TROLL, keep riding your boy's nutsack! He's enjoying every minute of it
Are you blind? Do you not see the size of Genghis Kahn's empire? It was 4-5 times that of Alexander's puny empire. The Mongols destroyed the Persian armies in UNDER 2 years time. The Indians were just minute roadblocks in the road. You seem to be spouting a bunch of bull and by the way, since when are all book sources credible? If you've actually learned anything most textbooks are extremely biased.
They don't need it. Heavy Infantry in no situation with a good general would ever come in to contact with the Mongols -- Heavy infantry are the weakest possible type of soldier to deploy against mongol troops.
We're talking 300,000 or so Mongol troops against a maximum of 50,000 of Alexander's. Alexander faced few competent armies with competent leaders, and mostly those were hellenes fighting as mercenaries with different fighting styles.
The Hoarde would quickly dispatch any archers, slingers and throwers of javelins from a greater range, and with amazing accuracy given they're firing from horseback. Quickly, they would then begin to harass and draw off the cavalry -- light cavalry would be eliminated extremely quickly by the arrows of the hoarde.
Alexander would, probably, be left with disciplined infantry, which could just be picked off with arrows -- they had no large bronze shields because of the extra weight of their longer pikes.
Alexander's chances of victory could only come from a massive terrain advantage, such as a battle in the woods -- this was tried before on them, and the Mongols knew better and moved on.
Genghis Khan's army was much more superior that Alexander's, bottom line. The mongols conquered almost all of Asia. They put fear into so many people's mind that the Ming Dynasty, for example, had to built one of the great structures ever...the Great Wall of China in order to fight off the Mongols. When a wall that streches for more than 6,700 kilometers through Eastern China is built, it should be enough to tell you how much they feared Genghis Kahn.
How on earth could the Mongols ever be engaged by any arm of the Greek armies, apart from the archers, which would be so outnumbered and beaten by the mongols? Especially in any large numbers? I don't understand.
Also forgetting Mongols greatest advantage, mobility. They were one of the most mobile armies, they could ride for almost ten days without stopping to light a fire, or to cook food. They could cover 70 miles in a day as they had no supply lines. Mongols were often out numbered numerically by armies, often 3 to 1, and they often routed those same enemies. Also, how much discipline did Alexander's troops have? Because Genghis Khan had probably the best discipline of about any time in his troops. Also, Genghis Khan would probably try and ambush or use trickery against Alexander, unless he was sure of victory. Often Genghis Khan would fight against infantry, admittly not with pikes, and would slaughter them.
Mongolian compound bow was a hideously powerful ranged weapon, and the Mongols could make rapid, aimed shots with them at full gallop. Things would seem to depend largely on whether or not Ghenghis would amend his tactics - a charge into the center of the phalanxes would accomplish precisely nothing. However, if the Mongols did use their standard attack-and-fade formula and succeeded in drawing out the phalanxes, it'd be a simple matter to destroy them in detail - once phalangites are out of formation, they're basically useless. It would be an extreme test of his ability to control his troops, but Ghenghis could very well win the day.
The Mongol forces defeated armies 10 times their size as well. In their campaign against the Kwarazmiam Empire and dropped the walls of the "imprenatratable" Samarkand in a mear ten days while being out numbered by nearly 20 to 1 by the defenders inside.
The Mongols faced all comers and faught more different battle tactics then any other force in military history and defeated them all, from the Heavly Armored Polish Knights to the Russian Horsemen to the Persian Spear collumns, the Chinese, etc.
My friend. They faced everything Alexander had and destroyed them and did it in so many different ways.
The average Mongol Archer could cut down a man at over 350 yards (or 320 meters away) away from horseback at full gallop. Great Mongol Archers were reported capable of killing men at over 400 yards.
Oh and just as a sidenote, the Mongols were the only force to ever succesfully invade and conquer Russia during the Winter and this was lead by Subedei.