Which parts of Denmark are thriving and which are not? This notebook explores how the distribution of people and wealth has changed in Denmark in the period 2013 - 2023. I find that most Danish municipalities are loosing settlers to a few urban areas and that there is an increasing gap in population, wealth, and average age between the thriving urban centers and the rest of the country.

A recent surge in interest rates combined with a previous surge in house prices suggests that right now (June 2022) might be a very expensive time to loan for a house. This notebook explores how much of an average salary has been required to maintain a loan for an average house throughout recent history. I find that mortgage expenses relative to salaries are higher now than they have been for 10 years, but the situation is still better than at the peak of the financial crisis. The data also shows that it was very cheap to loan for a house in the early 90's - especially if you brought savings to the table.

This notebook explores how the probability of winning a bidding round for a house depends on the size of the bid. I find that a bid 6% above the price yields a 90% probability of winning a random home sold above the price and that bidding more than this will only slowly increases your probability of winning the bid. Interestingly, the price class of the home does not have much impact on how many percent to bid above the house, but the type of house does. In general, one must bid a larger fraction above the price to ensure a villa.

This notebook explores how likely different tournament systems are to yield the best player as the actual winner. Tournaments are simulated based on data from the online chess community lichess.org, which allows us to derive the probability of game outcomes based on the rating of the individual players. We find that single- and double elimination tournaments are equally efficient at finding the best player, when taking into account the number of games played. Round-robin, however, is strictly less efficient than the other two systems.