Josekis

The word "joseki" is borrowed from the game of Go because of the strong analogy between Hex and Go corner play. There are certain sequences of moves played near corners of the board that often recur in different games. The corners are considered the key areas of the board (by the mini-max rule mentioned here). Hence, playing joseki often forces the opponent to keep playing locally. Knowing josekis narrows down the number of options to choose from. Nevertheless, that doesn't make the player's life very easy - picking a correct joseki is as difficult as picking a correct global move. Therefore, this subject is addressed mostly to advanced players.

Joseki's logic

When player A makes a move in a corner, she dominates the territory around this corner. Assuming that she picked her best strategy, she should stick to it and always defend her domination in the area. However, that doesn't mean that player B should give up that territory. Playing somewhere else will sometimes lead to losing the initiative around the previously mentioned corner, but there is a direct counterplay for player B. A game progresses in this manner: player B counterplays, player A holds on to her domination, player B counterplays again etc... This usually lasts 2-10 moves by each player, depending on how far from an edge the first move by player A was. When the final position is reached, player A has a fixed escape on one side of the corner and player B has a fixed escape on the other side (the second player's escape is always of shorter range).

Playing a joseki can often be delayed. This is a good choice if a player isn't sure which joseki is favourable for them. However, it's important to make sure that one gets the initiative back to play joseki. If the opponent can make forcing moves in other areas of the board then a chance to delay joseki is gone.

Examples

4th line josekis

A1) Red wants an escape on the bottom and Blue wants an escape on the top:

A2) Red wants an escape on the bottom, Blue wants an escape on the top and Blue knows that Red wants an escape on the bottom.
The move #3 is an improvement, because in some cases Blue might get an additional free escape on the bottom.
There is risk involved. If Red made an error on move #2 and in truth he wanted an escape on top he can correct the error by playing a different move #4.

B) Red wants an escape on the top and Blue wants an escape on the bottom:

C) This position might be reached if both players want an escape on the top.
Blue keeps a future option of playing in the cell marked with an asterisk.
This is a very risky plan by Blue, because Red has additionally got an escape on bottom. Blue should only play this joseki if he is certain that Red cannot use the escape on bottom. Otherwise a reasonable option is to give up the strong escape on top and go for position B).

D) If both players want an escape on bottom we get an unusual position where Red plays the last move of the joseki.
Blue's plan is to get a cell marked with an asterisk for free in future, so he shouldn't play there immediately. What he should do depends on the play in rest of the board.

5th line josekis

A)

B1)

B2)

B3)

B4)

C1)

C2)

C3)

C4)

D)

E)

F1)

F2)