value is simply the sum of all the pieces you’re wearing, even if they cover the same body parts.  So the math is only difficult when a particular piece of armor is created or acquired, and after that the only question is whether you’re wearing the same pieces or left something off.

So, what is the complication?

How well armor protects is based on two factors, one of which is also based on two factors.  The one factor is how much of the body the armor covers.  It is kind of the joke that people wear bullet proof vests but are easily killed by a shot to the head.  That’s why combat and riot gear includes helmets.  The system would be complicated indeed if we required the referee to work out how much protection was afforded to each part of the body, but we allow a sort of fiction here–if you’re wearing a bullet proof vest, you are that much harder to hit, and the “cover value” takes into account that blows against your torso are less likely to penetrate, even though your head is still vulnerable.  In theory, someone can aim for an unprotected head, but they’d take a size penalty on the shot.

The second factor is how difficult it is to penetrate.  We know from history that iron armor protects better than bronze armor, because iron weapons are more likely to penetrate bronze armor but not iron armor.  It thus follows that a suit of white dwarf alloy (if such a thing could be obtained and worn) would protect better than a suit of aluminum.  We cover this factor with a density number–nothing too scientific, just the application of a game concept of “density” extended to cover materials that have not yet been created.  We also allow the issue of thickness, when it comes to armor–if you make your armor twice as thick, it’s more difficult to penetrate–but that particular factor is usually ignored because thicker armor of that sort is overly restrictive:  armor that is twice as heavy is only twenty-five percent more protective.

So the system really comes down to these two factors:

  1. How much of your body is covered by the armor?
  2. How hard is it to penetrate the material covering it?

It’s not usually difficult.  For example, let’s suppose someone gets a full suit of jointed full plate armor.  The book suggests that such a suit covers ninety-five percent of the body–there are some slots for vision and air in the front of the visor, and a few small gaps where the metal comes together most of which open and close as the body moves.  It would be made of a relatively hard metal, but that could be a softer one like bronze or a harder one like steel.  Thus there’s a range of densities for hard metals, from 2@6 to 4@8.  From there it’s simple to convert the values to “decimalized” numbers and multiply.  If we’re looking at 95% coverage at 2@6 density, that comes to 26 x 0.95=24.7, which we round to 25, a 25 percentage point penalty on incoming attacks.  If we have heavier denser metal, say a 4@8, that’s 48 x 0.95=45.6, again rounded to 46.

It looks complicated probably probably for two reasons.  One is because of that table in the book that looks like this (you don’t have to read this table, it’s just here so you can see it):

From Multiverser: The Game: Referee's Rules, (c)E. R. Jones & M. Joseph Young

That makes it look complicated–add this, subtract that, put it all together to get a number–but ultimately, all it’s really saying is, figure out how completely the wearer is covered.  It tries to take into account things that should be considered–chain doesn’t really cover your entire body because it has little holes in it, and we’ve all read stories about the arrow or knife that went through the holes in the chain armor.  Ultimately, though, all the referee really needs to do is decide what percentage of the body is covered–or conversely not covered–to get his basic “percent covered”.  That’s all that that table is for.

The second complication arises, though, when players attempt to “game the system”.  They’ll usually try to make armor thicker to get more protection out of it–and sure, a phone book is harder to penetrate than a manila envelope, so thickness does matter.  It does not matter if the design uses layers–that is, if you’re wearing a chain shirt under solid breast and backplates, you get the full value of both.  It’s only complicated if you make the material thicker, such as making the breastplate half an inch thick instead of a (standard) quarter inch.  That requires a bit of math–but the thickness of the armor is not going to change, and wearing multiple layers of armor is simple addition, so you only have to do the complicated bit once.

After all, how many times does someone get a new suit of armor?  A few minutes to work out how effective it is should not be that much of a problem.

The game also has rules for ablative armor–armor which protects by absorbing damage–but these rules in essence say that unless the ablative armor is also stated to provide cover value, it does not provide cover value and so isn’t part of this calculation at all.  There can also be complications if someone is hiding behind a wall and someone else is destroying the wall, but that’s an attack on cover or structures, not at all about armor, so it’s not part of the usual “cover value” issue.

