The map of El Dorado County that comes in 2e and 3e Boot Hill shows the locations of mountainous and forested terrain, an area of badlands, a network of trails or roads, and major rivers and lakes, but it only shows two settlements, Promise City, the seat of El Dorado County, and Fort Griffin, an army outpost. The 2e rule book contains a list of features for referees - just names, in most cases - to add to their county map: towns, with brief descriptions of each, plus mountain ranges and hills, rivers and lakes, an Indian reservation and trading posts, and mines and ranches. It feels a little like B1 In Search of the Unknown for D&D or TS001 Operation: Sprechenhaltestelle for Top Secret, but with even less detail on the environment than those modules, or to the deck plans on the Warden in the first Metamorphosis Alpha. I love this approach to modules: it assumes from the motherlovin' giddyup that every campaign will be unique, that it's expected and desired for my El Dorado County to be different from someone else's El Dorado County.
The base map of El Dorado County and environs is gridded with hexes. The area covered by the map is impressive - the map itself is poster sized with a grid 111 hexes high by 148 hexes wide. with roughly 4.5 hexes to the inch. According to the rules (2e BH, "The Maps," p. 16), "The scale of the [county] map is one hex = 2 miles."
This means we're talking about a pretty extensive area for El Dorado County and those portions of its neighbors shown on the map, roughly 222 miles by 296 miles, or nearly 66,000 square miles of country to explore for the adventurers, and to populate for the referee. In terms of settlements, the rules offer twenty-two examples of towns and other communities for the referee to place on the map. The size of towns isn't give in terms of population, but in terms of number of buildings - the largest, Promise City, the only civilian settlement printed on the map, is given as "about 75 buildings," with the printed poster map showing "about 60 of them" (2e BH, "Towns," pp. 28-30).
Twenty-two settled hexes out of over 16,000 would seem to be the very definition of 'wide open spaces,' but are all those hexes really that empty? Many of the town descriptions describe nearby farms and ranches which the towns serve, but no other information beyond the names of a few of the largest ranches in the county is provided in the core rules. The most of the published adventures for BH don't add a lot to this - BH3 Burned Bush Wells, frex, only offers the locations of the ranch headquarters by their brands imprinted on the map - with the exception of BH4 Range War! which goes into significant detail, including a custom map with hexes representing 100 acres.
Before I dig into that, since Range War! tells us the area of its hexes, what's the area of the hexes on the campaign map? The formula for the area of a hexagon is A = (3√3 s2)/2 - deriving the length of a side from the height is s = h/√3. This gives an area of slightly less than 3.5 mi2 per hex - if we round off to 3.5 mi2, then we get 2240 acres per hex on the El Dorado County map.
Towns themselves take up an utterly insignificant portion of that acreage - Promise City, the county seat and largest settlement, occupies a mere 0.07 acres as shown on the printed town map - so how about those farms and ranches? As a baseline, let's start with that ubiquitous feature of the Western landscape, the homestead. Under the 1862 Homestead Act, settlers could claim a 160 acre parcel of land which they were then obligated to improve by building a dwelling and growing crops in order to obtain clear title after five years. The system was onerously abused by land speculators and most actual homesteads failed because the acreage allotted was insufficient for the climate west of the Mississippi River, but it's a useful means of estimating how many individual family farms might be found in a hex. A hex of 2240 acres will support fourteen homesteads, and a seven-hex cluster - the town hex and a hinterland of the six immediately adjacent hexes - may contain up to 98 homesteads.
Like the rest of the country, the population of the West in the late 19th century is predominately rural - in the 1870s, the period in which our campaign takes place, the US urban population as a percentage of total population was just under 26%, but this varied quite a bit in the western states: Nebraska and Kansas average around 16% while Texas an New Mexico are closer to 6%. I could very easily find myself going down the rabbit hole of researching the average rural versus urban household size in the US of the 1870s so I can derive a figure for the rural population surrounding an urban center based on the number of buildings in a town as indicated in the core rules, but while that would be an entertaining intellectual exercise, for purposes of playing a game I'd rather have a handy rule of thumb, so here it is: each building in a town supports, and is supported in turn, by five homesteads.
That takes care of the sodbusters - how about the cattlemen? As I mentioned a few paragraphs back, BH4 Range War! offers some ranch acreages with which to work. In the module, the "largest of the . . . County ranches," the McCloskey Ranch, "covers 26 square miles," giving it an acreage of 16,640 acres and a footprint on the campaign map of a little more than seven hexes - about the same as 100 homesteads. The Farrigan Ranch, on the other hand, is eleven square miles, or 7040 acres, covering slightly more than three hexes on the campaign map. The Hyde Ranch, which is shown on the module map but not described in the text, is closer to 11,000 acres or five hexes. Range War! is something of an oddity - it sets Promise City in Grant County, Oregon, not El Dorado County, 'somewhere in the Southwest,' and the author, Philip Taterczynski, clearly knows something of the settlement of the Oregon Territory, frex, referring to one of the farms outside Promise City as a "Donation Claim of 320 acres." Oregonian public land grants tended to be second in size only to those vast tracts granted to the railroads, so ranch sizes may be fairly large butthey provide a reference point for deciding how much land is occupied around a town by ranches. Moreover, a ranch of three to five hexes in size fits what's represented on the map for BH3 Burned Bush Wells, with the Rocking G perhaps being more in the seven hex range.
It's possible to reverse engineer this as well. BH3 Ballots & Bullets gives the number of cattle owned by the three big ranchers outside Promise City - as described in an article in The Dragon 18, a longhorn requires two acres of grassland, so this would suggest that, at a minimum, the Shaws of the Lazy S own "about 300 cattle," suggesting a range of, at minimum, 600 acres. Since all three of the big ranchers in BH3 are wealthy and influential in local politics, to the point of being a driving force behind one of the factions in Promise City, I would say this is an extreme low end at best.
El Dorado County should have plenty of small ranchers as well: "Four hundred and sixty acres might be little to you, Nathan, but it was a lot of country to me." For our campaign, to keep things simple, small ranches occupy 320 acres, equivalent to two homesteads, but they tend to be spread out more, such that there are never more than five in a hex. A settlement described as a cattle town will have 1-5 large ranches in its hinterland, with a number of small ranches equal to one-half the number of buildings in town. Stetson City, "a ranching town" of "about 20 buildings," has one large ranch of seven hexes and two of five hexes plus ten small ones occupying the equivalent of about two hexes.
All of this is subject to good judgement. In our campaign, frex, it's an established fact of the setting that the large ranchers - the Shaws, the Morands, and the Kings - drive small ranchers off 'their range,' so there aren't thirty-six small ranchers in the vicinity of Promise City. Plaza del Lobo, due to its "isolated locale" and "[r]ecurring rumors of bad water," doesn't have anything close to the seventy-five homesteads its fifteen buildings might warrant. Wild Creek, "a small but bustling lumber town," has only a couple of small farms and a ranch which provide supplies to the lumberjacks. These are guidelines, no more, no less.
So, to the titular question: how many hexes is the Ponderosa? According to a statement made in the first episode of Bonanza after the pilot, the Cartwright spread is a thousand square miles, equal to 640,000 acres. That puts the Ponderosa at a shade under 286 hexes, which is a lot of ground but still only a small piece of the more than 16,000 hexes which make up the BH campaign map.