How do the Monopoly odds change when the board is played in reverse?

One semi-popular house rule is to play Monopoly as usual, but move the pieces counter-clockwise instead of the usual clockwise - that is, hit the higher-end properties first and move down toward the lower-end ones. Another related house rule is to play in the normal fashion, but when someone lands on Free Parking, either that player or all players reverse direction. (Yes, that means different players could be moving in different directions. I didn't make up the rule.)

In the above versions, how does this affect the winning strategies? As discussed there, the properties landed on most often are the oranges and reds. Does reversing the board play for some or all of the game affect those odds to enough of a degree to make a difference in which monopoly rakes in the most revenue?

The key change in reversing the direction of movement is the fact that players now leave Jail in the opposite direction. The oranges and reds are particularly profitable because they are within 1-2 rolls of Jail, among other reasons. When moving counterclockwise, the dark purples and dark blues are now in a more often visited area, so I would expect their value to increase significantly, while the value of the orange and reds would decrease commensurately. Even the light blues, which are already among the best property groups, would get a boost from being in front of, rather than behind, Jail.

• @DonielF - True, but it's the only thing that would really change when moving backwards. Chance cards won't change, nor will the development cost/profitability ratio. Commented Apr 21, 2017 at 12:36

I haven't heard of this variation. Nuclear Wang's analysis is correct. Note the Dark Blues getting a frequency boost along with their high rent would cause ownership of that color group be key to winning a reverse game. To take the analysis further, take a look at the following site: http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml

This site includes the Markov chain analysis results for the forward game. Markov chain analysis is rather involved. The key results are shown in the Long Term Probabilities for Ending Up on Each of the Squares table.

Could estimate the reverse game's probabilities as the probability of the square opposite the Jail/Go to Jail axis. So as an example the Park Place gets the probabilities shown for Indiana Ave. Its "Probability % (Jail Long)" increases from 2.0595% to 2.5671%. This makes Park Place 25% more valuable in the end game. Calculating the boost for Boardwalk is complicated by having cards that direct you to this space, but no card directing you to its reverse counterpart, Kentucky Avenue.

You would usually not skip the Go square (and the chance to collect \$200) before going to Jail. The exceptions would be the Chance square between Oriental and Vermont (light blues), and the community chest square between the two dark purples. Even so, you would collect your \$200 on the tenth square after leaving Jail instead of the 30th, and you would not have to "run the gauntlet" of "Go to Jail before reaching Go.

"Jail" would sometimes spare you the relatively cheap Yellow and Red monopolies, (instead of the greens and dark blues) but when you leave, you'd be heading toward the relatively cheap Light Blue and Dark Purple monopolies.