What's the etymology of 'Deck' with a pack of cards?

The origin of deck applied to a pack of playing cards is not clear; John Ayto, in his Words Origin suggests that

The word’s application to a pack of cards, which dates from the 16th century, perhaps comes from the notion of the cards in a pile being on top of one another like the successive decks of a ship.

OED:

Deck n.

Etymology: In sense 1, apparently of Flemish or Low German origin. In sense 1, probably < Middle Dutch dec (neuter) roof, covering, cloak, pretext (apparently < decke < Old Germanic þakjom , from same root as deck v.)

But in the nautical sense, 2, the word is not known in Dutch before 1675–81, when dek (neuter) appears as a synonym of verdek [edit Greybeard = covering]:, Thus, deck in the nautical sense, appears to be known in English 160 years earlier than in Dutch. It may be simply a specific application of the general sense ‘covering’, or it may come more immediately from the Middle Dutch sense ‘roof.’

I. A covering, platform, or surface.

†1. A covering. Obsolete.In quot. 1466 apparently some material used for covering; with 1712 cf. Dutch dek ‘horse-cloth’.

1466 in Manners & Househ. Expenses Eng. (1841) 348 My mastyr paid to John Felawe, for xij. yerdes of dekke for the spynas, iijs.

This gave rise to:

2.a. Nautical. A platform extending from side to side of a ship or part of a ship, covering in the space below, and also itself serving as a floor; […]. The primary notion was ‘covering’ or ‘roof’ rather than ‘floor’: see the quote [...] 1466 at sense 1, where the ‘dekke for the spynas’ or pinnace, may have been a covering of canvas, tarpaulin, or the like.

1513 E. Echyngham Let. to Wolsey in A. Spont Lett. & Papers War France (1897) X. 152 And bycause I hade no rayles upon my dek I coyled a cable rounde a[long] dek, brest hye, and likwise in the waste.

The above seem to have been the earliest meaning (compare verbs to deck and to bedeck - to decorate by covering with items) but within a short time, we have our deck of cards

II. A pack or pile of things, and related uses.

5. a. [Deck:] ‘A pack of cards piled regularly on each other’ (Johnson 1765); also the portion of the pack left, in some games, after the hands have been dealt.

1594 1st Pt. Raigne Selimus sig. F4v If I chance but once to get the decke, To deale about and shufle as I would.

1594 R. Barnfield Shepheard Content viii. sig. Eiij Pride deales the Deck whilst Chance doth choose the Card.

The connection seems to be that the cards cover each other.

But looking at the verb which appeared later, we have:

II. To provide with a deck; to assemble or pile up.

4. Nautical. To cover as with a deck; to furnish with a deck; to deck in, to deck over, to cover in with the deck, in ship-building.

1624 J. Smith Gen. Hist. Virginia v. 175 At last it was concluded, to decke their long boat with their ship hatches.

1700 S. L. tr. C. Frick Relation Voy. in tr. C. Frick & C. Schweitzer Relation Two Voy. E.-Indies 6 Flat Boats..tho' small, yet so close Deck't, that in a rough Sea they will go quite under the waves and retain no water.

The sense of "assemble" is perhaps clearer in the 1700 quote.

The idea of a deck of cards thus seems to be a combination of the cards being assembled and the cards covering each other (so the players do not see them).