3♦ 4♣ 4♦ 4♥ + A♥ cut = 8 points

What the ace of hearts contributes

Holding 3 of diamonds, 4 of clubs, 4 of diamonds, 4 of hearts with the ace of hearts as the cut scores 8 points in the hand.

The ace of hearts contributes no scoring combinations. The remaining 8 points come from combinations entirely within the four held cards.

Other available cuts of this rank: ace of clubs (8 points); ace of diamonds (8 points); ace of spades (8 points). Changing only the cut suit leaves this score unchanged.

How this cut compares

For these four held cards, 0 possible cuts score less than 8, 28 score the same (including the ace of hearts), and 20 score more.

Across all 48 possible cut cards, the score ranges from 8 to 20 points, averaging 11.00 points. This comparison treats every card outside the four-card hand as equally likely; it does not exclude known discards or other seen cards.