Varying the Number of Companies

It's almost a year since I first posted here regarding the number of companies to include in the game, and over 6 months since I decided to remove some of the regional companies. Since then I have had a working set of 11 companies.

More recently, I decided to vary the number of companies for different numbers of players. In part, this is because 11 companies would be potentially unwieldy for three players. Also, having many more companies than players increases the opportunities for wanton asset stripping. My current draft has 2n+1 companies, where n is the number of players. I reason that each player should have the chance to start two companies (which is a rule of thumb I use when playing various combinations of 1825).

Thomas Lehmann's 1846 takes a similar approach. Tom's game uses n+2 companies, of which 4 are included in every game and the remainder are drawn randomly. This last element is appealing; it gives some variation between different games.

I'm currently wondering whether my 2n+1 approach is better than Tom's n+2. Many 18xx games use a fixed number of companies for different numbers of players, which suggests that a narrower range may suffice. Perhaps I could use n+5, giving 8-11 companies instead of 7-13. On the other hand, the BoardGameGeek review of 1846 suggests that it's rare for players to start a second company. That's not the sort of game I'm after.

Also, an n+5 formula would mean that for 5 players, the game would have exactly 2n companies. I'm worried that this might be a mistake, by being too symmetrical.

Whichever approach I take, I will need to vary the number of trains available as well (as indeed Tom did in 1846).