Winnable Spider Solitaire Games



32000 unique game/deals tested.
31997 --99.991% are proven to be winnable.



A program named plspider.exe has played a number of games of standard Spider Solitaire.

plspider's wins a typical game of Spider in around a minute on a 2.6gHz laptop.

Some of the results of plspider's play are listed below.

Inside plspider.zip are:


"Game Number"

The game number is a number that you may specify to the PySol program (Windows Version) to choose a specific deal of the cards to play.

In fact, the game number corresponds to the arrangements of the shuffled cards and to their order when dealt by the logic in the classic Windows FreeCell game. (Better FreeCell program: Freecell Pro )

plspider does not play the special game numbers -1 and -2, nor does it play the modern Window Free Cell games numbers between 32001 and 1,000,000.

Note: plspider plays Spider, not Free Cell. "game numbers" refer to the arrangements of the shuffled cards and to their order when dealt.

Below, the game number of un-won games may be followed by a number indicating the maximum number of empty stacks plspider has been able to achieve. Until the last deal, plspider is very eager to create empty stacks. On the last deal, moving cards out of play takes highest precedence.

"Moves"

The least number of moves that plspider has used to win the game.

... Or the most moves plspider has been able to make in a losing game.

In won games, plspider's moves are stripped of most redundant movement.

"Time"

The shortest (won games) or longest (lost games) play-times in minutes:seconds.


Note:

Game number 14934 appears to be unwinnable. It looks like this (printout from showdeal.py):


    Game number 14934

    10S   2H   4S   QD   3D  10D   9H   AS   JS   JD
     3C   4H   3H   QH   8C  10H   3D   4D   8H   AH
     KS   KC  10C   7C   8S   3S   7D   3S   6C   5C
     4C   3H   4D   7S   2S   3C   5C   8C   QC   5S
     JH   KH   2H   QC   JH   6H   QS   2C   KD   KS
     5S             2D             6H             5D

     6D   AH  10H   9S   9C   6C   AC   6S   9D   4C
     5D   9H   6D   8D   9C   KD   AS  10D   QH   JS
     JC   4H   2S   6S   7H  10C   KH   8D   8H   AD
     5H   2C   2D   4S   8S   AC  10S   7H   5H   7C
     9D   KC   AD   QD   JC   JD   7S   7D   9S   QS

    
The visible cards after the initial deal are the 5 of spades, king of hearts, etc.
The row of cards starting with the 6 of diamonds are the first cards dealt from the stock.
The row of cards beginning with the 9 of diamonds are the last 10 cards to be dealt.

First, remember this:

If the first 10 cards showing are, say, of only two card-values (e.g. all 6's and 8's), and all 16 cards that those two cards go on top of are underneath (e.g. all the 7's and 9's have been dealt face down), then the game is unwinnable, no matter what the distribution of the rest of the cards.

A special case of this unwinnable game is when one of the two card-values are a king. In that case, only the 8 cards that the other card-value may be played on must be hidden for the game to be unwinnable.

A further variant of this type of game allows the 10 cards to be anywhere in the deal, so long as the cards they play on are in unexposable positions underneath them.

So, examine game 14934, as shown above:

Notice the positions of the 3's, 2's, kings, and 6's. All stacks but the 6th and 7th have kings or 2's in them. The stacks other than the 6th and 7th cannot be emptied unless another stack is empty (to move a king to), or unless a 3 is exposed (to move a 2 to).

Simplified, that means that, unless 3's are available for the 2's to be played on, only the 6th and 7th stacks can be emptied. (And, without an empty stack, nothing can be done but play a whole suit built up on a king ... which won't happen if a 2 cannot be played on the king's stack.)

But the only 3's available to be played on are on the 6th and 7th stacks. Unfortunately, all of these 3's are hidden by 6's ... which cannot be moved before they are covered by kings ... which cannot be moved because there are no empty stacks to move them to.


And:


    Game number 1748

     AH   3D   4S   5H   6H   6H   8H   6C   6S   8C
     6D   2C  10C   5D   6C   6D   7D   KC   3C   QC
     2H   QD   5S   7D   QS   3D   2C   5S   8S   7H
     QH   KD   8D  10S   7C   5H   3S  10D   5D   5C
     KS   QC   4H   3H   KS   QH   6S  10D   KD  10C
     9H             AD             KH             8S

    10H   7H   5C   QS   8C   9H   JD  10H   9S   KC
     QD   9C   4C   4H   AH   3H   8H   AS   JS   KH
     9D   4C   JD   AS   JH   2H   4S   7S   2D   4D
     2S   9S   4D   AD   AC   JH   JC   8D   9C   7S
     JC   2S   JS   3S   9D   3C   AC   7C   2D  10S

    
Examine the 6's and 5's. Players will have a hard time moving 5's in this game. And all stacks have 5's and kings.

