You are making the approximation that each square is equally likely to be hit. This is not correct, due to jail and the chance/community chest cards but let's accept that. In that case, the chance of hitting a specific square on a given circuit is $\frac 17$ as the average roll is $7$. By the linearity of expectation, you expect to hit a color group $\frac 37$ times the number of circuits and to hit a railroad $\frac 47$ times the number of circuits. In the long run, you will hit the railroads $\frac 43$ times as often. Whether this is better also depends on the value at each hit. In the US version of the game the railroads collect 200, while a hotel on the greens collects 1275/1400. The railroads are actually some of the most trafficked squares due to the cards.

If there were no Chance or Community Chest cards or triple doubles rules landing you into Jail then every property would have an equal 1/40 likelihood, but that's not the case and that's what makes the difference, and that is what needs to be analyzed.

Those two decks have you advancing to the nearest utility or railroad (which depends on where you are located), or specifies a railroad (see a railroad theme going on here), or specific places (St. Charles, Go or Jail, etc.).

Also, the likelihood of triple-doubles rolled on the dice $\frac{1}{6^3}$ lands you into Jail no matter where you are located.

Also, a typical game of Monopoly is limited to laps around the board measured in dozens not infinity, this should make the realistic odds to strongly favor squares that are 7, 5 & 6 moves ahead (and repeated several time) from the key properties where a play is "advanced to" (e.g. nearest railroad and Jail being the largest odds).

In short, if someone wants to design a brute force game analyzer, I think you would be best served to determine the odds of being sent to various locations (like the railroads and others) and from those locations determine the odds with a limited number of dice rolls to see which properties end up being best.

We all know it's going to end up being the railroads, then utilities, and then favoring some orange, red and yellow (at least based on what my experience gut tells me), but then it's proving this with math.

## Best Answer

Answer:On average, you will pass Goapproximatelyseven times before hitting Boardwalk (where your very first move counts as passing Go).Explanation:Each turn, you move forward seven squares on average. This means you land on about one seventh of the squares of board on average during each pass around the board. In particular, during each revolution, there is about a one seventh chance you will hit Boardwalk. Therefore, it will take approximately seven revolutions on average to land on boardwalk.This is only an approximate answer, but computer simulations confirm it is very close to the truth. See for yourself.