How to defeat pikemen

With 50 pikemen and 50 archers vs 100 horse archers, 100 horse easily archers win. Iirc in Asia maybe a 4 to 1 footbased to cavalry ratio or more would be required. afaik, the ancient Han Dynasty militarily defeated horse archers often, by relying on immense armies of crossbowmen (including 'repeating crossbows') probably mixed with pikemen and alot of heavy cavalry.

The primary reasons for the horse archer, were logistical, tactical, and mental not mathematical. Food is easier to recieve when you have a larger radius to get from. Messages could be relayed much faster, wihtout the use of fire. Tatically, nomadic armies typically were much more flexible. They knew where the enemy was better, were able to hide its intentions, and able to react more quickly to changing circumstances. Pikemen might be more low level relatively recently trained recruits, whereas horse archers are brought up fighting with bow and horse.

Mountainous regions: Favor nomads. Pikemen have had a much harder time getting resources and getting to strategic locations. Its easier for cavalry to retreat and reappear at another corridor or hit vital supplies. Nomads often grew up in terrain having many mountains, e.g. Afganistan, Uzbekistan, western China. The fall of the Chinese Jin dynasty took place in a battle within a mountainous region against a smaller nomad force.

Mud: how many places actually have a lot of mud all over? The only reason horse archers would fight in swamp is in support of an infantry force having to march through swamp. Since horse archers are nomads, there rarely is such an infantry force.

Forest: If there's just one heavy forest hiding an army, the nomads will definitely set it on fire as armies always would. Ok if all the important towns actually are in forests (maybe like Vietnam for example) pikemen could win.. other than that..

Water: Probably, the terrain argument only holds when it involves water (but then we're not talking about pikemen :) )

:)