The lofty quality of a lottery is well known.1וְהִנֵּה יָדוּעַ בְּמַעֲלַת הַגּוֹרָל,
It transcends (not only intellect,שֶׁהוּא לְמַעְלָה (לֹא רַק מֵהַשֵּׂכֶל,
but also) the power of will that transcends intellect.אֶלָּא) גַּם מֵהָרָצוֹן שֶׁלְּמַעְלָה מֵהַשֵּׂכֶל.
For when a person casts a lot, he decidesשֶׁהֲרֵי כְּשֶׁאָדָם מַטִּיל גּוֹרָל הוּא מַחְלִיט
that the lot will determine his will.דִּכְמוֹ שֶׁיִּפּוֹל הַגּוֹרָל כֵּן יִהְיֶה רְצוֹנוֹ.
This indicates that a lottery reaches a level higher than willדְּמִזֶּה מוּכָח שֶׁהַגּוֹרָל מַגִּיעַ בְּדַרְגָּא שֶׁלְּמַעְלָה גַּם מֵהָרָצוֹן,
and thus the lottery can determine the person’s will.שֶׁלָּכֵן הָרָצוֹן הוּא כְּפִי הַגּוֹרָל.
Similar concepts apply Above.וְעַל דֶּרֶךְ זֶה הוּא לְמַעְלָה,
The concept of a lottery reflects the level of Baal haratzon, “the Master of the will,” a rung above G‑d’s will.דְּעִנְיַן הַגּוֹרָל הוּא בְּבַעַל הָרָצוֹן שֶׁלְּמַעְלָה מֵרָצוֹן.
Based on the above, it is possible to say thatוְעַל פִּי זֶה יֵשׁ לוֹמַר,
the connection between the two common factors shared by Yom Kippur and Purimשֶׁהַקֶּשֶׁר דִּשְּׁנֵי הָעִנְיָנִים בְּהַהַשְׁוָאָה דְּיוֹם הַכִּפֻּרִים וּפוּרִים
(that both of them feature a lottery and both of them transcend G‑d’s name Havayah)(שֶׁבִּשְׁנֵיהֶם הוּא עִנְיַן הַגּוֹרָל וְשֶׁשְּׁנֵיהֶם הֵם לְמַעְלָה מֵהֲוָיָ')
is rooted in the concept that the beginning of G‑d’s name Havayah is identified with the upper tip of the yudהוּא, כִּי הַהַתְחָלָה דְּשֵׁם הֲוָיָ׳ הִיא הַקּוֹץ שֶׁעַל הַיו"ד,
that alludes to will, which transcends wisdom.2שֶׁרוֹמֵז עַל הָרָצוֹן שֶׁלְּמַעְלָה מֵחָכְמָה,
The concept that Yom Kippur and Purim transcend the name Havayah,וְזֶה שֶׁיּוֹם הַכִּפֻּרִים וּפוּרִים הֵם לְמַעְלָה מֵהֲוָיָ'
(transcending even the upper tip of the yud,)(לְמַעְלָה גַּם מֵהַקּוֹץ שֶׁעַל הַיו"ד)
reflects [the concept that] Yom Kippur and Purim draw down and reveal the level of “the Master of the will,”הוּא שֶׁבְּיוֹם הַכִּפֻּרִים וּבְפוּרִים הוּא הַמְשָׁכַת וְגִלּוּי בְּחִינַת בַּעַל הָרָצוֹן
(which transcends will).3(שֶׁלְּמַעְלָה מֵרָצוֹן),
This is the root of the concept of a lottery.עִנְיַן גּוֹרָל.

Summary

A lottery transcends not only intellect, but also the power of will that is loftier than intellect. For when a person casts a lot, he decides that the lot will determine his will. Similarly, in a spiritual sense, a lottery reflects the level of Baal haratzon, “the Master of the will,” a rung above G‑d’s will. The association of Yom Kippur and Purim with a lottery reflects that both draw down and reveal the level of “the Master of the will.”