Re: “It is impossible for us to wake up the next morning to know who the Prime Minister will be.”
Not really.
If the core “right” (Likud, Bayit Yehudi, Yisrael Beiteinu, Yachad, Shas and Yaadut ha-Torah, plus Kulanu) have under 61 seats , there is no way Netanyahu can form a government, and it means Herzog has won.
Alternatively, if the left (Labor, Meretz, Yesh Atid) and Center (Kulanu and Yesh Atid), combined with the Arab Bloc and the two non-zionist Hareidim parties (Shas and Yaadut ha-Torah) come to less the 61, there is no possibility of Herzog forming a government and Netanyahu has won.
In those situation, the meetings with the President are a mere formality. Based on preelection polls, either side will be able to form a government if they can get all elements to cooperate (which is in doubt, since the hareidim demand no conscription, and several parties on both sides of the spectrum demand the opposite).