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How the game finds the “Best” train
Mexican Train For Windows, calculates the best train based on the following three basic rules: (Note that trains in the following examples start on the right side of the page with the 12, like they would be organized in our game).
- The train with the most dominoes is best.
In this example, the first train has more dominoes and is therefore better than the second.
- Given 2 trains of equal length, the best train has the most points in it.
In this example, both trains are of equal length, but the first train has more points than the second and is therefore better.
- Given 2 trains of equal length and equal point value, the best train has higher point value dominoes placed as far forward in the train as possible.
In this example, both trains are of equal length, and both contain the same number of points, but the first train has higher point-valued dominoes closer to the front.
What about doubles?
Double placement can be a very complex subject. Most of the time, the placement of doubles will be taken care of by satisfying rule #1 above. Finding the longest train possible, will usually dictate where the doubles are placed. So here, we're talking about those situations where a double can be placed in more than one place in your train. It's a good general rule-of-thumb to place doubles as far forward in your train as possible. But there are many situations where that is not the best choice. It depends on how many dominoes are in your train vs. how many spares you have, how many dominoes your opponents have vs. how many you have, and many other factors.
Too keep things relatively simple, Mexican Train For Windows considers doubles in calculating the best train only when there are 2 or more possibilities that are identical in terms of the three rules above. Then, the doubles will be placed as far forward as possible.
What is the best possible train, really?
The “Best Train” in Mexican Train For Windows is really an approximation. To truly calculate the best possible way to organize a player’s dominoes, one would have to consider every domino that has been played so far, and do quite a bit of math in order to calculate odds. The best play at any point in the game is dependent on what has been played up to that point.
Consider this extreme example: from your initial draw of 15 dominoes, you can put together two possible trains, both starting with the correct engine (say 5 for this example). One has 6 dominoes and a total of 31 points (5-0, 0-1, 1-2, 2-3, 3-4, 4-6). The other has 5 dominoes and a total of 97 points (5-12, 12-11, 11-10, 10-9, 9-8). The game will indicate that the train with 6 dominoes is better based purely on the fact that it is longer. But, in reality, the shorter train is better because there are 3 times the points in it, and since both trains are short enough to practically guarantee that you will be drawing before the hand is over. It would be better to play 97 points and draw after 5 turns, than to play 31 points and draw after 6 turns. The average point value of a domino is 12, meaning anytime you draw from the bone pile, you will add, on average, 12 points to your hand. So that extra draw will only cost you 12 points, but you were able to play 66 points more than you would have with the longer train.
In order to truly find the absolute best train, you would have to consider hundreds of circumstances and make rules for each one. The computer could do this relatively quickly, but what would be the point? The fun of the “Best Train” option is to discover why you didn’t come up with best train, and learn something from the experience and get better with each game. It wouldn’t be very much fun if, as hard as you tried, you could never match the computer’s choice for best train.
The game is designed such that it is possible to be the number one ranked player, even at the Expert skill level. If the full power of the computer was used to play for the opponents, you would rarely win. What fun would that be?