Do we have any reliable information on how two pike formations fought each other? Because I cant see it turn into anything but a mutually annihilative bloodbath very, very quickly.
From 'Instructions, Observations and Orders Mylitarie' by Sir John Smythe, published in 1591 (spelling modernised):
That the Sergeant Major or Captains would have their pikemen to charge or to receive a charge of another square of pikemen their Enemies, then are they to say to the first ranks of pikemen. `Straighten and close your ranks, couch your pikes and charge': which being pronounced, all the pikemen of the first rank must join and close themselves in front, letting fall the points of their pikes and carying them close breast high with both their hands steadily and firmly, the points full in the faces of their Enemies.
And the second rank likewise straightening and closing themselves by flank and front, and joining themselves to the back of the first rank, and following them step with step carrying their pikes above-hand over the shoulders of the first rank the points of their pikes likewise towards the faces of their Enemies. And the third rank closing and straightening themselves in flank and front, and joining themselves to the back of the second rank; And the fourth rank likewise straightening and closing themselves to the backs and shoulders of the third rank, and carrying their pikes firmly with both their hands over the shoulders of all the ranks before them, the points of their pikes likewise towards the faces of their enemies approaching.
And all the rest of the ranks of pikemen following step with step each one at the heels of the other must carry their pikes still upright in the palms of their hands, and in bolts of their armes as above said, but yet bending the points of them somewhat towards their enemies, that they may be seen ready in an instant to let fall the points of their pikes towards their enemies, and to succour the rank before them upon any necessity.
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And all those four ranks marching or moving forward together pace with pace and step with step, carrying their pikes firmly with both their hands breast high as aforesaid their points full in their enemies' faces, they do altogether give a puissant thrust, the points of the first rank of pikes, first lighting upon the faces of the first rank or ranks of their enemies; and the points of the second, third and fourth ranks, subsequently in a manner all in an instant, do all one after another in such terrible sort light upon the faces, breasts and bodies of the formost ranks of the enemies that do stand still pushing and foining with their pikes in their ranks opened and enlarged, that they never give them any leisure and ways to pull back and recover the use of their pikes to give any new thrusts, nor yet to close their ranks enlarged, but do overthrow, disorder and break them with a great facility, as if they were but a flock of geese; as all men of right consideration and judgement may easily consider and see.
But after all this it may be, that some very curious and not skilfull in actions of Arms, may demand what the foremost ranks of this well ordered and practised squadron before mentioned shall do after they have given their aforesaid puissant blows and thrusts with their pikes in case that they do not at first encounter overthrow and break the contrary squadron of their enemies:
Therunto I say, that the foremost ranks of the squadron having with the points of their pikes lighted upon the bare faces of the foremost ranks of their enemies, or upon their Collars, pouldrons, cuirasses, tasses, or disarmed parts of their thighs; by which blows given they have either slain, overthrown, or wounded those that they have lighted upon, or that the point of their pikes lighting upon their armours have glanced off, and beyond them; in such sort as by the nearness of the foremost ranks of their enemies before them, they have not space enough again to thrust; nor that by the nearness of their fellows' ranks next behind them, they have any convenient elbow room to pull back their pikes to give a new thrust; by means wherof they have utterly lost the use of their pikes, they therefore must either presently let them fall to the ground as unprofitable; or else may with both their hands dart, and throw them as far forward into and amongst the ranks of their enemies as they can, to intent by the length of them to trouble their ranks, and presently in the twinkling of an eye or instant, must draw their short arming swords and daggers, and give a blow and thrust (termed a half reverse, and thrust) all at, and in one time at their faces: And therewithall must presently in an instant, with their daggers in their left hands, thrust at the bottom of their enemies' bellies under the lammes of their Cuirasses, or at any other disarmed parts:
In such sort as then all the ranks of the whole squadron one at the heels of the other pressing in order forward, do with short weapons, and with the force of their ranks closed, seek to wound, open, or bear over the ranks of their enemies to their utter ruin.
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Something to remember is that yes, a formed pike formation charging into another formed pike formation head-on would indeed be very bloody. That's why you tried not to do that. You'd bring along musketeers, who would break up and disorganise the enemy with their fire first, and only charge once they were in disarray. Or you'd try to outflank them and hit them from behind. Or you'd wait for them to try and move, which itself would disorganise a badly-trained regiment. Or you'd send cavalry around their flank, so they had the choice of facing you or facing the horsemen.