Thanks for the advice

is typical when the speaker assumes that the listener(s) will be familiar with which or what advice is being discussed, whether we have in mind one item of advice or several.

We use a and the to introduce "uncountable" or mass nouns when they are implicitly or explicitly divided into units.

Thanks for the milk.

Or in Russian:

Thanks for the vodka.

We would use TRomano's perfectly natural alternative Thanks for all the advice only when we wish to emphasize that a lot of something was given, or to specifically acknowledge multiple pieces of such.

So, Thanks for all the milk carries a different connotation.

We also use no article to introduce uncountable nouns when we talk about a thing in general:

Advice is like snow - the softer it falls, the longer it dwells upon, and the deeper it sinks into the mind.

Samuel Taylor Coleridge

https://www.brainyquote.com/quotes/quotes/s/samueltayl100590.html

Thanks for the advice

is typical when the speaker assumes that the listener(s) will be familiar with which or what advice is being discussed, whether we have in mind one item of advice or several.

We use a and the to introduce "uncountable" or mass nouns when they are implicitly or explicitly divided into units.

Thanks for the milk.

Or in Russian:

Thanks for the vodka.

We would normally use TRomano's perfectly natural alternative Thanks for all the advice when we wish to emphasize that a lot of something was given, or to specifically acknowledge multiple pieces of such.

So, Thanks for all the milk carries a different connotation.

Also, we use no article to introduce uncountable nouns when we talk about a thing in general:

Advice is like snow - the softer it falls, the longer it dwells upon, and the deeper it sinks into the mind.

Samuel Taylor Coleridge

https://www.brainyquote.com/quotes/quotes/s/samueltayl100590.html

Thanks for the advice

is typical when the speaker assumes that the listener(s) will be familiar with which or what advice is being discussed, whether we have in mind one item of advice or several.

We use a and the to introduce "uncountable" or mass nouns when they are implicitly or explicitly divided into units.

Thanks for the milk.

Or in Russian:

Thanks for the vodka.

We would use TRomano's perfectly natural alternative Thanks for all the advice only when we wish to emphasize that a lot of something was given, or to specifically acknowledge multiple pieces of such.

So, Thanks for all the milk carries a different connotation.

Thanks for the advice

is typical when the speaker assumes that the listener(s) will be familiar with which or what advice is being discussed, whether we have in mind one item of advice or several.

We use a and the to introduce "uncountable" or mass nouns when they are implicitly or explicitly divided into units.

Thanks for the milk.

Or in Russian:

Thanks for the vodka.

We would use TRomano's perfectly natural alternative Thanks for all the advice only when we wish to emphasize that a lot of something was given, or to specifically acknowledge multiple pieces of such.

So, Thanks for all the milk carries a different connotation.

We also use no article to introduce uncountable nouns when we talk about a thing in general:

Advice is like snow - the softer it falls, the longer it dwells upon, and the deeper it sinks into the mind.

Samuel Taylor Coleridge

https://www.brainyquote.com/quotes/quotes/s/samueltayl100590.html