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:

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

2. one card from R and one from S, or

3. two different cards from S

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

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