**Note: This post assumes that the reader has a decent amount of Monopoly experience and fully understands the ideas behind mortgaging and unmortgaging.
For those of us who have been there before, it’s one of the trickiest late-game decisions to make: should you mortgage your valuable set of four railroads to help build an additional four houses on the oranges (or two houses on the dark blues, etc), or is it not worth the loss of significant income you are already getting ($200 per railroad hit)?!
Fortunately, there is a highly effective and easy solution to help obtain the best of both worlds. I call it the railroad shuffle.
The key behind this tactic is that the rent owed by someone landing on your railroad is based SOLELY on the mortgage-status of that particular railroad (NOT all four) and the number of railroads you OWN (regardless of their status). In other words, if someone lands on an unmortgaged Reading Railroad (one of four that you own), you are still owed $200 even if the other three railroads are mortgaged. Pretty sweet indeed!
So how do we use this gem of a rule to our advantage? Well, it’s actually quite simple. We mortgage three out of the four railroads we own (or two out of three), use the extra $300 to improve our houses/hotels situation, and continue to benefit from owning the full set of railroads.
But how to know which railroad to keep “alive”?? Well, since mortgaging/unmortgaging are allowed at any time, we can simply apply the following procedure before each roll:
1. Assess the current roller’s board position. Which railroad is within striking distance (note that there will ALWAYS be at least one railroad within 12 spaces or a single roll’s total)?
2. Is the closest railroad currently unmortgaged? If yes, then we are done.
3. If no, then we SWAP the currently-unmortgaged railroad for this one. The price for doing this…$10!!!
That’s right! It only costs $10 to mortgage one railroad and unmortgage another (this is because each railroad has the same value and there is a 10% unmortgaging fee on the mortgage value of any property).
So in short, what I like to call the railroad shuffle costs a mere $10 max (often it costs nothing if more than one opponent are near each other) per opponent roll to always have a chance at getting $200 on that roll. From a long-term expected value perspective, let’s look at the math to see when it makes sense to apply this strategy:
- Let C represent the cost of swapping an unmortgaged railroad (aka $10).
- Let p represent the probability of your opponent landing on the newly-unmortgaged railroad.
- Let R represent the revenue made if your opponent lands on the railroad.
For the cost to be justified, we setup the following break-even analysis/formula:
p*R >= C
To solve for p, let’s look at the aforementioned scenario of owning four railroads:
p*200 >= 10
p >= 1/20
So, it looks like this strategy makes statistical sense for all but two rolls: 2 and 12 (see footnote for caviat).
Now when owning three railroads:
p*100 >= 10
p >= 1/10
In this case, the railroad shuffle makes sense for the following space differentials/rolls:
So even from a strict numbers perspective, the railroad shuffle makes a lot of sense! And when we consider that the $100 or $200 gained from one railroad hit is often the difference between three houses on New York (for example) or two houses, the importance of the railroad shuffle becomes even more apparent.
Of course if you have plenty of cash on hand AND houses or hotels on a nice color group, then this strategy is not only unnecessary; it is counter-productive (remember that there are ways for your opponents to land on your railroads via Chance cards too).
** A quick note on the special case of an opponent being two spaces away from the nearest railroad:
Whenever this occurs, then your opponent is actually within striking distance of TWO railroads (2 and 12 spaces away). This, of course, doubles the probability of his/her landing on one of your railroads but requires having two (rather than one) railroads unmortgaged. So unless you’re ok with leaving two railroads unmortgaged, I would just stay away from doing anything for these rolls.