Now I had some time. Let's count a few. Here is a list in order by denominator of the fractions whose decimals terminate in either an even or odd digit.
Odd: 1/2, 1/4, 3/4
Even: 1/5, 2/5, 3/5, 4/5 even is now ahead by 1. Probability of an odd one 3/8.
Odd: 1/8, 3/8, 5/8, 7/8, 1/10, 3/10, 7/10, 9/10, 1/16, 3/16, 5/16, 7/16, 9/16, 11/16, 13/16, 15/16, 1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20 odd is now ahead by 23. Prob. odd 27/41.
Even: 1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 9/25, 11/25, 13/25, 17/25, 19/25, 21/25, 23/25 odd is still ahead by 10. Prob. odd 27/53.
Odd: the following numerators over 32: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31; the following over 40: 1,3,7,9,11,13,17,19,21,23,27,29,31,33,37,39. Odd is now ahead by 42. Prob. odd 59/85.
Even: over 50: 1,3,7,9,11,13,17,19,21,23,27,29,31,33,37,39,41,43,47,49. Odd ahead by 22. Prob. odd 79/105.
Odd: over 64: all the odd numbers, 31 in all. Odd ahead by 55. Prob. odd 110/136.
Even: over 80:32 numbers. Odd ahead by 23.
Odd: over 100, 40 numbers. Odd ahead by 63. Prob. odd 196/222.
Note the trend, the percentage of odd numbers in the stack is 3/8 or about .4, then 27/41 or about .6, 27/53 or .5, 59/85 or .7, 110/136 or .8, 196/222 or .9.Odds seem to keep climbing as we count higher, even though they do slip back sometimes.
The next two additions are 125 which adds 104 evens to the stack, and 128 which adds 64 odds. 160 then adds more odds. Odds seem to dominate. Do you still think it's 50-50?