Difference between revisions of "Swap rule"

Revision as of 04:01, 5 December 2020

Because the first player has a considerable advantage if he is allowed to make his first move without restrictions, the swap rule was devised. It states that one player first makes a move, and then the second player decides who plays with which colour. The swap rule is also called the "Pie rule", since it resembles the You cut, I choose rule when sharing a pie between two children. The swap rule can be implemented in two ways, as follows. (Assume that the colours are red and blue, with red moving first.)

1. The first player places a red piece in any hex on the board. Then the other player can either make a move with the blue pieces, in which case he becomes blue, or he can state that he wants to be red. After this the game continues without any more swapping.
2. The first player makes a move with the red pieces. The other player either makes a move with the blue pieces, or makes a piece swap. This means to remove the red piece from the board, and place a blue piece at the hexagon which is the mirror image of the hexagon in which the red piece was placed, with respect to the board's long diagonal.

In face-to-face play the first option is most practical, since it is easier to change colours of the players that removing and adding pieces on the board. It is also less error-prone. On game sites on the Internet the second version is more common, presumably because the colours are determined at the start of the game, and it is easier to change the board position than the colour designation.

When playing with the swap rule, the second player theoretically has a forced win. However, the second player's advantage is much smaller than the advantage of being the first player when playing without swap. Moreover, in either cases, the first player can study the move that he'll play before the game even starts. This provides an incentive for playing as the first player even when the game is played with the swap rule.

Hex combined with swap rule

According to some strong hex players, when a position is roughly balanced, having an extra stone on the board usually makes the game easier to play. This means that whenever one is in doubt about a move, it's a good idea to swap it. The first player should also take this into account by playing a first move that is probably losing under perfect play. This idea has been popularized by "lazplayer" at littlegolem/igg.

A more general swap rule

Instead of placing just one piece, the first player can place any number of red and blue pieces, and state which color has the next move. Let's assume that the first player has placed N stones in the board. The second player then can start playing hex with one color of his choice or, if he fears that the other player has an excessive advantage due to home preparation, he can swap roles with first player, remove all stones from the board and place at most N-1 stones as he wants. This rule has been first proposed by "lazplyayer" at littlegolem/igg, and it seems to be an improvement over the "simple" swap rule in current use.

The rule

After Red played the first move Blue player is asked wether she wants to swap or not, that is to invert the colors or to keep on this way. Detailled article.

Where to swap

The use of the swap rule is to force the first player to play not too good moves. Therefore it is intersting to find out what are the moves that should be swapped (the best moves), what are moves that should not be swapped (the worse moves), what are the moves for which no answer is known yet.

On every size a1, b1 and symmetrical moves are known losing moves (except 2 x 2, where b1 wins, see small boards).

• The red marked hexes are to be swapped.

• The blue marked hexes are not to be swapped.

• The star marked hexes are average moves, so the game should be balanced with or without swap.

Hex is not strongly solved on big sizes, therefor the result of optimal play is not known for every cells.

Small Sizes

See Small boards to know which cells lead to victory with optimal play. You might however assume that you and your opponent do not play optimally, and decide to play tricky losing moves in order to trap your opponent !

Bigger Sizes

The theoretical outcome is known for a few cells (for instance a1). For the other cells, stronger players' advice can give a hint on whether a move should be swapped or not. One could also try to recognize a pattern in the winning cells for small boards and extrapolate to bigger sizes.

Size 10

Size 14

TODO

Size 19

TODO

See also

Guideline for the 10x10, in the basic strategy guide.

External links

A faq about Hex

A more complete site with solution to sizes 7. Beware, the colors are inverted, vertical is blue there.