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Is the Monster (M) a valid target for a ranged Hero (H) attack through the Obstacles (█)?

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TL;DR No

For reference, "Line of Sight" (pg 12) from the Rules of Play:

In order for a figure to have line of sight to a space, a player must be able to trace an uninterrupted, straight line from any corner of that figure’s space to any corner of the target space.

If the line passes through the edge of a map tile, a door, or a blocked space (a space containing a figure or obstacle), the target space is not in line of sight (see “Line of Sight Example” on page 12).

If the line passes along the edge of a blocked space (see “Line of Sight Example” on page 12), the target space is not in line of sight. However, if the line only touches the corner of a blocked space (without passing through the space itself ), the target space is in line of sight.

Now let's address the possible lines from the Hero's space:

  • Top left corner

Any line from this corner must pass through the Hero's space. The Hero is a figure, so the Hero's space is a blocked space. So all lines are invalid because they pass through a blocked space.

  • Bottom left corner
  • Bottom right corner

For both of these corners, any line must pass through or along the Obstacle space. An obstacle space is a blocked space, therefore all lines are invalid.

  • Top right corner

Only a single line can pass from this corner through the obstacles. By geometry, that fixed line does continue to the Monster's bottom right corner, but passes through the Monster's space. A monster is a figure, so therefore the Monster's space is a blocked space. Therefore, the line passes through the edge of a blocked space and is invalid.

Summary: All possible lines are invalid; the Monster can't be targeted by the Hero.

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For context, the "Line of Sight" section from the Rules of Play (pg. 12), reads:

"In order for a figure to have line of sight to a space, a player must be able to trace an on interrupted, straight line from any corner of that figures space to any corner of the target space. If the line passes through the edge of a map tile, a door, or a blocked space (a space containing a figure or obstacle), the target space is not in line of sight. However, if the line only touches the corner of a blocked space (without passing through the space itself), the target space is in line of sight."

IMHO: It does not make sense intuitively for the target of an attack to count as an obstacle of said attack, so I believe you should have line of sight from the top right corner of the hero space to the bottom right corner of the monster space.

  • The line you suggest goes through the lower Obstacle space, and therefore against the rule quoted. There is no line of sight that adheres to the rule; the conclusion seems to contradict completely the rule. – Nij Aug 21 at 5:47
  • I imagine the original diagram might have made it easy to miss that the lower Obstacle existed. I've updated the diagram in the question. – doppelgreener Aug 21 at 13:39
  • @Nij I’m pretty sure poster meant top right of the Hero space. That can pass between the obstacles to the other point indicated. It’d be interesting to ask about passing through the attacker’s space though. – ricksmt Aug 22 at 13:14

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