mrbofus wrote:
every couple of days, either two monitors will display the same desktop image, or all three monitors will display the same desktop image. The odds of this happening with 132 images on 3 different displays is pretty small, and for it to happen regularly indicates to me it's more than just coincidence.
It took me a while to clear the cobwebs out of my brain to calculate the probabilities you mentioned, but I figured out that the probability of any one image showing up at the same time on two or three monitors, especially given the frequency with which they change, is rather high. I'd suggest: (a) adding several dozen more images to that folder, and/or (b) reducing the frequency that they change.
In any given half-hour, the probability of seeing the same image on any two or three monitors (A & B, B & C, A & C, or A & B & C) or all three monitors is 1/(132^2) + (131/(132^2))*3 = 0.0226124885 (2.26%)
Conversely, the probability of seeing three different images is (132
131130)/(132^3) = 0.977387511 (97.74%).
first consider this:
It would only take 22 hours to change desktop images 132 times across three screens.
Here's the math: 22 hours = 44 image changes x 3 screens = 132 image changes.
So, if you work on your computer 8 hours each day (8x2x3 = 48 changes), then sometime during the 3rd day your Mac would have changed the desktop image 132 times across your three screens. Less than that if you work on it more than 8 hours each day. The chances of one randomly selected image popping up at the same time on 2 or 3 of your screens every 2 or 3 days is highly likely.
If we assume that this event is binomially distributed with a probability of .0226124885 then we can actually calculated how many times we'd expect to see the same image on 2 or 3 screens in a given number of image changes. 45 is the magic number where that expected number is greater than 1. Why 45? For every 45 image changes, we would expect to see the same image on 2 or 3 screens once. As you said, this would mean that it happens fairly regularly.
On average, given the above assumptions, you'd expect that to occur about 1 time every 3 days: (0.0226124885 * 45) =1.01756198.
mrbofus wrote:
If I go into system preferences and manually change the wallpaper and then uncheck and recheck "Random order", nothing happens, whereas in Leopard, unchecking and rechecking that box would actually change the desktop image. I have to manually select another picture, then recheck the "Change picture" and "Random order" boxes, and then the computer will be fine for the next few reboots. Or I can select another folder and then my backgrounds folder again.
On this other topic: I wasn't able to exactly reproduce your 'system preferences' behavior.
System Preferences -> Desktop & Screen Saver -> select new wallpaper (automatically clears the check boxes for Change Picture and Random Order).
What I did find, which I also found quite annoying was this: if you manually select a new wallpaper image (automatically clearing the check boxes for Change Picture and Random Order), then re-check the Change Picture box, Snow Leopard automatically switches the wallpaper image displayed on my desktop back to the previous wallpaper image, but my manual selection remains selected in the System Preferences window. It does randomly switch the next time I boot up, but there seems to be a bug with switching the image when I check the Change Picture box.