On Sat, Dec 08, 2001 at 06:25:38PM -0800, Trent Piepho wrote:
> On Sat, 8 Dec 2001, Mark Mielke wrote:
> > Unfortunately, the problem still remains: (Range is -1000..999)
> >     -1000, -800, -600, -400, -200, 0, 200, 400, 600, 800
> >        5     4     3     2     1   0   1    2    3    4
> > This time, however, after Trent's correction, the issue is somewhat
> > reduced.  Instead of the extra location being 1 of 4 positions, it is
> > 1 of 10 positions.  The client may draw the ship up to 5 pixels left
> > or up from the actual location, but only 4 pixels down or right from
> > the actual location.
> You are still wrong here.  Each of those 10 positions isn't equally likely. 
> If the random number is 0-199, you get 0 pixels off.  If it's 200-399 you get
> 1 pixel right.  The only way to get 5 pixels left, is if the random number is
> exactly -1000.  Four pixels to the left is 200 times more common than
> 5 pixels to the left.  You are only going to get the 5 pixel case off
> 0.05% of the time.

Rounding is down, not 'towards 0'. Their is 1/10 chance that the number
will be -1000..-801. Correct? That entire range is -5 pixels. The next
range is -800..-601, and is -4 pixels. -600..-401 is -3 pixels,
-400..-201 is -2 pixels, -200..-1 is -1 pixel, 0..199 is 0, 200..399 is
+1 pixel, 400..599 is +2 pixels, 600..799 is +3 pixels, 800..999 is +4 pixels.

There is one more possibility out of 10 that the ship will show up far to
the left on the X axis, and one more possibility out of 10 that the ship
will show up far to the top on Y axis. (This, suggesting that there is a
1 in 100 chance that the ship could show up 7 pixels distance to the topleft,
but only a 1 in 100 chance that the ship could show up 5.6 pixels distance
to the bottomright)

Out of 100 possible positions (10x10), that the ship could equally be
displayed at, 1 position is accurate, 16 positions are in the bottom
right sector, 10+10-2=18 positions are on an axis, 100-1-16-18=65
positions are in the other 3 sectors. 3x16=48. 48 is quite shy of 65.

> You also aren't taking into account that the initial position of the ship
> isn't going to be 0.  You might have it be 1 or 199, in which case the
> rounding comes out differently.

This is the argument that invalidates my argument. If the position is
+100, it is already 1/20 chance of being -5, and 1/20 of being +5. If
the position is +199, ~1/10 chance of being +5 and ~0 chance of being
-5, etc.

Hmm...

mark

-- 
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