I put my sampling analysis into a spreadsheet with charts
It looks like when there are 10 cards in play, the probabilities for three of a kind, flushes, and straights all converge. However, when there are between 6 and 9 cards in play, the probabilities match standard poker rules, so statistically, it's best to avoid flushes before 10 cards in play.
Also interesting to note, there's almost always a pair among the cards in play, even in a 6-card game.