As others correctly note, God knew in advance that Pharaoh would refuse the seemingly unimposing request that Moses presented to him; allow the people of Israel to journey three days into the wilderness to sacrifice to God. That Pharaoh refused is somewhat understandable. Like any tyrannical ruler he would assume that allowing an enslaved body of people to collectively embark on a three day journey away from their regular places of abode, equated to his giving a subservient people a small taste of freedom, and that in turn would likely unite them in spirit and possibly result in a major uprising. Pharaoh and his counselors perhaps believed that of all who departed on a three-day journey into the wilderness, not all would return, speculating that various families or individuals would take advantage of the three-day excursion and plot an escape from Egypt.
Some may perhaps believe Moses (or God) was being a little coy with Pharaoh, perhaps even somewhat deceptive? Perhaps a belief is that if Pharaoh had in fact allowed the people of Israel to travel three days into the wilderness to sacrifice to God, the people would thereafter not return back to their Egyptian homes.
Momentarily assume Pharaoh gave in to Moses' request. Momentarily assume that under Pharaoh’s approval Israel was allowed to travel three days into the wilderness to sacrifice to their god. What then can we safely assume would have happened? Knowing God’s commitment to deliver Israel from Egyptian enslavement motivates us to believe the people of Israel would simply have continued their journey out of Egypt, leaving Pharaoh to feel he had been duped. If such happened, then the scenario might be as follows; Pharaoh, some three or so days after the people of Israel had traveled away, received word from his messengers, informing him that Israel didn't just offer sacrifices to their God after three days of travel, but instead they were heading straight for Egypt’s border. Kindly allow me to offer a different perspective, a belief that the children of Israel would have done exactly as Moses said, or perhaps said more correctly, they would have done what Pharaoh, in his mind, believed he was hearing Moses say, that is, Moses was requesting that the people of Israel be allowed to travel three days into the wilderness to sacrificed to God, and then afterwards they would return back to their homes. If Israel had returned from the wilderness as Pharaoh presumably was allowed to believe, then Pharaoh could never point a finger at Moses (or God) and say, I trusted your words, but in return you pulled off a real sneaky on me, I was deceived.
A fair question is, after traveling three days into the wilderness, why would Israel choose to return back to their homes anyway, back to conditions of slavery, especially when they knew that God's plan was for the people of Israel to not just go on a three day trek into the wilderness to offer sacrifices, but was instead that they depart altogether from Egypt? Several points to consider; first, a three-day journey into the wilderness by a massive army of people, with all returning back to their Egyptian homes afterwards, would provide some excellent traveling experience for a people formerly inexperienced in such an endeavor. Equally important, the three days going and three days returning would serve to fine-tune Israel's preparations for what ultimately lay ahead, a truly long walk out of Egypt.
On the other hand, a three day journey into the wilderness, followed by a subsequent refusal to return back to their homes, would essentially result in a largely impoverished people embarking on a strenuous journey, versus later, after Israel had observed the Passover, they left Egypt with a substantial amount of wealth bestowed upon them by the Egyptian populous.
Another point; as scripture says, God all along was going to deliver Israel from their enslavement under Pharaoh's authority, doing so by whatever means and manner He chose. Why then should it be thought that a short journey into the wilderness, followed by an immediate return to their homes and their enslaving job-occupations, would interfere with or somehow disrupt God's fulfillment of Israel’s promised deliverance?
For argument’s sake let’s momentarily assume that what God said wasn't going to happen, did happen, meaning let’s assume that Pharaoh actually allowed the people of Israel to travel three days into the wilderness, after which the people then, to Pharaoh’s satisfaction, returned to their homes. The position here is that if Pharaoh had given the people of Israel permission to journey three days into the wilderness, then under God’s direction the people of Israel would in reasonable time have returned back to their homes. Suggesting otherwise may unwittingly be arguing that God conjured up a scheme, a ploy if you will, to deceptively convince Pharaoh to let the people of Israel go, all the while allowing Pharaoh to believe that Israel was merely going on a three-day journey into the wilderness. However, all along, the supposition by some is, Moses knew that the people of Israel would in reality continue traveling further away from Pharaoh’s authoritative reach. Even if Pharaoh had granted Israel leave, and even if Israel had returned back to their homes following their three-day journey into the wilderness, Moses would yet again be found standing before Pharaoh, and God's plan would continue on unabated.
From scripture we know that God told Moses that Pharaoh would deny the requested three-day wilderness journey. Why then even bother having Moses ask Pharaoh to give the people of Israel permission to journey three days into the countryside just to offer sacrifices to God? Why the futile request? What rises out of the biblical narrative is; before the weight of God’s deliver-Israel plan was fully activated, God first gave Pharaoh an opportunity to exhibit some mercy, to perform an act of kindness by his allowing an enslaved people to enjoy a short seven to perhaps ten day break from their harsh routines. Pharaoh was given an opportunity to let Israel enjoy a brief period of relaxation, to experience some enjoyable family time together as a people. Allowing an excessively overworked people to have a momentarily reprieve could have been a little thing for Pharaoh. And, the enslaved people would probably then begin viewing Pharaoh in a more favorable light. Also, allowing an enslaved and unarmed people to travel say some 40 to 50 or so miles away from the day-to-day hubbub and turmoil of their Egyptian existence, thereby allowing them to enjoy a short vacation so to speak, would have been an a manageable risk for Pharaoh. Officials and spies would have kept a close eye on subsequent events, and if anything were to go awry Pharaoh’s mighty army would have received their marching orders; except for God’s protection (something Pharaoh didn’t know they had) the slaughter may have been enormous.
So why request just a three-day journey into the wilderness anyway, especially given the fact that God knew what Pharaoh’s response was going to be beforehand? What God did, that is what He did by having Moses ask Pharaoh to allow Israel to enjoy a brief reprieve, is somewhat comparable to a show-and-tell classroom type demonstration. Moses was instructed to submit a seemingly unimposing request to Pharaoh – let Israel travel three days into the wilderness to sacrifice to God – which Moses knew Pharaoh would not allow. However, the request by Moses and refusal on Pharaoh’s part would thereupon provide an unquestionably clear message for all of Israel, the message being that Pharaoh would never entertain any ideas of ever allowing the enslaved people of Israel to now-and-then enjoy some forms of relief from their current endless days of hard labor. The request and its rejection by Pharaoh was a message Israel needed to hear, that hard labor was going to be their plight throughout life if, that is, they remained in Egypt.
As a side note, in contrast to Pharaoh’s uncompromising lack of compassion and mercy for an enslaved people, his unshakable resolve to never allow a trodden-down nation of people, Israel, to enjoy even a small measure of relief, enjoying a temporary break from the struggles of their enslavement, God instead, upon His pouring out plague after plague on Egypt would always, whenever Pharaoh withdrew from his belligerent state and asked for relief from a plague, provided what relief could be provided.