Or did I miss something?

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#38: Multiverser Magic

This is mark Joseph “young” blog entry #38, on the subject of Multiverser Magic.

In a thread on Facebook on a completely different issue (an article I encountered on an effective non-lethal weapon) posters made some comments about the complexity of the Multiverser game system.  I don’t happen to think it that complex, really, but they did tackle two of the more complicated areas:  the spell system and the way to calculate cover value for armor.  I promised to provide answers, and since I no longer have the Gaming Outpost forum for such things, the answers are going to land here.  This entry will deal with the magic.

From Multiverser: The Game: Referee's Rules, (c)Valdron Inc, by Jim Denaxas

Harry Lambrianou (wow–I spelled that correctly on the first try without looking) raised the issue, and said in significant part:

My biggest problem – and the thing I houseruled away most frequently – is that MV’s magic system, as written, insists that /any change/ no matter how minute results in a completely new spell.

So if I have a “Battle Blessing” spell that normally takes 1 minute to cast, and I decide that today I need to rush it and cast my “Battle Blessing” in 10 seconds… normally you would think that this is my normal “Battle Blessing” spell, albeit with a skill penalty for rushing, right? That’s intuitive… No, it’s an /entirely new/, but /otherwise identical in every way/ spell… that does not inherit the Skill Ability Level for the spell its based on. So if I was 2@8 on the original Battle Blessing… maybe I’m 1@3 on the /identical/ rushed version…. and both need to be leveled up separately.

At one point I think my actual Verser self had something upwards of four different copies of this same spell, the only difference being one was a shorter casting time, or one affected three people instead of five, or something like that. It got out of hand very quickly.

I hated this from the first time I saw it happen, and consequently have never enforced it on the handful of players I ever ran for.

It’s a valid point:  if you know how to perform some kind of magic, shouldn’t you be able to perform it more quickly if you’re in a situation in which you need to get it done fast?  However, I have two answers for this.

The first has to do with “game balance” in mechanics.  That was always a big deal before Vincent Baker’s Lumpley Principle and Ron Edward’s Model, and it’s still a big deal in complex game design.  It means, among other things, that every power has limits so that it won’t dominate the game.

Magic, in Multiverser, has essentially two limits.  One is the same limit that applies to technology, psionics, and even to body skills:  bias, which determines what is possible or impossible in a given universe, and how difficult it is to do.  It’s a relatively simple system given the complexity of issues it addresses, but it’s not at issue here.  For any given magic outcome, either it is or is not possible in the present world, and it can be more or less difficult.

The other limitation is the one at issue.  In Multiverser, you can design your own magic skills.  You can say that you want to achieve this result–create fire or lightning, charm an enemy, pass unnoticed through the midst of a crowd, fly–and that you are going to take these steps to achieve it.  The simple form of the rule is that the power you get from a “spell” is proportional to the effort you put into it.  That effort can take the form of sacrificing objects of greater or lesser value, speaking loudly or gesticulating wildly in ways that call attention to yourself, saying words that broadcast what you are attempting to do so the target can take countermeasures, and, almost always, how much time it takes to cast it.  The battle blessing in particular is significant in this regard:  a two-minute spell to enhance your combat abilities means that for two minutes you have to stay out of the fray, which might not even be possible; the same spell in twelve seconds is going to be very nearly something you can do while drawing your weapon.  Obviously, though, if we assume that the battle blessing does exactly the same thing to the same degree at the same probability of success, no character in his right mind would take two minutes of valuable combat time to cast a spell he can cast in twelve seconds.  Thus part of the solution to prevent that is that the probability of success on the twelve-second version is considerably lower than that on the two-minute version.  Assuming everything else to be the same, the longer spell is probably about thirty percentage points more likely to be successful than the short one.  That can impact whether or not it works, of course, and also because of Multiverser’s relative success rules it can also impact how well it works, because a higher successful roll normally delivers a better outcome.

