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I'm looking for a word or phrase for the warning "If you do it for once, you will do it next time, and until infinity", usually with a negative connotation (like warning someone against taking drugs or other harmful and addictive things).

The Chinese phrase that conveys the meaning perfectly is 有了第一次就会有第二次, which literally translates to "If there's the first time, there will be a second time".

The phrase should probably fit as a noun in terms of "part of speech".

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One idiom is slippery slope, meaning that one step will inevitably take you much further, and you cannot stop. Farlex has

A dangerous and irreversible course
the slippery slope from narcotics to prison

and Lexico has

A course of action likely to lead to something bad or disastrous
he is on the slippery slope towards a life of crime

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There exist a family of idiomatic forms which allows one to specify the particular situation they have in mind; it is "once a (something), always a (something)".

(Free Dictionary) once a (something), always a (something)
proverb A person's innate or fundamental nature is not something they are willing or able to change. ♦ He says he's trying to leave his life of crime behind, but once a criminal, always a criminal.
♦ Even years after leaving the stage, she still can't resist performing—once an actor, always an actor.

In using it, you can't generalize, and you have to find the word that fits the given situation.

  • Once a crook, always a crook. (ref.)
  • Once a liar, always a liar. (ref.)
  • Once a leader, always a leader. (ref.)
  • Once a teacher, always a teacher. (ref.)
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domino effect

A domino effect or chain reaction is the cumulative effect produced when one event sets off a chain of similar events.1 The term is best known as a mechanical effect and is used as an analogy to a falling row of dominoes. It typically refers to a linked sequence of events where the time between successive events is relatively small. [emphasis mine]

Wikipedia

Like the child's game, if nothing sets off the first domino, nothing happens. However, the first domino falling onto its next in line can provoke a series of reactions, quite often creating a more serious reaction and so on...a type of:

chain reaction

1.2A series of events, each caused by the previous one.

definition 1.2A in Lexico

The other suggestion might be

He who punches first, punches twice satisfies the part of the question as I understand it:

The Chinese phrase that conveys the meaning perfectly is 有了第一次就会有第二次, which literally translates to "If there's the first time, there will be a second time".

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    Beat me to it. It was the first thing that crossed my mind. :) – user405662 Jun 24 at 5:28
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An idiom that half satisfies the numerical aspect of the question is:

“First step on the road to ruin”

Unfortunately, this has no explicit second step, which even getting your Mac onto the Internet used to have.

Citation

The expression “road to ruin” is very old. In the Wikipedia entry on the expression there is a reference to a theatrical work of that name from 1792. However I imagine it predates that.

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  • IKR? Users are becoming judgemental and parsimonious with their votes recently... – Cascabel Jun 23 at 22:25
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The expression a camel's nose under the tent may apply; it tends to imply that the progressive encroachment is something that is being actively pushed for by some interest (e.g., political operations):

A small, seemingly innocuous act or decision that will lead to much larger, more serious, and less desirable consequences down the line. (Free Dictionary)

A lighthearted version of the sentiment you expressed is betcha can't eat just one, which was an advertising slogan for Lay's potato chips.

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    I did not understand the DV on this... – Cascabel Jun 23 at 22:53
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A few phrases that convey there's no going back and when one thing leads to another:

  • You can't unring a bell: there are some things that cannot be undone.

  • In for a penny, in for a pound.

Once involved, one must not stop at half-measures. For example, All right, I'll drive you all the way there—in for a penny, in for a pound. This term originally meant that if one owes a penny one might as well owe a pound, and came into American use without changing the British monetary unit to dollar. Dictionary.com

  • You might as well be hanged for a sheep as for a lamb. Similar to In for a penny because the consequences were just as dire for a small debt as a large one. This has a more life-threatening resonance built into the phrase.

UK saying (also you might as well be hung for a sheep as for a lamb) said to mean that because the punishment for a bad action and an even worse one will be the same, you have no reason not to do the worse one. Cambridge (emphasis added)

In particular In for a penny, in for a pound has the gradient component that you mention. (So does Hanged for a sheep as for a lamb, but that might not sound as quantitatively linear.) It's not uncommon to hear "In for a penny..." in the context of drinking being justified by the "Well, I've already had one" logic.

  • Alea iacta est*, The die has been cast, attributed to Julius Caesar on crossing the Rubicon.

  • You can't put the toothpaste back in the tube. (H. R. Haldeman on Watergate. Wikipedia). A tangible metaphor that lends itself more recently to parenting psychology on the subject of making good choices.

*Iacta alea est for those native speakers, but it's been given a SV makeover.

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