Game 1748 appears unwinnable, too.


How many games are like these? That is, games that simply don't go anywhere.

Recent (April 8, 2005) versions of plspider print out whether plspider ever emptied a stack or not.

As of May 1, 2005, there are 4 games that plspider has not emptied a stack on. Games 14934 and 1748 appear to the eye to be unwinnable. Game 10957 also appears unwinnable, but less clearly so. (4 stacks have no Kings dealt to them initially. Each of those stacks seems to contain a card that cannot be moved.)

Figuring that there exist unwinnable games that a stack can be emptied in, my guess of the unwinnable rate of Spider games is now somewhere around 1 in 3000. The bounds for this guess are given by plspider's current (May 1, 2005) results: that is, there must be more than 1 in 16000 games (though 2 unwinnable games isn't a high enough number to imply that this ratio is accurate), and fewer than 1 in 500.

November 2, 2014

Things have changed. It looks more like there are only 3 unwinnable games out of the 32,000. Two other un-won games, 12177 and 24560 have the makings of being winnable.

Max Schamschula is finding convoluted means to solve games that are unquestionably hard to solve. plspider's has been recompiled with settings tuned more toward looking deep in the move tree of un-won games rather than being quick to find solutions to "normal" games. So, time will tell.

Anyway, it appears 1 in 10,000 is closer to the frequency of un-winnable, random Spider games than 1 in 3000.


Un-won games


    Game number 10957

    10H   6H   KS   JC   3S   7S   4C   AC   9S  10C
     KD   4D   8C   9D   7D   5D   7S  10C   3C   4S
     4D  10S   3H   JS   9C   5S   2C  10D   3H   7C
     4H   6C   KD   5D   7H   4S   JD   AS   QS   7D
     2D   4H   3D   KH   8D   KS   KC   8H   6S   QD
     4C             2S            10D             KH

     JD   6H   9H   6D   6D   8S   2H   QS   8S   2C
     JC   2D   5C   JH   6S   7H   3C   3S   3D   8D
     AC   9S   5C   AH   5S   9D   QC   9C   QD   8H
    10S   2H   AD   JH   QH   5H   AH   9H   2S   6C
     QH   5H   7C   8C   AD  10H   AS   QC   KC   JS


    


Committed moves

May 5, 2005

A "committed move" is a move that cannot be undone by normal play. That is, it must be undone with an "undo" function. Dealing the 10 cards from the stack is an example of a committed move. Moving a King to a free stack is another example. Any move that flips (reveals) a card is another example.

A script was run to determine what the longest run of un-committed moves in each game has been.

What is the longest run of un-committed moves in all won games?

10 - in game numbers 20221, 27803, and 31842. plspider has played none of these games very many times, so their 10-runs may be easily lowered.

What is the shortest maximum run of un-committed moves?

2 - in game numbers 3370, 7490, and 15938. Interestingly enough, plspider has won these games in 215-217 moves. That is, they are not notably short games.

What is the most common maximum number of un-committed moves per game?

4 - in roughly double the number of games as 5. And roughly triple the number of runs of 3.


Updates

October 21, 2014

Maximilian Schamschula has solved 8881, 20830, and 24614. Herculean effort.

Insprired by Max, with some settings changes, plspider has solved 288, 6654, 8881, and 27320.

And, Max, with the aid of a sequence from plspider setting up 4 empty columns, won game 19638.

October 22, 2014

Max has solved 14686.

October 23, 2014

Max has solved 16749 and plspider has won 19638 by itself.

October 24, 2014

Max has solved 12057.

plspider has solved 28241.

October 26, 2014

plspider has solved 25521 and 12057.

October 31, 2014

plspider has solved 24614.

November 1, 2014

Max solved 14992 and plspider solved 16749 and 20830.

November 2, 2014

Max solved 28023.

November 3, 2014

Max solved 24560.

November 4, 2014

plspider solved 12177.



GreenWon
GrayHuman-won
OrangeLost
RedLost with no empty stacks made.

