What are the Odds of Winning a 4 Suit Spider Solitaire Game? What are the best scores?

The two most frequently asked questions in card games are:

• What are the odds of winning?
• What is the highest score?

The answers are not always based on objective calculations or controlled experiments, but provided by players on various levels of experience and sophistication. It is necessary to go through a few forums to come to satisfactory answers.

Description of the Spider Solitaire Game

The aim of the spider solitaire game is to remove all cards from the tableau, assembling them in descending order in a suit (from King to Ace) after which the pile is moved in an ascending suit sequence to the foundation zone. The classic spider solitaire game (played with 104 cards) comes in 3 levels of difficulty:

• Easy – all cards are from the same suit;
• Medium – cards are dealt from two suits; and
• Difficult – cards are dealt from all 4 suits (thus two full card decks).

Initially, 54 cards are dealt to the tableau in ten piles, face down except for the top cards. The 50 remaining cards are dealt from the stock to the tableau ten at a time, at the discretion of the player, usually when no further moves are possible. This is the “classic” computer version of spider solitaire that first showed up in the 98 Plus Pack by Microsoft that came with Windows 98 and since then remained part of subsequent Windows releases. Although a computer version from Sun Microsystems dates from 1989, it is the free Windows releases that added to the game’s popularity.

An important variation within the Windows games is the versatility of the “undo” facility. In some versions, a player can only undo up to the last deal from the stock, or the last move from the tableau to the foundation. In other versions it is possible to “undo” back to the beginning of the game. This influences the odds of winning and is an important feature when calculating the odds.

The Vista version calculates scores differently by awarding bonus points and is thus not comparable to other versions in terms of scoring.

Apart from the classic version there are a multitude of variations. Thomas Warfield is the person who invented Pretty Good Solitaire which contains a large collection of unique versions of Spider solitaire.

This article focuses on the classic game in the Windows releases, the “difficult” level, with unrestricted “undo” facility and excluding the Vista Version.

The highest score

This question can be answered theoretically. Different players in different forums came up with the same answer and I confer to the logic.

The highest possible score is 1254.

The mathematical reasoning is as follows:

The base score you start with is 500. If you successfully build the 8 suits, you are awarded 800 points, which gives you 1300. However one point is subtracted for every move. If you have to build the 8 suits, you will have to move 12 cards (Queen on King, Jack on Queen, 10 on Jack) for each of the 8 suits, making 96 moves. This would bring the score to 1204. If however, by fantastic luck, in each of your 5 deals of 10 cards, each card falls exactly on its right cousin (Queen of Hearts falls on King of Hearts), you will not have to move these 50 cards at all. You will thus gain 50 points which makes the score 1254.

World rankings for Spider Solitaire (source below) are based on 935 players submitting 2563 games. This is not a tournament as such and not an organised system to identify the best players in the world. It is however the only “formal” recognition that could be found on the Internet in regard to high scores. The highest score submitted was 1197, with the 50^th position held at 1122.

The odds of playing out a game

Some sites claim that it is impossible to calculate the highest theoretical proportion of games that could be won. This should be possible however, through computer simulation of all the possible combinations of dealt cards and the best possible solutions for each of these combinations. So far it has not been done.  The only data available are those shared in the various forums.

There are of course many issues around self-reporting. This ranges from different ways to save the games on the different systems, to downright cheating and fiddling with the registry - or just plain lying.

Nevertheless, I make a hypythesis that the highest possible proportion of games that can be played out should be around 80%, based on the feedback from experienced and exceptional players who take care to play out every game, “undoing” back to the beginning various times and even taking days to play out one game. The really good players report about 50% and the average but frequent players around 30%. Many claim that they don’t get past 5%.

Game strategy

This article does not focus on game strategy, other than to point out that the strategy for getting a high score, and that for playing out a high proportion of games are in conflict with each other. To get a high score, a person plays many games and try to make as few moves as possible (thus not really using the “undo” facility). Once it is evident that the game will not lead to a high score, the game is discarded and recorded as a loss.

A person playing with the object to play out the game, uses the “undo” facility to its full potential, revealing face-down cards to exercise the best options and even go back to start from the beginning and use all the information available to them. One player reported even going into negative scores - I am busy testing that claim right now.

Source

http://www.goodsol.net/cgi-bin/forum/discus.cgi

http://cards.wikia.com/wiki/Spider

http://en.wikipedia.org/wiki/Spider_%28solitaire%29

http://spidercards.com/faq.html

http://www.solitaire-ranking.org/pages/rules_spider