In any given game of Probabilistic Tic-Tac-Toe you can do everything right and still lose (or do everything wrong and win.) However, the better player always rises to the top over time. These are characteristics that I find interesting about a lot of other games, and I thought they'd be fun to apply to an otherwise boring, solved game like tic-tac-toe.
They're also highly relevant to my life philosophy - that every outcome is effectively random, but our actions can often skew the odds in our favor. Bad breaks are inevitable, but good judgment is always rewarded (eventually, and given enough chances.)
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