Oh this is a neat problem, who could have guessed an atari 2600 game could hold this kind of a riddle.
Well I briefly looked into the code just to see how the time is kept track of. Here is the bit of code:
--If the racer hasn't finished the race
--If the countdown has reached 0
LDA $B7,X -- this is a counter that increments by 34 every other frame
LDA $B5,X -- notice that the carry flag can be set, so sometimes it adds 4
ADC #$03 -- add time for the current racer
One thing I noticed is that if you start from power on, your opponents time is incremented first, but after resetting, my time incremented first as the race started. I haven't looked too deeply into why yet, but I do wonder if this can influence the time you get.