Improbable Alliance — ruling 1

The triggered ability can trigger only once each turn. It doesn't matter whether the permanent with that ability was on the battlefield when the first card was drawn. If it's not on the battlefield when the second card is drawn, the ability can't trigger at all that turn. It won't trigger when the third or fourth card is drawn.

Improbable Alliance — ruling 2

If an effect instructs you to draw multiple cards, the ability triggers after you draw whichever is the second one for the turn. You choose a target (if any) for the ability after you've drawn and looked at all of the cards and finished resolving the spell or ability that caused you to draw them.

Improbable Alliance — ruling 3

If a spell or ability causes you to put cards into your hand without specifically using the word "draw," it's not a card drawn.

Improbable Alliance : règles, fonctionnement et interactions (MTG)

Improbable Alliance is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Whenever you draw your second card each turn, create a 1/1 blue Faerie creature token with flying. : Draw a card, then discard a card.

How it works : Improbable Alliance

Original English text — Wizards of the Coast / Scryfall

#1October 4, 2019· Wizards of the Coast
The triggered ability can trigger only once each turn. It doesn't matter whether the permanent with that ability was on the battlefield when the first card was drawn. If it's not on the battlefield when the second card is drawn, the ability can't trigger at all that turn. It won't trigger when the third or fourth card is drawn.
No other card is named in this ruling.
#2October 4, 2019· Wizards of the Coast
If an effect instructs you to draw multiple cards, the ability triggers after you draw whichever is the second one for the turn. You choose a target (if any) for the ability after you've drawn and looked at all of the cards and finished resolving the spell or ability that caused you to draw them.
No other card is named in this ruling.
#3October 4, 2019· Wizards of the Coast
If a spell or ability causes you to put cards into your hand without specifically using the word "draw," it's not a card drawn.
No other card is named in this ruling.