Number of Unique Ranks of High Card in Three Card Brag Well the game is called Teen Patti in India. Almost similar to Three Card Brag a British game. There are total $16440$ Unique High Card hands are present. (Considering the suit.) Hand $1 = 5$ Heart, $3$ Club, $2$ Diamond. Hand $2$ = $5$ Club, $3$ Diamond, $2$ Heart. Both these hands belong to High Card Hand Category. But these hands are ranked same. (There will be a tie between two players, if they have these hand.) $5$-Heart, $3$-Club, $2$-Diamond is ranked lower than $6$-Heart, $4$-Spade, $2$-Club. What will be the Total Unique Ranks present in High Card Category?

There are $\binom{13}{3}$ ways to choose $3$ distinct ranks. Exactly $12$ of these will be straights (i.e. $A23\cdots QKA$) an must be excluded. There are $274$ distinct high-card hands in $3$-card poker.$$\binom{13}{3}-12=274$$ Another way to arrive at the same result, knowing that there are $16,440$ unique high-card hands, is to divide by the number of ways $(4^4-4=60)$ that such a hand is not a flush: $\frac{16440}{60}=274$. This is also the number of distinct flushes (rank of flush, disregarding suit): $\frac{1096}{4}=274$