I'm reading Margaret Drabble's The Pattern in the Carpet: A Personal History with Jigsaws (for the subject matter—I've never tried one of her novels) and her brief description of the Game of the Goose is fascinating. As some quick googling will confirm, it's the original race-themed board game, an ancestor of Chutes and Ladders (a.k.a. Snakes and Ladders), invented (at least apocryphally) by Francesco de' Medici. I was peripherally aware of the game in Italian (and French and Spanish) culture, but I hadn't realized it had such a long history, probably as rich in cultural meaning as Lotería. While Jules Verne wrote a novel structured around it, it has been the basis for Italian and Spanish game shows, and there's a museum of the game in France, it appears no one has yet written a book about it—in any of the relevant languages! I call dibs.
But for now, I'm going to use it as lead-in to that other great parlor game, amateur etymology.
Square 58, just five spaces from the goal, is the unluckiest spot to land on: it sends your marker all the way back to the start. Though it's usually marked with a (human) death's-head, many of the rules and descriptions (including Drabble's) casually use the phrase "your goose is cooked" to describe what happens. But really, if you imagine a goose dying, wouldn't you assume it's because someone is going to cook it? I'm sure some scientists study goose mortality in other contexts, but for most of us, whether we eat them or not, the ideas of death and cooking are culturally linked when it comes to geese. Considering that there is no clear origin of the phrase—among the prominent theories is the notion that it refers to the burning at the stake of pre-Lutheran reformer Jan Hus!—I'm going to speculate that, when the game hit England in the 1590s (it was entered in the Stationers' Register in 1597) one popular edition may have turned the obvious connection into a joke by printing the legend "Your Goose Is Cooked" around an image of a fowl dinner in square 58. The proof, if it exists, lies buried somewhere in a historical archive.
That's also the period when Shakespeare's career was taking off; the game may have been well-known when Mercutio (in Romeo and Juliet, Act II, scene iv) compared Romeo's jokes to a "wild-goose chase." (Romeo and Juliet was also published in 1597, though when exactly it was written is unclear. But Shakespeare used plenty of Italian sources, so why not a board game?) The standard explanation is that Mercutio is referring to a horse-racing game (with actual horses and riders) popular at the time—but why would a horse-chase use another animal as a metaphor? Perhaps the horse race game was devised from the board game, or perhaps the board game (back in Florence) was patterned after the horse race. In any case, since Mercutio is complaining that Romeo is leading him on an impossible chase of wits—more like a parlor game than a hunt or a horse race—I think it's possible that Shakespeare was alluding to the board game as well.
My last unwarranted speculation is about the verb "to goose." When a goose (or anyone or anything else) bites you on the ass, it's natural to jump forward a few feet; using the verb for the physical act doesn't require any detours through the history of games. But the verb also has a metaphorical use, as a (rudely or at least unexpectedly delivered) prompt to motion and action, and that could be related to the game. In Sports and Pastimes of the People of England by Joseph Strutt (2nd ed., 1903) we read: "It is called the game of the goose, because at every fourth and fifth compartment in succession a goose is depicted, and if the cast thrown by the player falls upon a goose, he moves forward double the number of his throw." In other words, a "goose" was something unexpected that made your piece jump ahead. The choice of imagery for the board game may well have derived from the physical experience, but there probably came a time when the game was more familiar than the goose itself, and if this use of the word comes from that time, then the game's to blame. An OED would probably answer this one yea or nay, but I don't have one handy.
I'll probably have more to say about The Pattern in the Carpet; I'm enjoying it, though more as memoir than for what it has to say about jigsaws, at least so far.