Monopoly Question

[GTSamIAm]

Remember, there are 40 spaces counting Go as number 1. I have the green monopoly. My opponent has me beaten badly, has St. Charles monopoly, Boardwalk monopoly, yellow monopoly, three railroads. It's bad news.

I just landed on the third yellow, that's the 29th space, Marvin Gardens. I need to take one house off my greens to pay the opponent. My opponent had just landed on the third green, the 34th space, Pennsylvania Ave.

Which green should I take the house off of for maximum profit? The first, Pacific Ave., the second, No. Carolina Ave., or the third, Pennsylvania Ave.? Or in other words in most cases but not necessarily, which green does he have the least chance of hitting on the next rotation around the board?

[AaronBrown]

I did an article on Monopoly valuations once, but I only considered long-term questions like what is the value of various Monopolies and how should you build on them ignoring the square your opponent in on now. This article on Monopoly Probabilities (not mine) will show you how to solve the problem.

[MickeyHoldem]

Take the house off Pacific

Here's the chance each number (up to 40) has of getting rolled:

2 0.027777777777778
3 0.055555555555556
4 0.084104938271605
5 0.114197530864198
6 0.146626371742112
7 0.182227366255144
8 0.166345759983234
9 0.155526024996190
10 0.147783795687692
11 0.141275313987112
12 0.134199441151658
13 0.124703575323390
14 0.138567339985884
15 0.145771350282075
16 0.148354627183743
17 0.147889983414447
18 0.145672338925150
19 0.142886274610975
20 0.140764094418021
21 0.140744872286715
22 0.141558293889562
23 0.142503054290152
24 0.143243171224347
25 0.143649910420996
26 0.143670481132249
27 0.143207188969124
28 0.142763608813836
29 0.142528050732930
30 0.142514760658092
31 0.142651801849006
32 0.142836086293657
33 0.142971433394364
34 0.143002869896381
35 0.142959359946810
36 0.142889015168303
37 0.142829956855659
38 0.142801528128473
39 0.142805773389582
40 0.142832236336061