Rail Baron Strategies - Research with RB Player

by Steve Okonski

Are you a Builder, Connector, or Monopolist? When it comes to Rail Baron, the railroad purchasing strategy you employ can determine your success in the game. Builders prefer railroads that serve major cities, Connectors like railroads that connect well with their existing network, and Monopolists try to lock up cities in order to collect track use fees from opponents. But, which strategy is best? Does it depend on the number of players? Is it important to go first? Until recently, these questions have been difficult to answer. Now, a new Windows computer program, is beginning to shed some light on the topic. RB Player (or RBP, for short), is a shareware version of Rail Baron you can download free from http://www.insystem.com/rbp/.

RBP can play Rail Baron against you, as well as against itself. This latter capability is the key to analyzing the game in more detail. Via the "continuous play" option, RBP will play game after game against itself, and accumulate statistics. Depending on the speed of the computer, and other play options you select, the average game runs to completion in just a few minutes. If you let RBP run overnight, by morning, some meaningful statistics will have been generated.

JUST BUY THE BEST RAILROAD

When I last wrote about Rail Baron (Rail Gamer, April/May/June 1997), I described the importance of maximizing the value of your purchasing dollar by selecting railroads that serve the most probable cities. Basically, that's the strategy that dominates the purchases made by Builders, and, in most cases, is a good approach. However, there are specific game situations in which it's better to vary a bit from the Builder strategy. For example, if an opponent is headed for Miami, and is still far away, you should probably grab the SAL in order to collect the forthcoming railroad use fees. The optimal strategy is one that best balances the various factors that go into a purchase decision. But, what are those factors, and how much emphasis should be placed on each?

Here are some factors many people consider when deciding which railroad to purchase: the cities served, the cities monopolized, proximity to other cities, opponents' current use of the RR, opponents' future use of the RR, connections with existing RRs, duplication of routes, segmentation of existing network, value of this RR to opponents, and price. The RBP program looks at all these factors, and more, when deciding what to purchase; it then applies different weights (emphasis) to each and sums them. For each computer opponent, you control the amount of factor emphasis by selecting one of five Play Styles; the styles are associated with a famous person from railroading history:

Cornelius Vanderbilt - a Builder; emphasizes serving important (highly probable) cities

JP Morgan - a Connector; emphasizes assembling a well-connected network

Jay Gould - a Monopolist; emphasizes RRs that can lock out opponents from cities

James Hill - balanced; no special emphasis

IA Newby - random; no factors or emphasis (purchases RRs without performing any analysis)

RESULTS, BY STYLE

In order to empirically determine which strategies are the best, I had RBP play several thousand games against itself. I ran at least 400 games each of 3, 4, 5 and 6 players. In each, I included at least one Builder, Connector and Monopolist. The results (expressed as percentage of games won) are summarized in Table 1:

   

Number of Players

   
 

3

4

5

6

Builder:

35.2%

26.8%

24.4%

35.8%

Connector:

27.4%

21.4%

21.4%

27.8%

Monopolist:

37.2%

26.8%

23.6%

35.8%

Balanced:

-

24.8%

27.9%

-

Random:

-

-

2.5%

-

Table 2 shows the same information, except expressed as difference in percentage points from the expected average (3-player expected average is 33.3%, 4-player is 25.0%, 5-player is 24.4% (not 20%, due to adjustment for random player), and 6-player is 33.3% (twice 16.6% because there were two players of each style):

   

Number of Players

   
 

3

4

5

6

Builder:

+1.9

+1.8

0.0

+2.5

Connector:

-5.9

-3.6

-3.0

-5.5

Monopolist:

+3.9

+1.8

-0.8

+2.5

Balanced:

-

-0.2

+3.5

-

Random:

-

-

-17.5

-

The tables indicate that a Monopolist strategy works best relative to the others, but a Builder strategy is close (and slightly better in 5-player games). Determining exactly why this is the case is a whole study in itself. Monopolists dominate 3-player games; because there are so many railroads to go around, a Monopolist can spend time and money locking up cities without much worry of getting shut out of large areas. A Connector strategy fares poorly regardless of the number of players. I think this indicates it is more important to serve and monopolize cities than to access them conveniently (i.e. via the shortest distance).

