。
If it were me, I wouldn't bet on that horse.
Literal
I [if-なら] that horse [on-に] bet [list-たり] [topic-は] not-do.
~たりはしない is an emphatic negation pattern — the ~たり suggests 'things like [verb],' and は negates the whole list/category. More emphatic than simply 賭けない. 僕なら sets up the hypothetical. A decisive refusal phrased as a category-level rejection.