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I ran a few tests with 8mm6 to see how quickly it can find an opponent (for restarting a game upon meeting or for a rush strategy).
As a result, it turned into an exercise in pattern recognition.
The scheme is simple: start as Pikedram, use the first turn to place a scouting unit, then enter a cheat code for Archons and infinite movement. You can only move Pikedram; you cannot buy other heroes.
The task is to find the blue player as quickly as possible. When you capture a Castle, check how many movement points Pikedram has left (initially 1,000,000).
The second stage is a control comparison: buy another hero in the Castle, enter a cheat code for infinite movement, and head to the blue player's Castle along the shortest route. At the end, measure how many movement points are left.
Repeat N times and observe the search efficiency. I only ran along fast roads, and I calculated the distance to the opponent's Castle in days of travel with a 4x speed boost (1560 movement points).
Results (days of blind search - days of ideal search - loss coefficient):
1) 8.1 - 7.0 - +15%
2) 3.9 - 2.7 - +47%
3) 5.3 - 4.7 - +14%
4) 7.9 - 6.0 - +31%
5) 5.5 - 4.1 - +34%
6) 6.5 - 5.5 - +19%
7) 10.7 - 5.6 - +93%
8) 10.7 - 4.8 - +124% (heavily bugged map)
9) 9.1 - 4.8 - +91%
10) 8.4 - 5.5 - +53%
The percentage increases are high because the search costs also include the loss of movement points for picking up objects along the road. This is approximately 10-15%. That is, results from +10 to +20% represent runs that are almost along the shortest path.
The sample size is small, but preliminary conclusions can already be drawn.
1. The shortest distance to the opponent is, on average, 5 days along fast roads.
2. A correct search results in approximately +40% more time spent compared to an ideal search. There is a large variation here, and the main points are:
a) A fork leading to your own Castle or to the center. This adds approximately +20% to the losses.
b) A fork between the blue and green players. This is especially unpleasant if they are of the same territory type. This also adds approximately +20%.
c) A fork between the central villages; if you make a mistake here, you can end up with a +50-60% increase.
If all the forks are passed correctly (or are absent), the path to the opponent is almost the shortest - +10-20%.
However, in real games, it is slightly easier because by days 3-4, the AI opponents are also moving around, and the opponent may appear closer to the center, which significantly simplifies the elimination of incorrect directions.
I highly recommend this exercise as a training tool for 8mm6. When the average numbers start to match the ones indicated, there will be no particular problems with orientation in real games.