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The diagram shows the board and the pieces in the initial position. A cell is identified as the intersection of two oblique files.

• White begins. Players move - and must move - in turn

• If a player has no legal move he loses the game

In Draughts, having no move may come about in two ways: the player is either eliminated or blocked completely. In HexDame it is virtually impossible to leave a player literally without a move. Of course a player may be blocked in a strategical or tactical sense, which means he is left without a good move.

• A man moves one cell straight or oblique forward, provided it is vacant. If a man ends its move on the back rank, it promotes to king. A king moves any distance along an open line, as indicated

Capture

• Moving a man
• Moving a king

The mechanics of capture are identical to Draughts, but in six instead of four directions. Next to the oblique lines, like the central e-line and 5-line, we will also call the columns 'lines', like the central a1-i9-line.

• Majority capture has precedence: if the player to move can make more than one capture, he must seek out beforehand the one that captures the most pieces. If there's more than one way to meet this criterion, he is free to choose.
  It doesn't matter whether a man or a king performs the capture, nor whether it is a man or a king that is captured: both count as one piece
• Capture is multi-directional. A man captures an opponent's piece on an adjacent cell by jumping over it and landing on the cell immediately beyond, which must exist and be vacant for the capture to take place. In a multiple capture the man thus proceeds until the capture has been completed
• A king looks in six directions. If it sees, at any distance, an opponent's piece and immediately beyond one or more vacant cells in an unbroken row, it captures by jumping the piece and landing on any of the vacant cells mentioned. In a multiple capture it thus proceeds until the capture has been completed

The expression "...it captures by jumping the piece and landing on any of the vacant cells mentioned", does not necessarily imply choice in a multiple capture. Being subject to majority capture, the king will usually have no choice, except possibly after jumping the last piece.

• After - and only after - the capture has been completed, the captured pieces are removed from the board
• A piece may in the course of a multiple capture visit a cell more than once, but it may not jump the same piece more than once
• If a man ends its (capturing) move on the opponent's back row of nine cells, it is promoted to king. This marks the end of the move
• A man passing the back row in a capture, but not ending on it, does not promote
• The game may end in a draw by 3-fold or mutual agreement

A multiple piece-capture does not necessarily keep a particular line and may end on the square of origin. The 'x' sign comes after the indices, for instance e8g6x, eg8x or f6x.

You can play HexDame online in  

Signs used in notation are:

!	Good move
!!	Very good move
?	Bad move
??	Blunder
!?	Doubtful
?!	Risky
=	Equal position, draw
+	Won
-	Lost

Those were the rules, and they are not by me. They were put down in 1723 by a Polish citizen of Paris for the 10x10 square board. His name has been lost, but he did an excellent job. I only had to apply them to the hexagonal grid under addition of the 'straight or oblique' forward movement.