Hopscotch

The Upper Walk (and filing)
Always flip the top card up on a row 1 stack.  Each stack on row 1 blocks the row 2 foundation directly below it. Once an upper column's source stack is empty, you may then file, or accumulate cards of one rank beneath it.  This includes the ability to file on an upper column's foundation with its own last source card. 

The Lower Walk (and live plays)
A face-up card on a row 3 stack blocks the row 4 foundation beneath it.  Where a lower walk column is not blocked, play it live by placing a card upon its foundation and flipping the top card of its source stack up.  With Aces low, your eight lower walk ranks must ascend from left to right.  

The Slide Play
When you have created a completely empty row 3 position, you may slide one face-up card to it from row 1 or row 3.

Scoring: Count one point for each card stacked on rows 2 and 4 (max = 52). With good skill, Hopscotch can be won some of the time.

Hopscotch Strategy

1. Don't lead off of too many row 1 stacks at the same time, as each one will block 4 lower walk columns before a new row 2 foundation is made available. Each new row 2 foundation can only relieve blocking instances of one rank.

2. Beware blockades, where two or more lower walk columns block each other simultaneously; a condition which can only be relieved by a slide play.
    

Spikes

A spike is one of the group of cards at the bottom of the row 3 stacks whose ranks match their foundations.  Where spikes occur, they will never be able to flip themselves over. Score one point for each where only spikes remain. 

Lucky Seven

Dealt as one 5-column upper walk, one 7-column lower walk and one 4-card hand, Lucky Seven gives the player twice as much power over the cards as in Hopscotch. Alas, the lower walk is one column shorter than before.

Cards in the hand which cannot play live upon the 7 columns of the lower walk must stay in the hand. The hand score is a card count of its most frequently occurring rank, making four-of-a-kind a perfect ending hand. 

Power Play (Artwork by Bill the Cat)

Hand Play: (to the lower walk) A card from the hand is placed on row 4, and a card from row 3 is returned to the hand. After the return card to the hand has been selected, as in any live play, flip up the top card of the source stack above the foundation played.  

When the column played is blocked, the blocking card is returned to the hand and the next card on the source stack is flipped up. 

When the column played is not blocked, another blocking card from row 3 may be returned to the hand.  This is known as a power play.  As pictured above, the Fives column is played from the hand, returning the Ten from the Aces column.  The next card on the  Fives column's source stack is then flipped up.  In this case, collecting the Ten from the Aces column relieves an Aces and Tens blockade.

There is also the blind play to an unblocked lower column, where the player chooses to return to the hand the card that will flip on row 3 before seeing what it is.

Sqatsi

Dealt as in Lucky Seven... In Sqatsi, each of the two walks must be declared in ascending order from left to right. Having to keep track of this on both walks at the same time may cause blood or smoke to come out of your ears at first (but this will pass).

Trump Play: A card from the hand may (legally) file upon an upper walk column, returning any one card from row 1 to the hand. If there are no more cards on row 1, then trump plays can no longer be made.

High Trump Play: If both source stack and foundation, i.e. one upper walk column, is entirely void of cards, then the player may choose to play one card from the hand to that column's source position, and return to the hand from row 1 as before. The card played to row 1 will still be available as source for further play. 

The Perpetual Play Rule: Since it is possible to play high trump without having caused any other card on the board to flip (a.k.a. “juggling”), it is possible to do so back-and-forth without end.  And so, where a high trump play does not induce a flip, the card played to row 1 cannot from that time forward be gathered back into the hand until at least one other card anywhere on the board has flipped.

Cheshire

The walks in Cheshire are resized to six columns apiece, which makes this game more challenging in that respect, but Cheshire begins with four upper walk source stacks which may be coaxed. I believe that Cheshire can be won most of the time, when played very carefully.

Coaxing and Favors
Four of the source stacks in Cheshire start with all cards face down. The act of flipping up the top card of an upper walk source stack is taking a favor.

In Cheshire, prior to an upper walk column's declaration, a card can be played from the hand to the top of that column's source stack, where that source stack is not presently topped by a face up card. The player's choice of upper walk source card is then coaxed back to the hand.