Introduction

The goal of this article is to provide you some basic statistics about Ticket to Ride (USA Map), so that you can make well-informed decisions and optimize your strategy accordingly during a game. We do not study any strategies because that would make this article way too long.

This article is created by the knitr package of R. Since this is written for gamers but not programmers, I hide all the codes. Also, due to my motivation to practice ggplot2 I make a lot of histograms instead of using just a simple table to present the same informatiom. Comments and suggestions are welcome and can be sent to wanshunwong at gmail dot com.

Regions

Regions and Cities

We divide the board into 6 regions: Northeast, North Central, Northwest, Southeast, South Central, Southwest. The division criteria is given by the phyiscal board of the game, since it is made up of 6 equally-sized smaller boards. The distribution of cities over the 6 regions is as follows:

Regions and Routes

Next we look at the distribution of routes. Double-Routes are only counted once, i.e. they are treated the same as Single-Routes, while cross-region routes are counted twice. For example, Sault St. Marie-Winnipeg is counted as both as a route in NE and a route in NC.

SC has the most number of routes, which is kinda expected since it has the most number of cities, and most of them are connected to many neighbours.

By using the above distribution, we can calculate the means of route length and points of each region.

We see that on average, claiming a route in NC, NW and SW will cost you one more Train Car card than claiming a route in NE, SE and SC. This is also reflected in the mean of route points.

Here we see huge discrepancies among different regions (up to a difference of 85%). However we also need to take into account that long routes needs more Train Car cards and thus more turns to claim, therefore the actual difference in points during a game would be slightly smaller. Nonetheless, the point is that if you focus on claiming routes in NE, SE and/or SC, you will need more Destination Tickets in order to beat your opponents developing in NC and NW.

Destination Tickets

Destination Tickets and Points

A brief summary of the ticket points is as follows:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    4.00    8.25   11.00   11.63   13.00   22.00

Notice that the mean and the median are both around 11 points, which is only 1 point higher than claiming a length 5 route, and 4 points lower than claiming a length 6 route. This doesn’t automatically mean that you should just give up your initial Destination Tickets and focus on claiming long routes, since failure to complete Destination Tickets will deduct your points (on average a swing of 22 points for each ticket). However, if you are thinking about getting more Destination Tickets in the middle of the game then you should definitely keep this summary in mind.

Destination Tickets and Regions

In this section we classify the Destination Tickets according to the regions of the destination cities.

Out of the 30 Destination Tickets, nearly a quarter of them are NE-SE. Moreover, 4 are NE-SC. Another way to phrase this is that, since there are 11 tickets belong to NE-SE and NE-SC, you are expected to draw 1 at the beginning of the game and in the Draw Destination Tickets action.

We can also look at the region of each destination city of a ticket.

Half of the Destination Tickets have a destination city in NE. Therefore if you want to win by Destination Tickets, it is quite likely you have to get your hands on NE.

We remark that even though only 11 tickets having a destination city in SC, SC plays an important role in those NE-SW and SE-SW tickets (2 each). Hence we can also think that half of the Destination Tickets involve SC.

Destination Tickets and Cities

Here we take a closer look at the destination cities of the tickets.

##          name ticket_destinations region
## 1 Los Angeles                   5     SW
## 2    New York                   4     NE
## 3     Chicago                   3     NE
## 4    Montreal                   3     NE
## 5     Houston                   3     SC
## 6     Atlanta                   3     SE
## 7       Miami                   3     SE

Out of the 7 cities that show up on at least 3 Destination Tickets, 3 of them are in NE which is not surprising at all by the previous section. The surprising fact is that it is Los Angeles, a city not in NE, being the city showing up the most frequently on Destination Tickets.

Routes

Route Lengths and Colors

In this section we study the distribution of different colors. In particular if we ignore the Destination Tickets and just focus on claiming routes, which colors perform better than others?

First we plot a histogram of route length. Here Double-Routes are counted twice. For example, Boston - New York is counted both as a Red route and a Yellow route of length 2, and Boston - Montreal is counted as two Gray routes of length 2.

The first thing we notice is that there isn’t any huge difference among the different colors. Each color has exactly one route of length 6. At length 5, we see Green and White have a slight advantage by having two routes. However this is balanced by the fact that they have one less route at length 4.

The second observation is that while there are a lot of Gray routes of length 2 (because of the double counting), there are not many Gray routes of length \(\geq 4\). So if there are more than one player trying to win by claiming routes alone, those few long Gray routes are worth fighting for.

Next, we plot a histogram of route length, counting Double-Routes only once. We create a new label “Dual” for Double-Routes with different colors, e.g. Boston - New York. This is mainly for 2-3 player games.

The major observation is the absense of Orange at length 4 and 5, together with the absense of Purple at length 5. i.e. They only appear in Double-Routes at those lengths. This could be a big disadvantage in the late-game phase of a 2-3 player game.

Route Points

The maximum number of points you can get from claiming routes is 109, achieved by getting seven length 6 routes and one length 3 route. Obviously this fact is kinda useless because your opponents will surely compete with you on those long routes. Therefore a better benchmark is computed by the following method:

Suppose in a 4 player game players A, B, C and D all try to get as many points from claiming routes as possible. First they will split eigth length 6 routes. Then A will get the last length 6 route. Since there are no more length 6 routes left, B will start claiming length 5 routes, and so on. Note that there are ten length 5 routes in a 4 player game, therefore the process will go as B, C, D, A, B, C, D, A, B, C. After player C grabbing the last length 5 route, D will turn onto length 4 routes.

We will continue this process until every player uses all his/her cars, and compute the points for all players, and then take the average. The resulting number can then be used as a benchmark about how well you are doing in getting route points. Because of the lack of a better name we will just call it Benchmark Point.

In practice we will need to claim (at least) several short routes for our Destination Tickets, thus our points from routes are usually lower than the Benchmark Points. Nonetheless these numbers give you a good estimation of how well you and your opponents are doing.