Understand, too, that I believe in running an equitable game.  If when you create this spell you get this bonus for shouting, everyone should get that bonus for including “shouting” in any spell design; it becomes the “shouting bonus”.  I have a list of standard bonuses for standard “spell components”, and when someone comes up with some new component I had not previously considered I compare it to my list and then attempt to make note of what I decided so that if they do it again, or someone else at the table does it, I will treat it consistently.  When you create a spell, I look at everything you’re investing in success, and crunch the numbers, and I give you a number, a “situation modifier”, to record with the spell description that says that this spell is this percentage more or less likely to work than the baseline.  You get that bonus–or penalty–whenever you use that specific spell.  But if you modify that spell in any way, you’ve changed the bonus or penalty.

Of course, I could let you change the spell for a specific casting–but that means that when you do that, I have to recalculate the chance of success anyway.  And in doing so, I’m probably going to have to look up the baseline for the spell, figure out what elements you are using and what value I gave each of them originally, and work out the new chance of success pretty much as if it were a new spell–and seriously, how much of a two-minute ritual can you cram into a twelve-second rush casting?  And does it make sense to say that because you have done this two-minute ritual before a couple times you will be just as good at doing the same ritual in twelve seconds?  I think of the fast talker competition, where someone holds the record for the fastest delivery of a particular Shakespearean sililoquy (I cannot now recall whether it is from Hamlet or MacBeth).  Does the fact that you recited that sililoquy a couple times mean you can now challenge the record?  You can deliver such a speech at a reasonable pace and allow yourself time to think of the next line without looking as if you don’t know what you’re doing; you can’t spit it out at record time if you have to think of the words.  Believe me, I’ve sung a few songs that have incredibly rapid-fire lyrics, and you had better know them cold if you expect them to make it to your lips.  So I have to recalculate, and I probably don’t have the original calculation handy (why clutter your character paper with the detailed numbers, particularly when that’s not character knowledge?) so I’m starting from scratch.

And if you’re forcing me to start from scratch to recalculate your chance of success for what is necessarily a different ritual (because it runs a different length of time) that feels to me like you’re doing a completely different spell, and I want it on your sheet for the next time you decide you want to do it in twelve seconds instead of two minutes.  It really is not the same spell just because it has the same outcome, any more than striking a match, using a cigarette lighter, and rubbing two sticks together are the same skill even though they all produce fire.  You are attempting to achieve the same outcome a different way, and the simple fact that you want it to happen more quickly proves that this is the case.

Of course, it does make sense that if you’ve done the same skill enough times you would be able to do it in less time.  That’s true when I cook, certainly, as once I know the recipe I’m not stopping at each step to check it.  And that leads to the second answer.  It’s built into the system that when you have used or practiced a skill long enough/enough times to be good at it, your “skill ability level” crosses the line from amateur to professional, and whenever you perform that skill you do it in half the time.  Your two minute skill takes only sixty seconds.  Continue at it and eventually you will be an expert at that skill, and it will take only one third as long as it took when you were an amateur–in this case, forty seconds.  No, that’s not twelve seconds; but if your ritual requires singing four verses of Onward, Christian Soldiers at thirty seconds per verse (sorry, Harry, it was the first decent example that came to mind), you’re going to have a lot of trouble getting it as fast as ten seconds per verse.  So “faster” is built into the system, but only after a lot of practice.  If you want the same outcome in less time, you really are trying to figure out a “faster” way to do it.  There is a saying in business, something like “Fast, good, cheap, pick two.” If you’re trying to get fast, you have to trade something for it–you’re doing it a different way, and a different way means a different skill, even if it’s a choice between the American Crawl and the Breast Stroke.  Keep doing it the same way and you get better at it; change the skill, and you’re learning more skills.

There’s nothing wrong with learning more skills–if one fails, you can use another.  In fact, if you botch on a skill you’re not permitted to retry it again immediately, but you are permitted to try a different skill that does the same thing, so having multiple versions of a skill can be useful in a pinch.

