|John Bartholomew (Johnbartholomew)
New Solitaire Player
Post Number: 1
|Posted on Thursday, January 30, 2003 - 11:03 am: |
I have been playing Trefoil and La Belle Lucie with quite extensive utilization of the Undo/Redo feature, and have been able to win every game that PGS has presented to me. In other words, I never abort a game if the initial layout appears too difficult. This leads me to ponder if there is some mathematical analysis that can establish whether there is a possible solution for every deal in particular varietes of Solitaire. I am aware that Freecell is recognized as being in that category. Has anyone ever attempted to compile a definitive list of games for which a solution always exixts?
|Thomas Warfield (Support)
Post Number: 76
|Posted on Thursday, January 30, 2003 - 12:21 pm: |
>This leads me to ponder if there is some mathematical analysis that can establish whether there is a possible solution for every deal in particular varietes of Solitaire.
There is, you can prove that a game is unwinnable by trying every possible move and testing that every outcome leads to failure. This, however, is very time consuming even for a fast computer for many games where the number of possible moves explodes exponentially.
This method works reasonably well most of the time for FreeCell, so that is how we know for sure that some FreeCell games are unwinnable. It works OK for some other games where the number of possible moves stays low. It doesn't work well for games with lots of possible moves.
Due to the large number of different solitaire games of wildly different types, I know of no one who has systematically gone through a large number of games looking for solutions. It is usually done for a single game or family of games.
|Posted on Monday, February 03, 2003 - 8:47 pm: |
It may be ungracious to ask, given the many YEARs of pleasure La Belle Lucie has given me, BUT, I am a registered user of GoodSol on my main computer. Now I have a laptop as well. Do I need another license? i.e am *I* licensed, or are the computers licensed?
|Thomas Warfield (Support)
Post Number: 88
|Posted on Tuesday, February 04, 2003 - 10:59 am: |
>I am a registered user of GoodSol on my main computer. Now I have a laptop as well. Do I need another license?
Our policy is that you can install on as many of your computers as you like as long as you are only playing one copy at a time. So, for instance, if you have home and work machines, installing on both is fine since you can't be in both places at once. A laptop is likely OK since you probably aren't going to be using it at the same time as the desktop.
|Posted on Wednesday, March 10, 2004 - 5:26 pm: |
I don't know about a mathematical analysis for La Belle Lucie, but I doubt if there is one since the second and third shuffles mean that any game can be won no matter how bad the first two shuffles are if the third shuffle is lucky. And any game that can't be won on the first shuffle can be lost if you have a king blocking a lower card of the same suit on the second and third shuffles. Any game can be won if you just undo and reshuffle (not redo, which just repeats the shuffle you already got) often enough.
For the record, I consider getting a new shuffle with undo to be cheating, but redoing a shuffle is not cheating. If you're going to do that, why even bother playing a card on the first shuffle? Just reshuffle over and over until you get a nice easy win. Boring. But there's a lot of 100% winners on the scoreboard, so a lot of people must do it that way, or maybe they play the same easy game over and over. Without cheating, however, there are some obvious games that can't be won. For example, if all four aces are blocked by kings on the first, second and third shuffles, you lose without getting to play a card - without cheating, that is. But if you played that same game again, you might win on the second or third shuffle.
Bottom line, because of the random nature of the second and third shuffles, I don't think any mathematical analysis of a game from its starting position can tell you if it's winnable or not. For other games with only an initial shuffle, the answer might be different.
|Thomas Warfield (Support)|
Post Number: 607
|Posted on Wednesday, March 10, 2004 - 7:29 pm: |
You are right, Patrick, the shuffles would make any mathematical analysis very difficult. The game is not completely deterministic in the way that FreeCell is.
I would bet that La Belle Lucie is very nearly always winnable, regardless of the luck of the shuffles, though. Blocks through all 3 shuffles will be rare.