Worst-case gem check
This assumes every remaining free pull and every extra purchased pull is a duplicate. Your actual cost can be lower.
extra pulls for a hard guarantee
3x5 + 3x1
cheapest purchase mix
Enter gems
your gem coverage
Break-even math
A new pull gives you one piece directly. Five duplicates give you one missing piece through exchange.
ceil((5 x 17 - 3 - 64) / 4) = 5
FAQ
Does buying a piece guarantee a new one?
No. Purchased pulls can still be duplicates, so this calculator never treats a paid pull as automatically new.
Does buying 5 pulls guarantee at least one new piece overall?
Under the current 5-duplicate exchange rule, yes. If one of the five pulls is new, you gain a piece directly. If all five are duplicates, those duplicates trigger an exchange for a missing piece.
How is the free completion chance estimated?
The estimate runs a local simulation using 30 Blue, 20 Purple, and 4 Gold pieces, with pull rates of 78% Blue, 20% Purple, and 2% Gold. It also uses the same conservative exchange assumption as the community simulation: a guaranteed exchange fills a missing Blue first, then Purple, then Gold. Duolingo has not confirmed that exchange order, so treat the percentage as an estimate, not a promise.
How do I enter the rarity breakdown?
Enter the pieces you still need, not the ones you already collected. For example, if your event screen shows 3 Blue, 8 Purple, and 4 Gold still missing, enter 3, 8, and 4. Those three numbers must add up to your total missing pieces.
What does the gems probability mean?
It estimates your chance of finishing after using all remaining free pulls and then, only if needed, as many extra pulls as your current gem balance can buy. It assumes paid pulls have the same piece odds and can still be duplicates. Waiting until later gives you more information before spending.
What are the official rarity names?
Duolingo calls the three tiers Blue, Purple, and Gold. Gold is the rarest tier. This calculator uses those names instead of Common, Rare, or Epic.
How should I enter Days remaining?
For the cleanest calculation, collect today's free pieces first, then enter the number shown by Duolingo. Staff says the event lasts 30 days, even though users can see 29 days remaining on the first day because the countdown is showing whole days left. There may still be an active final partial day when the counter reaches 0, but that exact behavior is not officially confirmed. If Duolingo still lets you earn pieces at 0 days, count that active pull window then instead of adding an extra day in advance.
What does "must be naturally new" mean?
It is the minimum number of your remaining free pulls that must directly give you a piece you do not already own. The rest may be duplicates.
Should I buy pulls as soon as a gem cost appears?
Usually not. The gem number is a worst-case guarantee from your current position. Future free pulls can still lower it.
Can I use the 5,000 gem reward to pay for the pulls I need?
Not upfront. You receive the completion reward only after finishing the collection, so you need enough gems to buy any required pulls before that reward arrives.
Why can the worst-case cost be higher than the completion reward?
The reward is fixed at 5,000 gems. The amount needed to force completion depends on how many pieces and free pulls you have left.