RESULTS FOR SPIDER SOLITAIRE - MEDIUM
BACKGROUND
For quite a while, I was addicted to Spider Solitaire, a game which can generally be found as part of the Microsoft games package on most computers. If not, it can be played on many free game websites, such as Most Fun Games. The difficult level of the game, played with two full decks of four suits each, is almost impossible to win. I've only cleared the board once at that level. I find the medium level, played with two decks but only two suits, Hearts and Spades, more enjoyable as you actually have a chance of winning once in a while.
I became interested in the odds of winning and began to track the games I played as to number of moves by round and the number of full suits taken off the board and put into the scoring section. There are six rounds in the game. You start with ten piles of face-down cards on the board with the top card of each pile face-up. After you've made your moves from the initial position, you click on the reserve pile and a new card if placed face up on top of each of the ten piles on the board. (More often than not, these new cards will disrupt the strategy you've been developing.) There are six rounds; the initial deal and five refreshments from the reserve pile. To clear the board, you need to get eight suited sequences from King to Ace to the scoring area.
STRATEGY
From playing innumerable games, I developed the following strategic guidelines:
1. Play off the right side piles as they've fewer cards and can yield an open row.
2. Play any sequential suited moves first.
3. Then play any non-suited moves possible.
4. Get higher ranked cards off of lower ranked ones whenever possible.
Note that these are only guidelines, not strict rules. Given the wide variety of positions which may arise in the game, situations will arise which invalidate the above.
GAMES PLAYED
Given the nature of the game, low-scoring games are the most frequent. I stopped tracking results for any score after 100 games with that result, reasoning that 100 samples would be sufficient. Of the 334 games recorded, the scores, number of games and average moves per game are as follows:
| SCORE |
GAMES |
MOVES |
0 |
100 |
40.3 |
1 |
100 |
54.4 |
2 |
55 |
65.8 |
3 |
22 |
79.9 |
4 |
14 |
92.9 |
5 |
2 |
96.5 |
6 |
0 |
N/A |
7 |
0 |
N/A |
8 |
41 |
131.2 |
We see that for the 100 games recorded with a score of 0, i.e., where no suits were put into the scoring area, the average number of moves was 40.3, while for the 41 games with a score of 8, i.e., all the cards were sequenced on the playing field and moved to the scoring area, the average number of moves was 131.2. It looks like more moves tend to generate higher scores; not surprising.
But what happened to 6 and 7? If you stop and think about the game, it would be impossible to end with a score of 7 as that would leave only 13 sequential cards on the board, Ace to King, all of the same suit, and with 10 facing up. I can't think of any way that situation couldn't be easily won. Ending after a score of 6 would be possible but unlikely. For example, if you had two differently suited sequences left showing only the even cards up; two 10's, two 8's, etc. As you can see above, even ending after a score of 5 is relatively rare.
MOVE DISTRIBUTION
I also calculated the standard deviation of the moves per game by score. Using that information, I produced the graph below which approximates the normal distributions of number of moves for the various scores, excluding 5 because of the low sample size. I thought this graph was illustrative of the results of my study so I include it here.
OTHER DATA
I also tracked the average and standard deviation of the number of moves by round within scores. If you are interested in seeing that, I'll be glad to send you the Excel file containing the information. Just email me at pavel314@comcast.net
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