Lots of these stats are in earlier posts - in answer to your question, assuming going first (so drawing 8 cards by T3), and that there are 4 of each in a 39-card deck it's 24% - i.e. about one game in four.
Method: drawing one target card from four available in a deck of 39 in 8 draws is 61.75% (from this page). Doing this 3 times = 0.6175^3 = 0.24
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