The "board" in aboveboard is not a plank or a ship's deck. It is a table, and specifically a card table.
Old English bord meant a plank or flat surface. Etymonline says that by late Old or early Middle English it had stretched to mean "table." That sense survives in phrases about meals and meetings. Board meant food served at a table by the early 1300s, and a council table by the 1570s.
At the card table, the phrase described fair play. Word Histories explains that being above board meant keeping your cards in view, above the table, so no one could suspect cheating. Samuel Johnson's 1755 dictionary spelled it out. He called it an expression borrowed from gamesters "who, when they put their hands under the table, are changing their cards."
The earliest known use is from the pamphleteer Thomas Nashe. In The Terrors of the Night (1594), he wrote of someone who "playes aboue-boord," still in a card-playing setting. Five years later, in Lenten Stuffe (1599), Nashe used it figuratively. His Leander "durst not deal above-board," meaning he could not act openly. Etymonline gives a later first date for the word, the 1610s, with the sense "in open sight, without trickery."
The Phrase Finder adds a 1616 example from Beaumont and Fletcher's play The Custom of the Country. A character warns, "if you play not fair play and above board too, I have a foolish gin here."
The opposite came along early too. Etymonline records underboard, "secretly, unfairly," by the 1580s. In 1603 Sir Christopher Heydon compared a trickster to jugglers who distract the audience while he "plaies vnder board." In 1611 Cyril Tourneur wrote "He does it under hand," and underhand became the lasting opposite. The Phrase Finder notes that "below board" and "beneath the board" are not recorded.
A popular alternative story claims the phrase comes from ships, with pirates hiding below deck to fool their victims. The Phrase Finder finds no evidence for it. The card table explanation is the one the early quotations support.
The table idea still works today. Something done under the table is dishonest, Etymonline notes, while an aboveboard deal has nothing hidden beneath it.