6♠ 9♦ 10♣ J♣ + A♥ cut = 5 points

What the ace of hearts contributes

Holding 6 of spades, 9 of diamonds, ten of clubs, jack of clubs with the ace of hearts as the cut scores 5 points in the hand.

The ace of hearts contributes no scoring combinations. The remaining 5 points come from combinations entirely within the four held cards.

Other available cuts of this rank: ace of clubs (6 points); ace of diamonds (5 points); ace of spades (5 points). The cut suit changes the score here because of a flush or nobs.

How this cut compares

For these four held cards, 0 possible cuts score less than 5, 18 score the same (including the ace of hearts), and 30 score more.

Across all 48 possible cut cards, the score ranges from 5 to 13 points, averaging 7.04 points. This comparison treats every card outside the four-card hand as equally likely; it does not exclude known discards or other seen cards.