Anyway, that’s how it works and why.  I know it frustrated you; it frustrated me that you couldn’t see that to be the same skill it had to be done the same way.

Eric does all of this by the seat of his pants, and you can do it that way.  I don’t, because I am not good enough to keep the playing field level if I don’t keep track of the rules–but Eric is more like Ed in that regard, and doesn’t much care whether the playing field is level as long as it tells a good story.  It’s harder for a good player to play in a world like that, though, because things are not predictable–a spell that should be easy winds up being hard, because the same standards aren’t maintained from one to the next.  Part of play is learning what works, and what makes it work better.  If the standards shift, you can’t learn that.  It can still be fun, but it’s not quite the game we designed.

I also sympathize with your feeling, Harry, that you were trapped in the same world for a long time.  It’s not entirely my fault–people who stay with the ship take risks of being versed out in a lot of ways, and people who settle into city life, even taking a job with the city watch and starting a fire department, are not taking the same risks.  My second world was a modern vampire setting, and before long Ed was becoming frustrated trying to find ways to get me out of it, because I kept playing smart enough to beat his killer monsters.  Eventually he stopped running the game, and I was never really out of there; two other referees tried to pick it up, but they couldn’t see how to get me out, either, and both gave up on it.  Kyler was stuck in NagaWorld so long that he had to dream up something plausible but truly dangerous to try to get himself out of there.  Being stuck in a world in Multiverser seems to be proof that you’re a good careful player who knows how to stay alive.  It’s a compliment.  Reckless players jump from universe to universe.  You were never that.

I’ll address the cover value thing in a couple days, probably.

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#34: Happy Old Year

This is mark Joseph “young” blog entry #34, on the subject of Happy Old Year.

At this time of year, readers are bombarded with “year in review” pieces, part of the media’s need to have news even when there is no news, to make news out of nonsense and trivia–the reason Time Magazine first created its “Man of the Year” issue (the first was Adolph Hitler).  When I was at The Examiner, I began doing something of the same thing, creating indices of articles from the year for readers who missed something or who vaguely remember something.  Quite a bit has been published this year, and it might help to have a bit of a review of it all, as some of you might have missed some of it.  We have articles in quite a few categories.

The web log is of course self-sorting, and you can find articles in its various categories by following the category links, or in subjects by following tag links; still, it will be worth touching on those pieces here, and there are also quite a few “static pages”, that is, regular web pages added to the site, that you might have missed.

At the beginning of the year we were still writing for The Examiner; all of that has been republished here, much of it which was originally done in serialized format consolidated into larger articles.  My reasons for that are explained here on the blog in #8:  Open Letter to the Editors of The Examiner, if you missed them.  It is still hoped that the Patreon campaign will pick up the slack and pay the bills needed to support continuing the efforts here at M. J. Young Net.

img0034MJYNet

Let’s start with the law and politics pieces.  This is a good place to start, because when at the beginning of the year we moved everything from The Examiner, we included a final New Jersey Political Buzz Index Early 2015, with articles on Coalition Government, Broadcasting, Marriage Law Articles, Judiciary, Internet Law, Congress, Discrimination, Election Law, Search and Seizure, Presidential, Health Care, and Insurrection, most subjects covering several articles consolidated with other articles, along with links to earlier indices.  There was also a new main law/politics index page, appropriately Articles on Law and Politics, covering the old and the new, and we added a static page to that, continuing a series on tax we had begun previously, What’s Wrong with the Flat Tax?.

We’ve also had a number of law and politics posts on this blog, including

We also covered New Jersey’s 2015 off-year election with a couple posts, #12:  The 2015 Election, and #15:  The 2015 Election Results.

There were a few web log posts that were on Bible/theology subjects, particularly last week’s #32:  Celebrating Christmas, about why we celebrate, and why this particular day; plus some that were both political and theological, including #3:  Reality versus Experience, #23:  Armageddon and Presidential Politics, and #24:  Religious Liberty and Gay Rights:  A Definitive Problem.

