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As the only way of getting to the End, the stronghold is an important structure. Locating the stronghold is a major mandatory hurdle, requiring lots of eyes of ender, though it can be made easier through knowledge of certain aspects of this part of the game.
Strongholds generate in a unique pattern that is dependent on the edition of game you are playing.
Strongholds generate throughout the world randomly. Three extra stronghold generate below the meeting points of a village, and usually occur a bit above, but never below, 453 blocks from spawn.
Strongholds are spaced roughly evenly throughout concentric rings radiating from spawn. The number of stronghold in each rings follows the triangular numbers, the sums of the integers from 1 to a certain other number.
When you make your first portal in the nether, preferably at coordinates (±150, ±150) or (±220, 0) (an advanced chart can be found here), you will arrive at a brand new location which is relatively close to the stronghold. Throw an eye of ender and point to it. Record the angle of the eye. It is recommended to type it in chat. Then sprint jump 4 times in any direction (preferably one with the best terrain) and throw another eye. Point to it and record the angle. Check the angle difference. Some basic numbers to remember is that if the difference is 0.5°, it is around 2000 blocks away. 1° is around 1000 blocks away and 2° is around 500 blocks away. A detailed chart can be found here.