tag:blogger.com,1999:blog-7718462793516968883.post6359906072741649363..comments2024-02-19T23:16:40.042-05:00Comments on MadMath: Winning Solitaire?Deltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger58125tag:blogger.com,1999:blog-7718462793516968883.post-59631372178600628532022-02-20T23:33:11.413-05:002022-02-20T23:33:11.413-05:00Interesting, thanks for that info!Interesting, thanks for that info!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-10281908165210299402022-02-20T21:48:12.435-05:002022-02-20T21:48:12.435-05:0011446 wins out of 42420 Klondike games played. 26...11446 wins out of 42420 Klondike games played. 26.98%. Windows 10, random difficulty, 3 card draw. Fastest game is 1:22. Longest win streak is 8 games. Longest lose streak is 29 games. I use a “selective” approached of making sure the games played have a movable card from the far right tableau column and at least two other opening movable columns from what is dealt (an “uncovering” of two additional face-down cards - 1st column move would not count since moving it would uncover nothing). I NEVER, EVER utilize undos – the moves I make are the ones I stick with even when, on the rare occasions, I make an error. In my opinion, using a selective process is NOT cheating, but undoing (going back to fix) IS. Also, remember if you're dealt what would look like a good 7 card poker hand, skip it and move on – unless it's at least 3 aces. Good Luck & Peace!Sparkyhttps://www.blogger.com/profile/08328092967551919953noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-44912897414222234102021-09-23T13:38:17.331-04:002021-09-23T13:38:17.331-04:00Thank you for sharing that!Thank you for sharing that!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-32494986435173945652021-09-22T21:20:31.140-04:002021-09-22T21:20:31.140-04:00I've played 49,262 games, draw 3, random, infi...I've played 49,262 games, draw 3, random, infinite deal, and won 14%. flannelmanhttps://www.blogger.com/profile/17185760244199590300noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-67649644492779712962021-01-19T14:53:21.247-05:002021-01-19T14:53:21.247-05:00Agree that using infinite-undos is basically equiv...Agree that using infinite-undos is basically equivalent to thoughtful solitaire. Thanks for that data!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-38425127038879695152020-12-29T18:35:34.584-05:002020-12-29T18:35:34.584-05:00I'm a compulsive solitaire (Klondike, 3-card d...I'm a compulsive solitaire (Klondike, 3-card draw) player here, too. With "undos" and unlimited times through the deck, I've played 5551 games on my phone now and have won 2906 (52.35%) of them. I seem to be approaching my upper limit, though. When I used to play without undos, my win rate was more like 10-12%. My gut feeling is that playing with unlimited undos is equivalent to "thoughtful solitaire", but don't know how to actually prove that is true. Unlimited undos is essentially being able to play the game an infinite number of ways from the beginning, and one of those ways should be the way you would play it if you had knowledge of all of the cards and were really, really smart. Wendy Bhttps://www.blogger.com/profile/00499076636319809702noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-27368959680991077322019-12-01T07:50:56.608-05:002019-12-01T07:50:56.608-05:00I play standard draw 1 and I have a win percentage...I play standard draw 1 and I have a win percentage of 91%, to mantain this average everytime I reach a dead end, I hit undo and and then change my moves.(During the game I always note instances where I had two of the same card and had to decide which one to move, if the one I chose lead to a dead end I come back and choose the other card. This works all most all the time) I hardly ever lose. T play mostly in expert levelAnonymoushttps://www.blogger.com/profile/12082647724497681099noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-43946826353629981212019-10-17T16:41:14.009-04:002019-10-17T16:41:14.009-04:00I play Vegas (draw three, three times over the dec...I play Vegas (draw three, three times over the deck), but different version for Android phone. My average is over 17% while using unlimited undo. So I am actually finding the solution. Of course, I do not try all the possibilities, only in case of good game with bad end I vo back and I am trying to change some of my previous decisions. Sometimes it helps, sometimes I can even get worse result. If I stop using undo, I fall down to 8.5%.JayCeehttps://www.blogger.com/profile/08909242417884333590noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-65676433349054044632019-06-14T11:10:22.134-04:002019-06-14T11:10:22.134-04:00That's definitely very good!That's definitely very good!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-70559230576352214102019-05-29T18:37:15.365-04:002019-05-29T18:37:15.365-04:00Not a mathematician here, just a curious player. I...Not a mathematician here, just a curious player. I play Microsoft's klondike solitaire on my cell phone kinda compulsively. Random mode, 3 draw, no limit. I've played 10,637 games, and won 1393 with a win percentage of about 13%. My average game takes 1:53, and my best time was 1:15.<br /><br />Based on what you guys are saying, my 13% is pretty good!Anonymoushttps://www.blogger.com/profile/17559813781968751742noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-41307090038786885332019-03-12T23:53:40.754-04:002019-03-12T23:53:40.754-04:00In some sense, the two different classes/populatio...In some sense, the two different classes/populations being joined here are entirely transparent: wins vs. losses. (The former is entirely ordered, while the latter maintains some disorder, by definition.)Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-34867306489266390682019-03-10T11:24:54.982-04:002019-03-10T11:24:54.982-04:00Jack, that's such a fantastic comment, thank y...Jack, that's such a fantastic comment, thank you greatly for that! <br /><br />It's interesting that you point out Bill's results are so similar to mine. My feeling is that there's a lot of room for improvement. E.g., in a multi-pass situation, if the machine remembered where all the cards in the deck were (something we humans don't normally do), the game would partly turn into "thoughtful [omniscient] solitaire" and would seem to support a higher success rate.<br /><br />Now the Knapp observation on bimodal cards left is interesting -- but that seems natural and not surprising to me. It feels to me while playing that the game is trying to "break" or not. The first analog that sprang to mind is S. Gould's "Full House" book, where his overall argument is that a graph of evolutionary complexity exhibits a limiting "wall" and one side, and then by necessity a skewed curve falling away from that (<a href="https://kk.org/mt-files/thetechnium-mt/gould-fullhouse2.jpg" rel="nofollow">https://kk.org/mt-files/thetechnium-mt/gould-fullhouse2.jpg</a>. <br /><br />[... searches memory/Wikipedia...]<br /><br />Ah, here's a better explanation. Arising from chaos theory/physics, there's the idea of <a href="https://en.wikipedia.org/wiki/Self-organized_criticality" rel="nofollow">"self-organized criticality"</a> (SOC) which (in part) notes a "critical point of a phase transition", a fundamental shift between chaotic and organized behavior. So it feels right to me that, as we play Solitaire and try to organize it, we're normally on the chaotic/random distribution side, unless we hit that "critical point" and so shift to the fully-organized side. (Note that Gould is also referenced in that article on SOC.)<br /><br />Especially thanks for the link to the Knapp book -- I haven't processed all of it yet, will make a note to do so. Also I'll make a note to see about adding output distributions to my program, it should definitely be feasible. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-34124366342548011362019-03-09T19:52:16.829-05:002019-03-09T19:52:16.829-05:00I just got around to reading the “games won” stati...I just got around to reading the “games won” statistics for your program. They are pretty close to those obtained from Bill’s Solitaire Tester. I have run several large-N experiments with that software the results of which may be interesting to you. The largest (10 Million each) produced the following proportions (not certain what “Lots” means):<br /> <br /> 1 Pass 3 Passes “Lots”<br />Draw 1 .046 .510 .534 <br />Draw 3 .002 .087 .178<br /><br />It looks to me like your results and those from Bill’s program support each other and, essentially, answer the basic question regarding what a consistent and attentive player can expect--playing the game that most of us play.<br /><br />With that, there is another provocative Klondike phenomenon that, I guess, bothers only those of us who have played with both solitaire and statistics long enough. The only other person I know of that has brought it up is retired statistics professor, Thomas R. Knapp, http://www.statlit.org/pdf/2016-Knapp-QRM.pdf . A frequency distribution for scores counting the number of cards in the foundations stacks is very strangely bimodal. Most cases fall into a positively skewed “bell,” ranging from 0 to 49. Scores of 50 and 51 never appear. And 52 shows up disproportionately. How disproportionately depends on the game parameters. In the case of “Draw 1, Lots” more than half of the cases score 52. For “Draw 3, 1 Pass there are nearly zero 52’s. The means for the non-52 portions of the distribution are easily calculated from data available from Bill’s program, but that is about all, and there is my frustration. I would really like to be able to make some inferences about a model that would produce this kind of data, and to do that I need reliable data from really large-N distribution tables. That data is not available from any source I know of. Is your program capable of producing such tables?<br /><br />Multimodal distributions usually occur when comingling more than one class of scores or scores generated by more than one process. Its hard to see how that would be the case when shuffling and dealing cards, but I haven’t been imaginative enough to think of a single process that would generate the data in question. After much fiddling and guessing, I think that some variation of the negative binomial distribution is likely to work.<br /><br />Anonymoushttps://www.blogger.com/profile/15985814946283185974noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-59133757064896705002019-02-09T10:59:53.699-05:002019-02-09T10:59:53.699-05:00Actually, it's been a few years so I need to r...Actually, it's been a few years so I need to refresh myself on the computer strategy myself. If you look <a href="https://github.com/danielrcollins1/SolitaireSolver/blob/master/PlayerComputer.java" rel="nofollow">here</a> and just read the comments (English lines starting with //), you may get the gist of it. <br /><br />Basically there's 8 tactics my program tries in sequence: (1) Check to flip a table pile top face-up, (2) Check for any moves to table, (3) Check for any moves to foundation, (4) Check if foundation card can join table subpiles, (5) Check if moving a subpile can free up a card for foundation, (6) Check for more cards to flip from deck, (7) Check to start a new pass, (8) Surrender the game. <br /><br />The order and details of those tactics got moved around some as I tested different strategies. Probably someone could use modern AI to do a significantly better job than that.