A couple thoughts on Monopoly that have been clattering around my brain since a Thursday morning game.
The total amount of money in a Monopoly game is an upward-biased random walk, since money enters and exits the game through passing Go and landing on the tax squares. If you play with the standard rules then each player gets $200 on each pass around the board (for passing Go). On the other hand they’ll lose $200 each time they land on Income Tax (experience suggests the option of paying 10% is very rarely the right one) and $75 for each landing on Luxury Tax. Since the average die roll is 7, you have a 1/7 probability of landing on any square on each time around the board, so the average tax loss on each time around the board is $275/7 or about $39. So the average player takes in $200-39, or $161, on each time around the board. (This is obviously a very simple analysis – in particular I’ve ignored Community Chest and Chance cards and the existence of Jail, which collectively make certain squares more or less likely to be landed on.)
But now say you play with the house rule that you get $400 if you land on Go. That increases the average take on one trip around the board by $200/7 or about $29, to about $190.
Now say you play with the rule that taxes get put in a pot that is claimed by a player landing on Free Parking; that rule change is worth $39 on each trip around the board, since taxes remain in circulation. (The actual amount is more, since fees due to Community Chest or Chance usually end up in that pot when playing with this rule.)
The biggest change is seeding the Free Parking pot with, say, $500 whenever it’s empty; this gives each player, on average, an extra $500/7 on each trip around the board, or roughly $71. (It’s probably a bit higher, in fact; since Free Parking is downstream from Jail it should get landed on more by people getting out of Jail.)