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The odds
of pulling variants at each level are spelled out in the help test for the variant boost page. I'll summarize them here.
Perfect (1 card per 200 packs, about 50% are eligible to have variants) 1 in 50. So you should pull a perfect variant once in 20,000 regular packs, once in 100 perfect or rainbow packs, and once in 50 historical perfect or historical rainbow packs.
Diamonds (1 card per 30 packs, again about 50% are eligible to have variants) Odds of an eligible card being a variant, 1 in 50. So you will pull a diamond variant once in every 1500 regular pack, once in 100 diamond or rainbow packs, and once in 50 historical diamond packs or historical rainbow packs.
Golds are about 1 in 500 regular packs, once in 100 gold or rainbow packs, and once in 50 historical gold or historical rainbow packs.
1 in 100 eligible silver is a variant, and they are about 1 in every other regular pack. So you should get one of them about in every 200 packs. And Irons and bronzes are 1 in 200, so the odds of pulling a bronze variant are about the same as for a silver. And the odds of pulling an iron variant are about 1 in 45 regular packs.
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