Purim in Adar: Haman's choice or a toss?

Question

בַּחֹדֶשׁ הָרִאשׁוֹן ... הִפִּיל פּוּר הוּא הַגּוֹרָל לִפְנֵי הָמָן
מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ שְׁנֵים־עָשָׂר הוּא־חֹדֶשׁ אֲדָר׃ (Ester 3.6)

In the first month ... pur—which means “the lot”—was cast before Haman concerning every day and every month, [until it fell on] the twelfth month, that is, the month of Adar.

I understand that the lot is used when one is not sure of or doesn't know the result. So says Rashi:

הִפִּיל הַגּוֹרָל בְּאֵיזֶה חֹדֶשׁ יַצְלִיחַ:
He cast lots to determine in which month he would succeed.
מִיּוֹם לְיוֹם. בְּאֵיזֶה יוֹם בַּחֹדֶשׁ יַצְלִיחַ:
For a specific day. On which day of the month he would succeed

And seemingly Ebn Ezra asks this question (ad loc) - did Haman chose the date himself or was he unsure and let the lot decide?

Answer 1

Esther Rabbah 7:11 records the full story. Because of its length, I'll let you look at the Midrash inside, but the gist of it is that he first threw lots on the days of the week, and when that failed, he threw lots on the months, confirming the second lot by checking the corresponding zodiacs.

From the fact that each day and month in the lots was checked individually Above, and that it was possible for nothing to result from the first lot, my educated guess is that he used a spinner wheel, rather than drawing papers out of a hat. My mental image is that each month or day with a merit protecting the Jews produces a "negative charge" that repels the needle; the spinner for the days therefore would continue spinning indefinitely, while the one for the months would settle on Adar.