RESULTS, BY RAILROADS

Another way to garner useful information from this study is to look at which railroads are most often associated with victory. RBP knows which railroads were owned by the winner, and keeps a running total. In the information below, "best RRs" means the five railroads most frequently owned by the winner, and "worst RRs" means the five railroads least frequently owned by the winner. It is important to note these are not the groups of railroads owned by the winner; they are simply the individual railroads owned most and least frequently.

3 players

Best RRs: PA, UP, AT&SF, C&NW, SAL

Worst RRs: B&O, C&O, B&M, MP, T&P

4 players

Best RRs: PA, UP, AT&SF, SLSF, SP

Worst RRs: B&O, C&O, B&M, L&N, CB&Q

5 players

Best RRs: PA, UP, AT&SF, SP, CRI&P

Worst RRs: B&O, C&O, CB&Q, IC, GM&O

6 players

Best RRs: PA, AT&SF, UP, SP, T&P

Worst RRs: C&O, B&O, B&M, SAL, CB&Q

Regardless of the number of players, the PA is most often associated with victory. In fact, the PA was owned by the winner in over 50% of the games! Expressed another way: make the PA the cornerstone of your network and you'll win more than half the time! The three large railroads (UP, AT&SF and SP) all show up frequently in the best lists; that makes sense because a player without any of them will have difficulty finding inexpensive routes in the west. The B&O and C&O appear in all worst lists; I suspect the geographic overlap with the PA is the cause. If you own either B&O or C&O, usually you don't also own the PA; however, if you do also own the PA, the usual result is your network is too weak in other areas of the map to win.

It is very interesting that two railroads appear in both the best and worst lists: SAL and T&P. The SAL (which monopolizes Miami) is one of the best in 3-player games, and one of the worst in 6. This confirms the result found earlier that monopolies are more valuable when there are fewer players in the game. The T&P is the opposite: it monopolizes nothing and mostly serves cities already well served by other railroads. Therefore, the T&P is a better choice in games with more players.

You may suspect that these results are biased because RBP's computer players (except IA Newby) are making decisions about which RRs to purchase. That will influence the frequency with which the railroads are owned by the winner. Since that's a valid argument, I also tried a 5-player game with only Newby computer players. Newby makes railroad purchases at random, based on available cash. Here are the results:

5 players, random purchases

Best RRs: UP, PA, AT&SF, NYC, CB&Q

Worst RRs: IC, SLSF, B&O, C&O, MP

There is some variance compared to the non-random 5-player game, but a fair amount of duplication. Since in most human-only Rail Baron games, people do not purchase railroads in a totally random fashion, the earlier (i.e. non-random) results are probably more indicative of the true relative value of the railroads.

RESULTS, BY TURN ORDER

Who goes first in Rail Baron is decided randomly, so you do not have much influence over this aspect of the game. But, just how important is it to go first? RBP also tracks the results based on the turn order. In every situation (3, 4, 5 or 6 players), the player going first had the highest winning percentage. This is probably because the player going first has the best chance at buying the best railroad: the PA. The player going last or next to last had the lowest winning percentage. The difference was the most extreme in the 5-player game, in which the player going first won 26.4% of the time, and the player going last won only 10.2% of the time. So, try to go first!

IMPORTANCE OF THE MAP

How much influence does the map have on the game? I suspect a fair amount; this can be investigated with RBP's help. RBP is an "open system" which means that not only does it work with the standard USA map, but also with other maps. You can even create your own maps. One alternate map that is already available is named UNE. UNE zooms into the northeastern United States and includes 30 historical railroads with over 50 cities stretching from Bangor, Maine to St. Louis, Missouri. I ran a 400-game test with 4 players (the same players as for the test with the USA map). Table 3 compares the results:

 

USA Map

UNE Map

Builder:

26.8%

21.1%

Connector:

21.4%

23.4%

Monopolist:

26.8%

30.2%

Balanced:

27.9%

25.3%

On the UNE map, which has more and shorter RRs than the USA map, the Monopolist strategy does even better. Also of note is the Builder's drop into last place. What is the cause of these effects? More experimentation is necessary to learn if these findings hold for games of 3, 5 and 6 players. Perhaps you'd like to investigate, or perhaps you'd simply like to play Rail Baron. RBP can help you with both