Hi, I posted in sci.math re card game, but I'll put it here in a less traveled place, and a quick description.
Where do I look to summarize the problem in this game mathematically?
As single-player, start with a few cards up and the rest down. 8 face values, or ranks may play at the start on an ascending order 'walk', but the other 5 cannot. The player chooses which ranks fit for now, and then clears spaces for the last 5 ranks to play to win. For each additional rank to file away, 4 blocking cards have to come into play.
I have seen many solitaires, and I have not seen this. I have seen large numbers with FreeCell type games, but with all 52 cards up at the start, and no probability. I have also seen the other types, such as klondike, where cares are face down but the player doesn't really have options.
I think the player options and up cards represent a large amount of calculations to the player, as then multiplied by the (what must be) much larger numbers in the probabilities of the down cards (around 40 or so to start), giving a net result of a calling for calculations on another scale.
Like maybe on the scale of a traditional board game? But with single-player. I think with these games the number of calculations has to be much larger than with games like FreeCell.
I am not a mathematician. I'll have to learn, but I have played these games thousands of times, and I know much more in playing than I did years ago, but these games are still mysterious to me.
1) I see a "spread" as appearing to have an ultimate effect in the game. Since 8 ranks play at the start, and while clogging up the playing area one more rank may be added at a time as you go, then the problem of the "spread of ranks showing" appears to become game-defining possibly no matter what you do - possibly not. For example, if there are 2 of each of 13 ranks showing (26 cards), and only 9 ranks play, then at least 2 of each of 4 ranks (8 cards) are in play, not playable, and blocking the playable area - for anyone who tries.
2) The math of the clearing of the 5 stacks and the damage done doing so seems pretty straightforward. There are 8 open/live columns to start, so 8 ranks will play, but in the 4 plays that clear the next stack, 4 more of those 8 columns will be blocked, before the new opening for the 9th rank becomes available. Next, another 4 columns will become blocked making way for a 10th rank to play. The 9th and 10th ranks better clear things out well, because to get them all 8 "live" columns got blocked, and the blocking cards need to file off or play within what is now a playable range of 10 out of 13 ranks. And so, the math based upon this is to not lead too many of the 5 stacks simultaneously - that just won't work.
Bigger Questions) I want to know how far a human can go in calculating this game. I am also curious about how math would put the player's problem.
I am very appreciative to anyone taking the time to look at it, and you don't have to like any of it, and I guarantee that it's a pretty easy game to enjoy on occasion, and can be very recreational and also very calculating and engaging, and mysterious and beyond calculation.
I made an internet home for it, with "how to" and a program for Windows if desired. I'll be adding them to PySol next, but I am picking up Python programming to do that, and it then gets more involved, because I think this game would work best in competition play (like golf), and not just single-player. Thanks for your time in looking... http://bwsgames.org