<br /><br />I have a saying about random processes: "Random numbers will mess with your head". That is, you get way more patterns and matches than people usually expect. Quick example: If you draw 5 cards from a deck randomly, you'll get at least 2 cards with matching rank very nearly half the time. [Specifically: 1 - (52/52 * 48/51 * 44/50 * 40/49 * 36/48) = 1 - 0.507 = 0.493, or 49.3% of the time.] So the draws I see, with frequent matches of ranks and colors, is about what I expect from that process.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-41477620850785335432019-02-08T15:23:20.334-05:002019-02-08T15:23:20.334-05:00You are way over my head in creating a PC program ...You are way over my head in creating a PC program to solve solitaire. How does it operate? (if you care to reveal it, that is).<br /><br />But I have done enough of those "Klondike" games on "random deal" to suspect that it isn't actually "random". To me, "random" would, more often than not, give you a pretty good mix of red/black and cards up and down the line from A to King. But too often, their "random" gives all (or all except one) one color and/or too many close-clustered numbers--such as all 3s and 4s across the board. And, too often, all of a certain groups of cards seem to be "buried"--you never see a jack or you never see a 3, for example. Even dealing "random" from an un-shuffled deck would just have to produce a more diverse mix, it seems to me. Now and then, maybe one deal in ten, I feel like I got a "normal" deal in random mode.<br /><br />I think I'll switch back to "medium". I already said I suspect they switch unturned cards around there--but at least there it helps you win. I'm also going to try and kick the habit. ☺ Stanhttps://www.blogger.com/profile/03042316003561734440noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-71974996849030589142019-02-05T23:40:01.494-05:002019-02-05T23:40:01.494-05:00FYI, I just uploaded my solver code (in Java) to a...FYI, I just uploaded my solver code (in Java) to a <a href="https://github.com/danielrcollins1/SolitaireSolver" rel="nofollow">GitHub</a> repository, if anyone wants to look at that. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-38349836317278813252019-02-05T22:51:00.692-05:002019-02-05T22:51:00.692-05:00Glad this is engaging for both of us! :-) I agree ...Glad this is engaging for both of us! :-) I agree with you, I wouldn't want to abort games just based on the deal. I don't know the exact number, but as a ballpark I think that might reduce the number of games I win by something like half (I suppose if your goal is to minimize absolute time to any win, that might be a tactic, though.) <br /><br />My initial stab at how the difficulty is set would be to (behind the scenes) deal a bunch of games, have the computer play them knowing all card positions, and then pick one that is provably winnable. E.g., My own solver can play about 500 full games per second on fairly old hardware, so that's probably the easiest way (programming effort-wise) to do it. I'm just guessing, though. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-16306489682970778582019-02-05T20:21:42.593-05:002019-02-05T20:21:42.593-05:00I never thought I'd be talking to anybody abou...I never thought I'd be talking to anybody about "solitaire strategy" but it's kind of fun. So here's two more cents worth. One, I disagree with Tom Pate above who said he would skip a game if he couldn't see two moves and an ace on the opening deal. Well, not "disagree" actually--it's not a matter of agreeing--I just don't see the point. For example, if you have all red or all black cards showing initially, doesn't that increase the odds that you will turn over the opposite color? So why give up? So go for it, Tom! Same point late in a game, when, say, all but a dozen or so cards have been turned and you desperately need a red queen or something---the odds get better of that card turning up every time you turn one over.<br /><br />Now, one other thing I "suspect" MSFT programmers might be up to, as a way of "grading the difficulty" of deals, is to secretly move unturned cards to (or away from) where you need them to be (depending on whether you're in "medium" or "advanced" difficulty mode), as you play. In other words, the program sees what you need and moves unturned cards to make them easier or harder to get what you need. That would be a way of grading difficulty w/o completely stacking every deal.<br /><br />btw, you CAN WIN in random mode--I just did it--3 minutes, 11 seconds, w/o even trying to go fast. ☺ Now I'm quitting.Stanhttps://www.blogger.com/profile/03042316003561734440noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-49465438329659904922019-02-04T22:23:20.115-05:002019-02-04T22:23:20.115-05:00That's interesting; I'm not on Windows 10 ...That's interesting; I'm not on Windows 10 (yet), so I haven't seen this version of the game with "difficulty" levels. I agree with your deduction, that simply must imply stacking the deck. <br /><br />For what it's worth, I have a simple-ish Solitaire solver program with known random shuffles that solves Draw 3, Pass 3 7% of the time; Draw 3, Pass infinite 16% of the time. (Personally when I play Draw 3, Pass 3 on Win7 I keep a win rate a bit above 8%, so there's at least some room for improvement in the program.) <br /><br />Thanks for the information about that version!