I am referencing this analysis to analyze expected incomes and the number of rolls needed to recoup a given investment.
I was able to compute the expected number of rolls to recoup the cost of a simple property, but was not able to compute it correctly for the other columns in this table.
Apparently, it says "These numbers were calculated by taking the cost of whatever was bought and dividing it by the increased average rent from the table above".
By this logic, it makes sense that for Mediterranean Avenue single property, the number of rolls is 60 (the price of the property) / 0.0426 (the expected single property income given in this expected income table)
I'm struggling to compute the other numbers in the first table I linked above. For example, for one house, the purchase cost is 50, and the expected income is 0.2131 from the expected income table.
But, 50 / 0.2131 is nowhere close to 390.9837. What am I missing?
$0.2131$ is the total expected income per roll from Mediterranean Avenue when it has one house on it. In order to earn that expected income, you have to buy the property and build a house on it (which means you also have to own Baltic Avenue).
Before you built the house, you owned both of the properties in that block and had an expected income of $0.0853$ from Mediterranean Avenue. Buying the house increased your expected income, but only by $0.2131 - 0.0853 = 0.1278$; that is, the benefit of buying the house is just how much more you earn with the house than you were already earning without it. In the explanation of the tables, this is called the increased average rent.
This implies that the expected number of rolls to recoup the cost of the house is $$ \frac{50}{0.1278} \approx 391.2. $$
In the paragraph just before the table of "Expected Number of Opponent Rolls to Recoup Incremental Cost (Short Jail Stay)", the author points out that the table is calculated using full-precision numbers from the previous calculations, but the tables give only four digits of precision for the earlier numbers and therefore will not produce the exact same answers seen in the tables that come afterward. The result above is within about $0.1\%$ of the corresponding tabulated figure, which is within the accuracy we might expect.
The column "Last Property on Block" seems to take into account the fact that when you own the whole block, all of the rents for unbuilt properties on that block are doubled. For example, the "Last Property on Block" entry for Mediterranean Avenue assumes that you land on Mediterranean Avenue when it is unowned, that you already owned Baltic Avenue by that time, and that you then buy Mediterranean Avenue for full price ($\$60$).
Before you buy Mediterranean Avenue, you have $0.0865$ expected earnings from Baltic Avenue plus whatever you expected from any other properties you already own. After you buy Mediterranean Avenue, you have $0.1730$ expected earnings from Baltic Avenue, plus $0.0853$ from Mediterranean Avenue, plus whatever you expected from other properties. The increased average rent therefore is $$ (0.1730 + 0.0853) - 0.0865 = 0.1718,$$ and the expected number of rolls to recoup the price of this particular purchase (based on these numbers) is $$ \frac{60}{0.1718} \approx 349.2, $$ which again is close enough to the tabulated result.