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Your question can be re-written like this: What are the odds of having 4 cards with the same suit, from the 5 available community cards? The answer can be found by using basic probabilities and computing probabilities of composed events. You can have 5 boards in which 4 cards are of the same suit: XXXXY XXXYX XXYXX XYXXX YXXXX Here, X means the suit ...

The odds of hitting a five flush, given four suited cards on the "flop" in hold'em are about 35%. They are 47% starting from four cards, all to a flush, in seven card stud. Your chances of eventually making the flush go down with each new card that does not "hit" the flush. If it "hits," you chances go up to 100%. Actually four to a flush (or straight) is ...