The Mayans were one of the very last civilizations from Age of Empires II that I decided to give a shot at, ultimately becoming a favorite of mine for multi-purpose uses and for when facing the unknown!
The Mayans are simply that reliable, being their only and greatest weakness the lack of cavalry- generally considered the main force of action in the game. However, they have found ways to counter this, emptying units even more efficient than cavalry in some of its functions.
Economic and Archer Civilization
Start with +1 villager, -50 food
Starting with 1 more villager is what will give the Mayans a really nice starting edge above many other civilizations. Since you have one extra work force from the get go, you can put 2 villagers on food right away, 1 on wood and take the chance to research Loom while the fourth vill is building the first house. This might no seem like much, but it is just enough to keep the villager production continuous through the Dark Age, allowing for a very fast economic growth. Use your Eagle Warrior to spot those sheep and wild game.
Resources last 20% longer
In the long game, this is what makes the Mayans an economic force. This means that every resource piles on terrain will give the player 20% more resources than normal. Not only does this make the stockpiles of resources to last longer, but it also allows for a slight better efficiency in the gathering of resources, as villagers do not work through them as fast and are therefore not made to walk as far when dropping off.
Archers cost -10% Feudal, -20% Castle, -30% Imperial Age
A welcome discount in archers, this will give you the change to create your ranged forces without the risk of hitting the economy too hard. Want to rush an enemy with archers? With the additional villager advantage and the 10% archer discount in Feudal Age, quickly build 2 Archery Ranges as soon as you advance to Feudal and start working on your unit production!
"The natives of Central America had developed the bow and used it in combat. Their bow technology was not far advanced, in comparison to the Asian composite bow or English longbow. Archers could be ordered to wound when capture of enemies was more important than killing. Like all other Mayan warriors, archers wore distinctive costumes so commanders could distinguish their troops and place the right group where needed. The status of archers was low in comparison to other warrior ranks, so men of lower standing and skill entered their ranks. Men of status and ambition joined the ranks of the Eagle Warrior where they could have the opportunity to take captives."
The Mayan Plumed Archer is an interesting addition to the archer family of Age of Empires II. It does not have particularly good attack or range, but it is sturdy and fast, making it a great complement to use with the Eagle Warrior. Plumed archers are great units to use to hunt villagers down, slay infantry and even kill other archers thanks to their higher hit points and superior speed.
"War is often most cruel and terrifying when markedly different cultures collide. The native populations of South and Central America were shaken by the appearance of Conquistadors wearing armor, wielding steel weapons, riding horses, employing war dogs, and using firearms. The blood sacrifices, rituals, and fanaticism of the Americans unsettled the Spanish, in turn. The Mayans proved very tough opponents when whipped into battle frenzy in defense of their hidden wealth."
Eagle warriors are practically exclusive units since only the Aztecs and the Mayans have access to them, and each one receive specific upgrades. In the case of the Mayan Eagle Warrior, El Dorado gives it +40 hit points, making it the closest thing to a cavalry unit the Mayans will ever have. With a total of 100 hit points and 4 natural piercing armor, eagle warriors can venture through unwalled or breached enemy towns to slay villagers and wreck siege units. They can also charge archers with plumed archer support, and since they receive a small bonus against mounted units, they also fare well against cavalry archers and scouts. Just don't go sending them against paladins! Leave that task to your halberdiers.
Walls cost -50%
Not the most useful team bonus the game has to offer. However, since the Mayans player's resources last longer, it is always a good idea to protect them and take advantage of the discount at the same time.
A civilization that could benefit from this team bonus could be the Byzantines in a defensive playing style. On the one hand their defenses are sturdier and last longer, on the other hand the 50% wall discount would save precious stone, or simply allow for the setting up of the defenses faster and more efficiently. In return the Mayans would benefit from the +50% Monk healing speed, which would greatly aid the survivability of the valuable eagle warriors.
The Teutons are a civilization that relies heavily on building strong defenses and creating far-reaching fortresses, so it is one other civ that could benefit from the team bonus of the Mayans.
There is a lot that can be done
Perfect Arbalests and Elite Skirmishers
The Mayans can fully research arbalests, as these have a greater damage potential than plumed archers, and elite skirmishers, the cheap counter to pesky archers that are usually sent in early rushes.
Since the Mayans benefit from a complete Blacksmith (only lacking the cavalry upgrades), they can produce great infantry units as well, with the only loss being really the Champion. They can use halberdiers to defend against cavalry, and the very useful eagle warriors for a multitude of functions, including: raiding enemy villagers, charging archers, sneaking on siege units and wall incoming enemy infantry.
Siege Rams and Heavy Scorpions
There is the need for siege weapons for the Mayans to be able to breach through heavy fortifications. For this they benefit from decent siege, including siege rams and the ever-reliable trebuchets. For extra back row support and fire power, they can also produce heavy scorpions. Siege engineering is missing, though.
To add to their already superior economy, the Mayans can research all resource-gathering related upgrades from the Mill, Lumber Camp, Mining Camp and Market, with the only exception being the Gold Shaft Mining research. These are important to keep that economy in Imperial Age going strong, and enable you to keep producing the more expensive Siege Workshop units.
The Mayans, similar to the Chinese, are a very versatile civilization able to look for support in every (available) section of their tech tree. In addition to all that was mentioned, they also possess good supporting monks and can keep up in water maps, since their Dock is really only missing on the cannon galleons.
When trying to counter the power of the Mayans, heavy cavalry comes to mind, since they lack a really tough unit that can face the likes of war elephants and catapracts. So consider the Persians or the Byzantines when going against the native Americans. The Franks are also an option, since their superior paladins can wall anything the Mayans can throw at them, while hitting eagle warriors from behind with throwing axemen or hand cannoneer fire.
That's it for the Mayans. Do believe me when I say how unappealing they may seem at first sight, but you really have to try them out to discover their potential. I can tell you one more thing about the Mayans: they are one of the funniest and most enjoyable civilizations to play with in Age of Empires II. Coincidentally, they are the civ that has given me the most wins in the online of Age of Empires II - HD Edition. I guess fun, is indeed, the most important factor.
Read my 10 of the Best Civilizations from Age of Empires II: The Conquerors for more info on other great civs!