People in other countries usually think that the standard Russian toast is “Na zdorovye!” (literally, "To health!"). That is not exactly right. When pronouncing a toast, Russians are more likely to say "Vashe zrodovye" or "Tvoye zdorovye!", which means "To your health!", depending on the form of address.
Strictly speaking, however, this is not a proper toast. A classic toast has a more complex structure. It usually takes the form of a short story or anecdote, followed by a jocular or paradoxical conclusion, with an invitation to drink in affirmation of that conclusion.
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