Depends on whether you're hunting in the Glimwood Tangle or the Old Cemetary. Either way, authentic Sinistea has a 1% spawn rate out of everything overall, but the rate of forged Sinistea varies, meaning that your ratio of forged/authentic changes.

In Glimwood Tangle, the chance of finding any Sinistea is 11%; 10 for forged, 1 for authentic. Ignoring phases from other Pokemon, this gives you a 1/11 or 9.09% chance of getting an authentic Sinistea.

Source

The Old Cemetary varies, both for overworld spawns and random encounters. In every weather except Sandstorm, authentic Sinistea has a 1% chance overall, while forged Sinistea has a 19-20% rate via overworld spawns and a 13-19% rate via random encounters. Here are all the rates:

Sinistea cannot be found during a sandstorm.

Clear weather, random encounter: **19:1 ratio; 1/20 or 5% chance**

Thunderstorm, random encounter: **13:1 ratio; 1/14 or 7.14% chance**

All other weather (except sandstorm), random encounter: **17:1 ratio; 1/18 or 5.55% chance**

Blizzard or fog, overworld: **20:1 ratio; 1/21 or 4.76% chance**

All other weather (except sandstorm), overworld: **19:1 ratio; 1/20 or 5% chance**

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