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This is a tough question to answer, because like with a lot of the actual mechanical elements of early modern warfare, there's a ton of guesswork and outright bullshit out there, often amplified by games and movies and other pop-culture elements. The scene - depiction the battle of Rocroi in 1643 - is to my mind a fair interpretation of pike warfare in some respects. But even keeping strictly to historical sources, there are some problems with interpretation of the way one pike formation would engage another: one is that we have a relative dearth of firsthand descriptions of this kind of fighting that give details that satisfy a modern audience; another is that the historiography of this period of warfare tends to be dominated by late 19th and early 20th century historians who are combing through these sources looking for very specific aspects that satisfy the prevailing theories of the time. I'll address each of these in turn, and then offer my perspective on how these things might go.

Firsthand Accounts

Describing a battle from 1502 (from the distance of more than half a century), robber knight Götz von Berlichingen wrote of the Nuremberg infantry and artillery advancing on a force of the Margrave Friedrich von Ansbach:

We had about 700 horse and the margrave’s Land-volk, about 300 Landsknechts and 300 Swiss. When it was time, the Nurembergers marched to us with their cannon, Wagenburg and instruments of war, all that they had, they were really not clumsy, but well ordered. When the battle began, we and our captains sent to Margrave Casimir a request that His Princely Grave reinforce us, because we were losing and they were winning, so that we must not tarry.

This is a pretty standard example of the kinds of firsthand accounts of warfare in the period. The concern is the overall strategic and tactical situation, the desperation of losing, the coordination and might of the enemy. There is very little description of the battle apart from that it began, and that his side was losing. Another similarly sparse description comes from Georg Ackerman, a captain of pikemen in Heinrich Pappenheim's infantry regiment:

Before the storm that began between 8 and 9 a.m., the general had distributed good Rhenish wine to all officers and men to give them courage.

We called up the pikemen because we encountered stiff resistance from horse and foot in Lakenmacher Street; but they [the pikemen] thought that the city was already won and, wanting to plunder, had broken their pikes in two to be able to search the houses and so came up holding only sticks. We were accordingly beaten back a second and third time to the wall and scaling ladders.

Meanwhile, the Adjutant General had been sent in and ordered that a few houses be set on fire, thinking that this would force the burghers to drop their weapons to put the fire out. It was now a fine, bright, still day and two houses by the Hohenpforte were duly set alight, but against our will; they burned well over an hour as bright as a light. No burghers wanted to abandon their weapons to put them out, but instead fought on desperately in all parts of the city together with the cavalry, so that we lost our strength.

Marshal Pappenheim meanwhile had a ramp hacked diagonally into the wall with hatchets and pikes so that he could break into the city with four companies of arquebusiers and a few Croats. The fighting in the alleys, that were in part occupied by detachments, had so exhausted our nine storm columns, that were each 3,000 men strong, that we could scarcely pant.

Again, the emphasis isn't on how men fought hand to hand, it's on a more overall vision of the situation and how the witness himself - if applicable - was faring, and the lengths the commanders went to deal with the problem

Firsthand accounts of the "pike and shot era" of roughly the 16th and 17th centuries are often sparse and have a dearth of details. Of those that do contain details, they are often details of things other than the "push of pike," and instead concentrate on individual heroics, the discipline or steadiness of whole formations, or the deadly power of arquebus volleys, artillery, or infantry and cavalry charges, and any peculiar strengths or weaknesses of position. Of the actual engagement hand-to-hand there is seldom any mention. It is also important to note that the kind of force-on-force engagement on flat terrain with no earthworks or other defensive bulwarks seems to be fairly rare; most of these kinds of hand to hand fights occurred on or around natural or man made defenses that would problematize an attacker's assault.

The comparative power of various weapons are also sometimes attested. The length of pikes can either be a great advantage or a sever disadvantage, depending on the situation. It was a common complaint among writers of military treatises that men, to lighten their marching loads, would cut off several feet of their pikes, or would wield them by the middle rather than the end to shorten them in combat. This makes sense, given that a weapon of 12 feet or greater in length can be extremely unwieldy, but we should also be aware that numerous writers of fencing books also included instruction on the pike, and showed that in practiced hands it could be a subtle and nimble weapon.

Historian’s Work

But let's take a look at a single example. The following is from the Battle of Ravenna, fought in 1512 between the Holy League and the forces and allies of France. An infantry engagement took place in near the Spanish camp, and became a prominent example of the bloody mess that hand-to-hand combat could devolve into all throughout the period. After some attempts to force a ranged engagement across the ditch and earthen bank that protected the Spanish camp, German landsknechts (in the pay of the French) stormed across the ditch, taking small-arms and artillery fire on the way, and poured over the ditch to meet the Spanish pikemen. According to Charles Oman:

... the great column of German landknechts under Jacob Empser delivered their assault. Braving the fire which was poured upon them, they rolled up to the ditch, after passing a water-cut which was found to lie across their path. Jacob Empser was shot through the body as he scrambled over the ditch, but one of his lieutenants, Fabian von Schlabrendorf, made a gap in the line of Spanish pikes by taking his own pike by the butt and using it like a flail, whereby he broke down to the ground a dozen hostile weapons, and allowed his men to scramble in--though he himself was mortally wounded.

So, here's a fairly detailed description of a desperate action, showing an individual hero - von Schlabrendorf - using an unusual technique specifically to knock down the enemy pikes, allowing room for his men to pour in. This is a critical detail, if it's true, and shows an answer to a common problem: how to get past the enemy pike points. By knocking them down or breaking them, it allows his men to move forward without harm. This also reflects the common utility of men with large, two-handed swords, who were meant to do similar things - either break or knock down enemy pikes to aid an assault or to plug a similar gap in one's own line. You can't fight very well if your pike is broken or knocked down, and if you resort to a shorter sword, you can be easy prey for a man at a distance with a pike. In short, von Schlabrendorf's action disrupted the Spanish pike line, turn a hedge of pikes from a deadly wall of steel to a confused mass of disarmed men.

But there's another element here which Oman also describes - men slipping past the point of the pike. Oman again:

At several points the Germans crossed the ditch, and got to hand-strokes with the Spaniards, but could make no great way forward. We are told that the sword-and-buckler men from the rear ranks slipped in among them, and did great damage with their short weapons - against which the pike was practically useless. After a long struggle the Germans were expelled from the works - it is said that the French infantry lost another 1200 casualties in this storm over and above the men killed in the previous cannonade.

So while the French lost the infantry battle, they won the battle, as the allied cavalry stove in the Spanish cavalry in other parts of the field. However, this last bit actually shows something depicted in Alatriste - men slipping past the killing point of the pike and doing great harm by dint of their shorter weapons. This is an example of what commentators and even artists called the "bad war," famously depicted by Hans Holbein the Younger some time in the early 16th century. The engraving shows a gigantic bloody mess, men fighting with daggers, swords, and halberds, pikes exploding out from the middle of the engagement like crooked teeth, going in all directions. Men are grabbing hair, trampling wounded men, crowding in on each other, each having little enough room to breathe, let along fight. It's a striking image that depicts the confusion and horrific violence of a pike engagement that continued past the first initial charge.

The important element here is that the pike, when both forces were motivated enough to stand their ground or press a charge, became much more difficult to use. This is when the sword and buckler men had an advantage, and against them, men with halberds or two handed swords could try to restore order for their side. This is what Oman terms an "undisciplined multitude."

Oman's description of Ravenna comes from several firsthand accounts, from Chevalier de Bayard, Fabrizio Colonna, a Spanish report, and numerous other secondhand accounts.

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