# Hex theory

Unlike many other games, it is possible to say certain things about **Hex**, with absolute certainty. Whether this makes Hex a better game is of course debatable, but many find this attribute charming.

The most important properties of Hex are the following:

## Contents

## Winning Strategy

- When the swap option is not used, the first player has a winning strategy.
- When playing with the swap option, the second player has a winning strategy.

These two statements come from the fact that without swap, Blue has no winning strategy and from the fact that draws are impossible in Hex.

### No winning strategy for Blue

While nobody seriously believes that black has a winning strategy in chess, nobody has been able to prove that such a strategy doesn't exist. In Hex, on the other hand, a simple argument can show that the second player certainly does not have a **winning strategy** from the starting position:

### No draw

If a Hex board is full then there is one and only one player connecting their edges. See draw.

## Complexity

- The decision problem associated to generalised Hex is
**PSPACE-complete**. - The detection of dominated cells is NP-complete. (
**To be checked**then sourced) - The detection of the virtual connections is PSPACE-complete. Reference here

## Solving Hex

- Hex has been solved on small boards.
- The game can not end in a draw. (Proofs on Javhar's page)

## See also

## External links

- Thomas Maarup masters thesis