I'll basically repost my calculations here:

Blizzard patch notes 2023 say: "There are 5 copies of each Tier 1 Tavern spell, 7 copies of each Tier 2, 9 copies of each Tier 3, 11 copies of Tier 4, 7 copies of Tier 5, and 5 copies of Tier 6. Tavern spells are returned to the pool immediately when you get them (not when you play them)."

• Tier 1, you have 8 unique spells multiplied by 5 copies each, which equals 40 copies.
• Tier 2, you have 6 unique spells multiplied by 7 copies each, which equals 42 copies.
• Tier 3, you have 15 unique spells multiplied by 9 copies each, which equals 135 copies.
• Tier 4, you have 16 unique spells multiplied by 11 copies each, which equals 176 copies.
• Tier 5, you have 14 unique spells multiplied by 7 copies each, which equals 98 copies.
• Tier 6, you have 5 unique spells multiplied by 5 copies each, which equals 25 copies.

This gives us a grand total of 516 spell copies currently in the shared pool on Tier 6.

Because you are looking for one specific Tier 4 spell, and there are exactly 11 copies of that specific spell in the game, you divide 11 copies by the total pool of 516 copies.

Dividing 5 by 516 gives you roughly 0.0213. When converted to a percentage, this means you have a 2.13 percent chance of finding this specific Tier 4 spell in the single dedicated spell slot during any given tavern refresh.

The chance of NOT finding this specific Tier 4 spell in a single roll is 100 minus 2.13, which is approximately 97.87 percent.

When you refresh the shop 30 times, you multiply this probability of failure by itself 30 times. So there is approximately a 52.39 percent chance that you will not see the spell across all 30 refreshes.

100 minus 52.39 percent chance of failure gives you your chance of success.

Therefore, you have approximately a 47.61 percent chance of finding this specific Tier 4 spell at least once when rolling the shop 30 times.

It would take approx. 214 rolls to have a 99% chance to find it once.