Calculate your expected winnings (or losses) if you throw away all but the 4♦, 5♠, 6♠. You might get a pair, 2 pair, 3-of-a-kind, straight, or nothing. This means you have thrown away the J♦, K♣. Let R be the set of cards of face value {2,3,7,8,9,10,Q,A} and S be the set of remaining jacks or kings (not the ones we threw away).

a pair of kings or jacks (plus the 4♦, 5♠, 6♠)

a pair of queens or aces (plus the 4♦, 5♠, 6♠)

2 pair: two 4s (incl 4♦) and two 5s (incl 5♠) and the 6♠

2 pair: two 5s (incl 5♠) and two 6s (incl 6♠) and the 4♦.

2 pair: two 4s (incl 4♦) and two 6s (incl 6♠) and the 5♠

3-of-a-kind: two more 4s or two more 5s or two more 6s

straight: high card 6 or high card 7 or high card 8

nothing: this will be C(47,2) minus all other possible or you should compare it with:

two different cards from R (but not getting a straight), or

one card from R and one from S, or

two different cards from S

a pair of 4s or a pair of 5s or a pair of 6s and one other card from the remaining 38

a pair of {2,3,7,8,9,10}