Then there was the time travel material.  This also included some that were originally published at The Examiner and moved here, sometimes consolidated into single pieces.  We started the year with a serialized (and now consolidated) analysis of Predestination, followed by one of Project Almanac.  We also gave a nod to (Some of) The Best Time Travel Comedies and (Some of) The Best Time Travel Thrillers, before moving here.

Once here, we began our temporal insights with a couple of web log posts, the first #6:  Terminator Genisys Quick Temporal Survey, and then #17:  Interstellar Quick Temporal Survey, both thanks to the generosity of readers who provided for us to see these films.  We eventually managed to add a new analysis to the web site, Terminator Genisys, one of the longest and most complicated analyses we have yet done–but we were not done.  Remembering that our original analysis of the first two films in the franchise made some suggestions concerning a future direction for the series, and having commented on the problems with continuing it after the latest installment, we wrote #28:  A Terminator Vision, giving some ideas for a next film.  Then in response to a reply to the analysis, we added #31:  A Genisys Multiverse, explaining why we don’t think a multiverse-type solution resolves the problems of the film.

The site was expanded on another long-neglected front, the Stories from the Verse section:  the directors of Valdron Inc gave me permission to serialize Verse Three, Chapter One:  The First Multiverser Novel; as of today, the first forty-seven of one hundred twenty-six chapters (they’re mostly short chapters) have been published; there is an index which conveniently lists all the chapters from the first to the most recent published in the left column and from the most recent to the first in the right, so that you can begin at the beginning if you have not read it at all, or find where you left off going backwards if you’ve read most of it.  The chapters also link to each other for convenient page turning.

I don’t know whether it makes it more interesting or takes away some of the magic, but I also began running a set of “behind the writings” blog posts to accompany the novel.  These are my recollections of the process that brought the pages to life–where I got some of the ideas, my interactions with the editor and other pre-publication readers,, changes that were made, and how it all came to be.  There are now seven of them in print–

  1. #18:  A Novel Comic Milestone,

  2. #20:  Becoming Novel,
  3. #22:  Getting Into Characters,
  4. #25:  Novel Changes,
  5. #27:  A Novel Continuation,
  6. #30:  Novel Directions,
  7. #33:  Novel Struggles,

–and I expect to publish another tomorrow for the next six chapters.

Looking at the few posts that have not yet fit in one of these categories, whether logic or trivia or something else, one, #29:  Saving the Elite, was really advice for writing a certain kind of story.  Our first post in the blog, #1:  Probabilities and Solitaire, was a bit of a lesson in probabilities in card games, and #26:  The Cream in My Coffee applied physics to how you lighten and sweeten your hot beverages.

So that’s what we’ve been doing this year, or at least, that’s the part that sticks above the water.  We’ve answered questions by e-mail, posted to Facebook (and PInterest and Twitter and LinkedIn and MySpace and Google+ and IMDB and GoodReads and who knows where else), kept the Bible study going, worked on the novels, and tried to keep the home fires burning at the same time.  That’s all important, but somewhat ephemeral–it passes with time faster than that which is published.  Here’s hoping that you’ve benefited in some way from something I wrote this year, and that you’ll continue encouraging me in the year ahead.

Happy old year.

Happy new year.

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#1: Probabilities and Solitaire

This is mark Joseph “young” blog entry #0001, on the subject of Probabilities and Solitaire.

solitaire

I expect that this blog is going to tackle a lot of issues–I am already working on another on marriage and another on copyright and another on why I left TheExaminer–and judging from past response I will get a lot more hate mail than thank you notes (although I appreciate both). However, I thought it best to begin with something light and inconsequential, something that has been nagging at me periodically for a long time that more than anything else shows how foolish we “superintelligent” people can be, as we get mentally stuck on little things that bother us.

