@Richard ...

Thank you very much for the code.  I modified it to behave somewhat in the way I am trying to do my thing...


...and attached the results in the first attachment.  I then did the same for 14,400 steps, if you will, and the results are in the second attachment.

Those outliers that you talk about - I guess that can be lived with, as that would impact every horse in a race, not just one.  I am encouraged by the results of the second run - the more loops, the more varied the times seem to be, even for the same number of loops to complete the test.

Thank you, bplus...I will try implementing the more-accurate storage of TIMER, maybe that changes things a bit.

I wonder if...

A=RND
Randomize(TIMER + A)

...would work.

I really appreciate all time you are taking to look at this, but again - it isn't about the various results, it is about using TIMER.  If you used the TIMER function to actually time how long each race took each horse, and you had a number of horses in different races run in the exact same time, down to the 1/100000th of a second...wouldn't you think that was a bit strange?

Thank you, Steve, for the insight here.  I have removed the second RANDOMIZE and only triggering one RANDOMIZE (TIMER) at the beginning of the program.  The goal of that 100-loop accumulation was simply to introduce a random delay on each sweep of the code that determines movement of the horses, because I am consistently getting identical times, which is really what I am asking about.

I agree 100 percent that the mean of a series of random numbers between 0 and .999999 approaches .5, and that loop wasn’t doing much, except that probably WASN’T exactly .5, and because _DELAY can use 1/1000ths, it should have been enough to prevent the identical times (to the 1/100000th) happening.  It wasn’t.

I am not the most optimized coder, no question about that, but when I time events using TIMER, with that precision, I still cannot figure out how I am getting identical times all the way to the 1/100000th of a second.  That should be, to my mind, quite impossible….or, since anything is possible, FAR less frequent.

There is too much code to paste here, but the gist of it is….

BEGIN
START RACE
StartTime = TIMER
Race is 1,440 pixels long
Begin Loop
Random numbers between 1 and 3 determine how many pixels forward each horse moves
All 6 horses move, in random order
All horses move forward
Eventually, each horse has moved 1,440 pixels (enough passes of 1, 2 or 3 have happened to add up to 1,440)
First horse crosses finish line
FirstTime = TIMER
FirstTime = FirstFinish - StartTime
Second horse crosses finish line
SecondFinish = TIMER
SecondTime = SecondFinish - TIMER
.
.
.
Sixth horse crosses finish line
SixthFinish = TIMER
SixthTime = SixthFinish - StartTime
End of loop
Race is done - display results
END

Sometimes, there are EXACT ties in a race.  Dead heats happen in horse races, I have no issue with that, though, again, a tie to the 1/100000th of a second seems kind of wildly unlikely.

But run a few of these, and I get some identical times, all the way down to the 1/100000 of a second (I posted a list of 10 races x 6 times).  The 4th place finisher in race #6 will have the identical time to the 2nd place finisher in race #3, for example.  Again, to the 1/100000th of a second.  That just should NOT happen. 

I tried this.  If I run a race where all horses move 3 pixels at a time, all 6 finish at basically the same time, but the first horse to move that last cycle wins by 2/100th of a second.  Makes sense, there is processing time being used.  However, all the other 5 horses have the exact same time down to the 5th decimal place.  Something is strange about this type of thing.

Thanks bplus...

I use RANDOMIZE (-TIMER) at the very start of my program, and it is called only once.

Are you saying I shouldn't bother with the second RANDOMIZE (TIMER)?  Or is there just a better way to pick a random number? 

All I am doing is trying to figure out how the heck two separate events can time exactly the same to the 5th decimal point when everything that contributes to that time is a series of apparently random numbers.

Yeah maybe, how are you coming along?

Well, I got away from it for a few days with other stuff to do (bought an Apple III, 6 Apple IIe and a II+), and chores and the like, but got back to it last night and things seem to be coming together.

I have decided, though, to use the framework I have created and instead of auto racing (which would involve collision detection and user inputs, and an AI I am prepared for just yet), I am going to make this a horse racing program.  Wagering model, stable management, etc.

One of my favorite games ever was Sport of Kings by Omni-Play (later Virgin)…

https://www.myabandonware.com/game/sport-of-kings-19p

…so why not?

You guys are awesome.  :)

Thank you so much for the help and the laughs, first thing in the morning.