Sim­ply put: What is Soli­taire, and what are the best ones?

Every com­puter user knows at least one Soli­taire game. You might pre­fer Klondike, or Can­field, or maybe one of the hun­dreds of lesser-​​known ver­sions. Spend some time look­ing around, and famil­iar­ize your­self with the basic design pat­tern that rep­re­sents “a soli­taire game”.

What does it include?

• One or more decks of cards, per­haps with cer­tain cards (Jok­ers, or low-​​value cards) removed.
• Two or more “stacks” in a tableau — generic posi­tions where cards can be placed.
• Some rule for how to ini­tial­ize the game: shuf­fling and ini­tial place­ment. These involve what cards are face up, face down, whether they are known or hidden.
• A “round loop” that describes a set of one or more shifts of one or more sub­stacks of cards between loca­tions, pos­si­bly includ­ing mov­ing some cards from the hid­den undealt stack to a stack where they can be “used”. Allowed moves within a round may be gov­erned by a com­pli­cated set of con­straints involv­ing posi­tion, suit, value, prece­dence and how many cards may be moved.
• A win con­di­tion, typ­i­cally involv­ing a par­tic­u­lar state of cards being in par­tic­u­lar order in par­tic­u­lar stacks. For the pur­poses of this exer­cise (and pos­si­bly with­out loss of gen­er­al­ity) the win con­di­tion may be taken as a sin­gle spe­cific order­ing of the entire set of cards in play, over the set of stacks.

[Did I miss much?]

So.

Limn the set of soli­taire games. Present a for­mal, nonbrit­tle lan­guage in which any soli­taire game may be writ­ten. By being nonbrit­tle, your lan­guage will allow ran­dom sam­ples of the set of all fea­si­ble soli­taire games to be made by sim­ple aggre­ga­tion (fill­ing in words with­out the need for back­track­ing at any point), and will also allow one game to be trans­formed into another by local changes (sub­sti­tu­tion, dele­tion, swap­ping and inser­tion of words).

Bad soli­taire, good soli­taire. Present a suite of rea­son­able quan­ti­ta­tive mea­sures that will cap­ture the com­plex­ity, dif­fi­culty, and enter­tain­ment value of any given soli­taire game.

hint: Think about sudoku games. What makes a dif­fi­cult game? What makes an enter­tain­ing game?