8♦ 9♠ 10♦ J♣ + A♥ cut = 4 points

What the ace of hearts contributes

Holding 8 of diamonds, 9 of spades, ten of diamonds, jack of clubs with the ace of hearts as the cut scores 4 points in the hand.

The ace of hearts contributes no scoring combinations. The remaining 4 points come from combinations entirely within the four held cards.

Other available cuts of this rank: ace of clubs (5 points); ace of diamonds (4 points); ace of spades (4 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 4, 15 score the same (including the ace of hearts), and 33 score more.

Across all 48 possible cut cards, the score ranges from 4 to 11 points, averaging 6.58 points. This comparison treats every card outside the four-card hand as equally likely; it does not exclude known discards or other seen cards.