I had been thinking about part of this article for a number of years, and kept saying it would be a silly waste of time. Then probably a year or more ago I was watching the TV series Scorpion. As one episode opens, math savant Sylvester has been charged with entertaining Paige until the rest of the team returns from somewhere, and he hands her a deck of cards, recommends she play Solitaire for a while, and then–this was the part that bothered me–tells her the odds of winning. The more I think about it, the more I think he can’t know that.

I have played Solitaire since before high school, and I won’t argue as to whether he did the math right; my argument is that there are too many variables, things he cannot know. Never mind that Hoyle has an entire chapter on solitaire card games, even if we assume agreement that it is the standard seven-pile variant in which there are increasingly from one to seven cards in each pile with the top card faced, there are still too many variants. Even in the popular MicroSoft® computer version you can switch between advancing the pile three cards at a time (the traditional version) or each card individually, and with the latter your odds of winning rise significantly (because with the three-at-a-time rules there are often cards you cannot put in play that would move the game forward). Too, I was taught that with the three-card variant when you got to the end of the pile you went back to the top, but with the one card variant you got only one pass through the deck–which significantly lowers your odds. I have also known players who believe that after each pass they are permitted to shuffle the deck before beginning the next pass, or that if as they reach the end they have only one or two cards (not three) in the pile these go on top of the others so that what was the first card becomes the second or third (both rules making it much easier to free cards from the deck). Before you can calculate the odds, you have to know the rules.

So maybe Sylvester was thinking of “standard” rules–three cards at a time, repeated passes, no rollover or shuffle–and maybe on that basis you might calculate the odds. However, there is still the matter of strategy, and some people enforce rules that interfere with strategy.

I know about this because when I played Solitaire for years as a youth (what, you thought I was a popular kid always out with friends?) I played with real playing cards. Whenever I lost, I faced all the cards to see why I lost–I learned that you could be stopped if a card on top of a pile was sitting on the card you had to have to move it, and exactly what that meant, and how sometimes to avoid it. I think it a shame that the computer version does not let you do this, look at cards in the piles when you lose. It was a significant part of my education in game probabilities. In the game, you can make choices, and the way you choose impacts your ability to win.

What you have to understand is that winning Solitaire is achieved by freeing all the trapped cards. As the game begins, twenty-one cards are trapped on the board–six under the right-hand pile, five to its left, down to one in the second pile from the left end. In order to free these cards you must legally move the cards above them. There are also cards trapped in the deck from which cards are drawn. In traditional rules games the hardest of these to reach is the top card, as you must move both the second and the third to reach it; note that you can reach the fourth card in any of several ways, as it can be reached by moving the sixth and fifth, or by removing the third and waiting for the second pass, or by removing the third and second then on the second pass removing what was the original fifth and is now the third. Because of this, cards in the deck are the easier ones to free, and progressively more so the further down the deck they are. (There are initially twenty-four cards in the deck, and on the first pass eight will be accessible if none are removed.)

So how do you improve your odds of winning?

The first rule is do not make a move simply because you can; make a move because it improves your position. There are people who play that if they can move they must move, but if for example the three of hearts is sitting in the left pile (atop nothing) and the four of spades is on the right pile (atop six cards), there is no advantage to moving the three of hearts to the four of spades, and in fact it can cost you the game. It might be that the only way to move that four of spades is to play it to the spade pile atop the three of spades, and putting the three of hearts on it will prevent that. It might be that the three of diamonds will appear in a position in which it must be moved. Assuming the rule does not say that you must make any move you can make, the only reason to move a card that leaves an open space is that you have a king to place in that space immediately. As long as the three of diamonds does not appear, you can move the three of hearts when it becomes useful; if the three of diamonds appears and must be moved, you will be glad you did not move the three of hearts.

Second, always target moves that release the maximum number of cards. At the beginning of the game, there are six cards blocked by the card on top of the right-hand pile. That is at that moment the most important card to move. Once it has been moved, there are five still blocked–the same as the pile adjacent to it on the left–and so they become the most important cards to move. Throughout the game this changes, and when you have a choice of moves you want to be aware of what move will free the largest number of cards. It is almost always the case that moving the top card from the piles is a better move than moving one from the deck, by this measure. The computer version is your friend in this regard, because at the top of each pile the edges of the cards below appear, permitting you to count how many are still in each pile. Absent that, you probably have to remember.

