How to recognize hexagonal tiling in boardgame?
1st Approach:

Use the haartraining methods of opencv according to this tutorial http://note.sonots.com/SciSoftware/haartraining.html -- this should give the best results, but I haven't worked with haartraining myself so far...

2nd Approach:

I would suggest to use methods of "markerless tracking" of the individual tiles of the board. You can implement this using OpenCV, too..

Preparation


For this purpose you'll need some photos of each type of tile. Take a picture of all tile types (each one as one picture), with a homogeneous background from top-down-view tile in the middle of the picture.
Then use some feature detector (OpenCV has multiple algorithms for this, but SIFT/SURF are non-free algorithms; I would suggest to use "FAST") to find distinctive points in the images.
Use a feature descriptor to describe the feature found in the image (use e.g. "BRIEF").


Detection

Now you can detect the tiles in an image by applying the same feature detector/descriptor algorithms to this image. When you've acquired the features/descriptors you can apply the FlannBasedMatcher to find the tiles.

Here's a code example / tutorial from OpenCV:
http://docs.opencv.org/doc/tutorials/features2d/feature_homography/feature_homography.html#feature-homography

Notes

The Matcher Method will give you only one match and will possibly have problems if there is more than one tile of that type found on the board. You could work around that problem by masking out only some parts of the input image. I suggest to do this using the pixel coordinates of the detected features. If you - somehow - detect the outline and size of the tiles first, you can roughly estimate the tile positions and size on the picture. Filter your detected feature-list (e.g. only features within x-pixel radius from expected midpoint of the tile) before matching and then use the strongest match. As a result you'll be given the exact position of the tile on the image (including it's orientation). If it's too complicated to detect the map outline, you can let the user "point" at the corner tiles to mark the outline manually...

Alternative Approach

You can also use this method to find just any of the tiles by its outline. Draw a sample "schematic" grayscale picture of a tile (hexagon) without any image on it. Note that the "dark" and "light" regions in this image need to be correct in the schematic, not just some "lines".
You'll probably need to experiment with this. You could try to average multiple photographs of different tiles to generate an "average" image of a tile. Make sure the corners are at the same position (move/scale pictures accordingly) and sharpen the picture when finished (clear corners/edges should be visible) and adjust the contrast a bit, if needed.