Shortest Game NumbersMoves   LongestMoves   FastestTime   SlowestTime   Shortest LossesMoves   Slowest LossesTime
23181168   22641393   197030:23   146863:59:54   1748:092   10957:11:00:42
14900170   28078393   31680:25   245603:39:42   14934:092   1748:025:36
693172   21260392   303390:25   208302:39:00   10957:1167   14934:015:59
25360173   3692385   106440:26   246142:37:12
718176   19952383   159820:26   264662:34:11
19167176   21320381   191670:26   169302:21:46
13492177   22544377   224160:26   88812:19:49
28226177   4258376   8830:27   81382:09:42
27959178   4237375   166030:27   167491:59:13
5425179   14346374   239120:27   2881:53:59
25462179   1563371   16090:28   282411:52:35
15993183   9280371   143980:28   242341:46:41
30152183   10719371   173020:28   232281:45:18
3899184   8081370   46850:29   83181:40:08
18992184   10322370   137900:29   311061:39:45
20578184   28614370   188470:29   279821:38:44
7435185   10475369   233870:29   294411:38:20
14398185   11460369   53690:30   217411:34:36
21585185   19470368   89090:30   285391:28:57
26906185   4353366   126940:30   149921:28:26
24127186   12366366   143110:30   73851:27:33
25457186   9920365   220810:30   111431:23:54
1527187   20914365   262530:30   273201:22:40
5361187   30908365   315980:30   203841:21:14
8224187   24782364   96270:31   26361:19:17
19752187   4397363   125860:31   47191:18:00
23943187   7917363   154400:31   46051:16:25
27347187   10682363   186990:31   66541:15:46
27976187   23731363   264340:31   172191:14:36
28097187   28066363   268720:31   280231:14:36
2597188   30057363   291000:31   269391:13:32
5437188   2068362   29440:32   129371:13:28
13865188   5718362   115130:32   81171:12:24
16271188   6161362   262430:32   153131:12:08
29884188   6817362   301430:32   96911:11:41
8100189   7631362   315200:32   244321:11:02
9987189   8678362   316000:32   45081:10:27
11533189   9397362   10190:33   1381:10:15
17658189   11136362   14140:33   285821:10:12
23005189   13164362   43230:33   92341:10:01
3870190   16453362   62400:33   9661:09:56
6264190   16875362   212880:33   108581:09:56
9036190   17173362   249180:33   42581:09:43
10816190   22961362   276120:33   96111:08:07
18286190   23416362   293010:33   20831:07:55
20392190   26313362   38140:34   174421:07:45
20435190   28275362   44180:34   87011:06:11
26228190   7012361   69320:34   149721:06:07
30749190   8079361   79180:34   183641:05:31
10094191   8112361   89410:34   71671:05:27
13999191   8485361   107070:34   225441:04:23
15186191   9087361   148710:34   238601:04:00
16301191   9409361   184600:34   213181:03:49
19703191   12302361   221580:34   286751:03:47
22081191   16003361   231270:34   275511:03:27
27937191   19077361   301520:34   269931:02:48
2144192   19214361   302430:34   142111:02:17
2522192   20069361   302770:34   59861:02:10
7483192   25903361   305810:34   269141:01:37
8064192   26579361   16560:35   83291:01:28
17869192   31605361   27440:35   282371:01:21
21791192   110360   41210:35   281991:01:15
22664192   342360   55190:35   84111:01:03
23209192   937360   70200:35   56851:00:59
23284192   1308360   128440:35   278321:00:54
25127192   1791360   174570:35   26801:00:47
30164192   3158360   183030:35   108041:00:23
190193   4861360   208490:35   305711:00:21
216193   5727360   209050:35   524559:52
753193   8828360   271210:35   1585659:24
4072193   9086360   289380:35   537459:22
5495193   15918360   290270:35   1217759:09
7395193   17919360   295820:35   3154658:54
13156193   19268360   302120:35   1863858:43
17810193   20476360   42430:36   805758:13
19935193   20639360   56940:36   2015958:13
23387193   20873360   72160:36   2986258:11
31831193   21316360   74700:36   3139258:08
31933193   22659360   76560:36   2984057:59
3499194   23835360   78050:36   829157:47
5145194   27327360   81540:36   3022257:26
14895194   27378360   93170:36   149557:20
15598194   29712360   101250:36   1160257:19
17501194   29917360   122970:36   1137657:08
22416194   31066360   131480:36   156056:38
26602194   31112360   134920:36   2342856:24
26868194   2014359   144170:36   1954156:23
545195   9521359   147350:36   2507856:18
1312195   12614359   175190:36   1425156:10
3093195   13017359   175810:36   16356:05
6271195   16672359   216440:36   2125456:05
9113195   18968359   227470:36   1198555:44
9399195   19073359   234720:36   1198755:40
12189195   20563359   257200:36   2918055:38
13894195   21345359   273690:36   2143655:31
15824195   22421359   290430:36   2578455:31
16541195   23056359   299290:36   2864755:15
19973195   23482359   316740:36   3151754:54
22257195   28607359   8570:37   531954:46
23250195   29509359   12280:37   1584554:43



32000 unique game/deals tested.
31997 --99.991% are proven to be winnable.



plspider.htm
Tue Nov 4 14:58:16 2014
plspider at tranzoa dot com
Copyright (C) 2005 Tranzoa, Co.