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<blockquote data-quote="Nom" data-source="post: 4049559" data-attributes="member: 56980">Could you quantify &quot;blatant&quot;?Using any form of grid creates a quantisation effect.Using a primary only grid creates a further effect where distance along a &quot;diagonal&quot; is 1/(cos grid_angle/2) longer than euclidean distance.Using a 1.5 diagonal square grid adds a measuring deviation where distance along a diagonal is (on average) 1.5/sqrt(2) longer than euclidean distance.&nbsp; For very short distances, this deviation can increase to x1.5.&nbsp; Off the four axes, distances are around +10% longer than euclidean distance.Using a Chebeyshev grid adds the opposite measuring deviation: diagonals are x1/sqrt(2) shorter than euclidean distance.Which of these deviations are &quot;blatant&quot; and which are not?&nbsp; What determines when a deviation becomes &quot;blatant&quot;?&nbsp; What is the mathematical basis for this metric?My experience has been that if the mechanic is easy enough the player adapts.&nbsp; The &quot;diagonal = +1&quot; mechanic used in Mage Knight Dungeons seemed odd to me at first, but after a few games I didn't even notice it.&nbsp; In contrast, after several years of D&amp;D / D&amp;DM I still notice the 1.5 diagonal mechanic because it is inconstant.&nbsp; Holding that 'carry' bit in my head has a surprisingly high mental cost.The only way to avoid deviations from euclidean geometry is to remove the grid entirely.&nbsp; At which point you have a new set of tradeoffs, including where to measure distance from (center / any corner / each corner / ...) and how &quot;large&quot; moving and stationary pieces are considered to be.Tangent: at what distance does measuring become quicker than counting?&nbsp; My gut feeling is that from about 10-15 squares the time taken to set up the ruler is less than the time taken to actually count the squares.&nbsp; Of course, counting time is roughly linear with number of squares, dropping to zero for distances up to about 3 squares.&nbsp; In contrast, measuring a long distance is only a little longer than measuring a short distance.&nbsp; Any gridless rules would be advised to write the mechanics such that there is no need for short-distance measurement.</blockquote>

[QUOTE="Nom, post: 4049559, member: 56980"] Could you quantify "blatant"? Using any form of grid creates a quantisation effect. Using a primary only grid creates a further effect where distance along a "diagonal" is 1/(cos grid_angle/2) longer than euclidean distance. Using a 1.5 diagonal square grid adds a measuring deviation where distance along a diagonal is (on average) 1.5/sqrt(2) longer than euclidean distance. For very short distances, this deviation can increase to x1.5. Off the four axes, distances are around +10% longer than euclidean distance. Using a Chebeyshev grid adds the opposite measuring deviation: diagonals are x1/sqrt(2) [i]shorter[/i] than euclidean distance. Which of these deviations are "blatant" and which are not? What determines when a deviation becomes "blatant"? What is the mathematical basis for this metric? My experience has been that if the mechanic is easy enough the player adapts. The "diagonal = +1" mechanic used in Mage Knight Dungeons seemed odd to me at first, but after a few games I didn't even notice it. In contrast, after several years of D&D / D&DM I still notice the 1.5 diagonal mechanic [i]because it is inconstant[/i]. Holding that 'carry' bit in my head has a surprisingly high mental cost. The only way to avoid deviations from euclidean geometry is to remove the grid entirely. At which point you have a new set of tradeoffs, including where to measure distance from (center / any corner / each corner / ...) and how "large" moving and stationary pieces are considered to be. Tangent: at what distance does measuring become quicker than counting? My gut feeling is that from about 10-15 squares the time taken to set up the ruler is less than the time taken to actually count the squares. Of course, counting time is roughly linear with number of squares, dropping to zero for distances up to about 3 squares. In contrast, measuring a long distance is only a little longer than measuring a short distance. Any gridless rules would be advised to write the mechanics such that there is no need for short-distance measurement. [/QUOTE]

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