As to the deck, keep track of how many cards remain in it. If the number is evenly divisible by three, you are going to see the same cards on the next pass. This is the most difficult bit strategically, as unless you have the kind of memory that allows you to keep track of the order of all the cards in the deck (and I do not) you are not going to know what moves are still possible from the remaining cards in the deck. However, on the first pass through the deck you need either to remove a number of cards from the deck, preferably nearer the top, that is not divisible by three, or you are going to have to change the board sufficiently that cards near the top are going to come into play in the next pass. Sometimes you will pass on a possible move because it will worsen your situation rather than improving it. It is better to play a card that will shift the deck on the next pass than to play a card that will restore it to the same sequence.

As an example, with the situation previously suggested, the three of hearts on the left pile atop nothing and the four of spades to the right atop six cards, you might well turn up the three of diamonds in the deck. At this point you have to decide whether or not to play the three of diamonds on the four of spades, and there are several competing issues in answering that. If the three of diamonds is the first faced card, that is, the third card in the deck, or if you have not yet played a card out of the deck on this pass, there is a strong argument not to play it–it will be in exactly the same place on the next pass, and you can see what other moves are possible before making that decision (e.g., if the king of hearts appears as the next card, and you need to move the queen of spades off the fifth pile and so moving the three of hearts is the better choice). This applies, too, if the three of diamonds is the last card in the deck, because it will be there on the next pass. On the other hand, if moving the three of diamonds out of the deck will give you new cards on the next pass, you want to do that, as it frees up cards in the deck. Note that deferring the decision to the next pass in the first instance has merit, because you might play two more cards from the deck in the next turn or two, and had you played the three of diamonds that would mean you played three cards from the deck and will see mostly or all the same cards on the next pass.

Another factor in the probabilities is that there are more ways to move a low card than a high one. If you are trying to decide whether to open a space for a king by moving the three of hearts or the eight of diamonds, it is probably better to put the three of hearts on the black four because once the ace-two of hearts are played it will be possible to remove the three. If you put the eight of diamonds on the nine of clubs, it is going to sit there until you get seven other cards played to the ace pile, or you have the unlikely opportunity to move it to the nine of spades (which again is something some players do not allow: splitting a pile to move part of it).

It is also advisable that you not let your ace piles become too disparate. If your diamonds pile gets up around seven or eight and you still don’t have your black aces, it is going to be much harder to find places for all those black cards that have no ace piles and no diamonds on which to be played. This is again a balancing issue: it is more important to get the cards in the piles into play than to worry about the disparity on the ace piles, but that ace pile disparity can prevent you from doing so if it goes wrong. You can (in most games, again some have a rule against this) play cards back from the ace piles to the main piles, but only if there are places for them, and that, too, can be blocked.

One last note: kings are ultimately the easiest cards to move after aces. (It is never a bad move to start an ace pile, unless moving the ace will lock your draw deck.) A queen can be moved to one of three places–the two black kings and the proper suit ace pile. A king can go to the ace pile and to any of the seven board piles once they are open. That makes moving kings a lower priority than moving any other card, and the other cards should be moved first if you have both moves available, unless it is clear that the king is blocking a significant number of other cards and the other move is not.

Hopefully this is enough to get you thinking about what moves in Solitaire will improve your position and what ones will reduce your chance of winning. Before I drop the subject completely, I will mention a strategy rule I got from a Contract Bridge expert: if you can only be prevented from winning if the cards fall one way, you must play as if that is how they fall; if you can only win if the cards fall one way, you must play as if that is how they fall. Note, then, that understanding the odds of how the cards might fall will help you win more games than solitaire, and will even carry to other games of chance such as dice games.

I hope this nonsense was at least entertaining; and perhaps it was educational as well. It also probably won’t be too controversial, but if anyone has comments you know how to find me.
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