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-17125695334121523632019-02-04T17:42:03.465-05:002019-02-04T17:42:03.465-05:00Here's my two cents worth: I stayed away from...Here's my two cents worth: I stayed away from "solitaire" for about twenty years (since Windows 3.1, actually), preferring Bridge Baron for what little "gaming" I do. But back around Christmas, for some reason, I decided to play "solitaire" (Klondike, Classic, three-card rotation, no limit, if two or more moves possible, make the move on the left first) in Windows 10. I set it to "Medium" difficulty and logged 1,010 games in about six weeks, all on "Medium". My winning percentage was over 73%! <br /><br />I wondered how Windows knew "Medium" from any other level of difficulty, unless the deals were cataloged and ranked--in other words, unless the deck was stacked. I had no idea what a "normal" winning percentage would be. So a few days ago, I switched the setting to "random" deals. I don't know the precise count, but I cannot have "won" more than 3 or 4 out of maybe 40 or 50 tries. <br /><br />If it doesn't bother you to lose, there is one big advantage to playing "random" over "medium": you don't have to wait for the cards to dance around so much after a game AND there seem to be far fewer ads to wait out. ☺ <br /><br />Stanhttps://www.blogger.com/profile/03042316003561734440noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-33782275738268307642018-11-28T16:12:11.734-05:002018-11-28T16:12:11.734-05:00Nowhere does there seem to be a statistic of compa...Nowhere does there seem to be a statistic of comparison of card solitaire, and computer solitaire. They all seem to deal with the possibilities, but not with a definitive, yes you win more with cards or no you don't it is even. I have found it easier to win Windows 95 and earlier versions than current version and op systems, perhaps it is a truly effective shuffle electronically. I have gone back in games and changed card decisions, and worked my way to the end, not won, gone back again, trying every combination of moves I might have had the option of making, and still only win about 25% of those. As a time waster, the speed of computer solitaire can't be beat, but as a bigger time waster, having to shuffle and deal uses more of that 'wasting time' function, and I think I feel better with cards since I seem to win more, even if I don't cheat.CW45https://www.blogger.com/profile/18100707787428372633noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-4739006595058516632018-03-23T07:05:17.618-04:002018-03-23T07:05:17.618-04:00I play The Klondike Solitaire draw 1 on my iPad 12...I play The Klondike Solitaire draw 1 on my iPad 12.9 and my iPhone 6s. Once, I actually won 18 games in row. No clue how that happened. I do frequently use the undo button but, not obsessively so. Using a predictor that one usually can win about one game in every 5.4, 18.5%, I came up with a probability of 0.185 x 10 to the power of minus 7. So, I guess that says that the impossibly improbable is still possible. Go figure. I just accepted that it happened and, went on. It is not all that uncommon for me to win 3 or 4 games in a row. Go forth. Have fun! I suppose if The Klondike Solitare statisticians could find the incident in my history. I played all 18 one night on my 12.9. Whoopdeedoodlehttps://www.blogger.com/profile/06036287543651233415noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-11413182530977523992018-01-29T09:48:30.778-05:002018-01-29T09:48:30.778-05:00I play Klondike on my cell phone and actually win ...I play Klondike on my cell phone and actually win 74 % of my games... but I also start my games over and over again, if I have the feeling my cards can be played smarter. That's for me more interesting than just starting a new game over and over... -to find a strategy of how to play the cards.<br />Before, I just used to start new games and my score was about 25 % wins... but it bored me!Pernille Bhttps://www.blogger.com/profile/17992835065867573121noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-60508229877181731952017-07-03T11:37:09.949-04:002017-07-03T11:37:09.949-04:00At one time I became obsessed with playing Vegas s...At one time I became obsessed with playing Vegas scoring, where you are only allowed one time through the deck, and are awarded points (only if the card comes up from the foundation, so you need to put an ace on an available two before moving it in order to score). I achieved the maximum number of points a few times out of hundreds (and I do mean hundreds) of games. So that is possible. But I don't think I'd play solitaire in a Vegas casino. Allison Elainehttps://www.blogger.com/profile/08127584096174430464noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-90552913655406742742017-06-20T22:05:09.135-04:002017-06-20T22:05:09.135-04:00Thanks for the link; I'm pretty sure I have se...Thanks for the link; I'm pretty sure I have seen that before. The results listed on the home page (8.7% win rate on draw 3/decks 3) is quite close to my personal play rate (currently 201 wins in 2371 games, for a 8.5% win rate). I have my own solitaire simulator program that wins around 7.7% with the same rules. I do think there are some strategies that could improve my simulator's play.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.com