Domino

The excluded domino is number 2 and 2

After cataloging all 27 dominoes visible in the image and comparing them to the standard 28-tile double-six set, the [4, 4] (double-four) tile is the only one missing.

By systematically identifying all 27 visible dominoes in the image and comparing against the complete 28-tile double-six set, the domino [1,1] (double-one) is not present among the tiles shown. All other dominoes from [0,0] through [6,6] that should be in a standard set are accounted for.

After counting the pips on all 54 visible halves, the faces with 1-pip and 5-pip appear only 6 times each (all other numbers appear 7 times), so the missing tile pairs 1 and 5.

By analyzing the 27 visible dominoes in the image and counting the occurrences of each number (0-6), I found that the number 0 appears in 6 dominoes instead of the expected 7, and the number 4 appears in 6 dominoes instead of the expected 7. All other numbers (1,2,3,5,6) appear exactly 7 times. The visible dominoes containing 0 are: [0,0], [0,1], [0,2], [0,3], [0,5], [0,6]. The domino [0,4] is the only one with 0 that is missing. Similarly, checking the 4s: [1,4], [2,4], [3,4], [4,5], [4,6], [4,4] would be expected, but [0,4] and [4,4] are candidates; however, [4,4] is present in the set (visible in row 4), confirming that [0,4] is the missing domino.