What is the broad match modifier for in Google AdWords?

Question

Google Ads

Hello.
Quotes from Google.
Broad match:

shows ads for all relevant variations , including synonyms , singular and plural forms, misspelled spellings , cognates (like bath and bathroom), and related queries . In addition, the user's web search history is taken into account.

Broad match is understandable. If the key is "buy a bike", then word forms are taken into account (change in numbers and cases + errors). There are also synonymous words. For example, "buy a scooter"
Broad match modifier:

By adding a modifier to broad match keywords, you can only show your ad for search queries that contain those words. The broad match modifier ensures that your ads appear on searches using at least one of your keywords .
With the broad match modifier, you can specify which words must be present in the search query for your ad to appear.

"At least one of your words." Those. keywords "+buy +bed cheap", and the ad will appear for the search query "bed cheap". So after all, only this contradicts the information that follows - "must be present."
What exactly is the modifier of this ... broad match for? Can someone explain clearly and point by point, as if you were writing an algorithm for a program? Those. if 1, 2, 3, 4, then something will happen.
PS By the way, there is some strange terminology, or I misunderstood something.
Key words are called and such - "buy something somewhere." So it's just a phrase, not a word.
Somewhere it says "keyword 'buy an iron cheap'". What kind of rubbish is this? Are phrases really called keywords within the Google thesaurus?
Upd: I re-read the manual again. Write a keyword and then give a phrase. What kind of perversion is this?

Answer 1

From the end - the term "keyword" in this case should be taken not from the point of view of the semantics of the Russian language, but as a designation of a unit of the semantic core of contextual advertising systems. In a professional environment, the terms "keyword", "key phrase", "key query" are already so mixed up in use that they are understood by everyone as one. This is not the thezarus of Google.
As for the broad match modifier, it was introduced by Google not so long ago and, in principle, Yandex also has this operator, it’s just that it doesn’t have such an urgent need to mark each word and only prepositions, conjunctions are marked with it.
Now why do you need it in Google. Google Adwords has a very frivolous attitude towards keywords in broad match (that is, in writing without any operators). Any word from such a query can be omitted, replaced by a synonym, a word close in meaning. Also, the display can be carried out on a completely different request, if the user previously searched for something according to your request. This is often detrimental to the effectiveness of advertising.
Example. You are advertising for the sale of real estate. You have a query "buy residential property" in a broad match. In this case, Google can easily show your ads for queries such as "buy commercial property", "rent residential space", "rental housing" or, in theory, even "housing for a hamster". More often, of course, he tries to show ads to those users who are most likely interested in it and will make a click, he is also not a fool - a high CTR is also important for a contextual advertising system, but nonetheless. To avoid such situations, you can use the broad match modifier: "+buy + residential + real estate". Then he will not be able to omit words or replace them with others, except for changing their order or replacing them with a close variant.
Thus, using, for example, only two broad match modifiers in the query "+buy residential + real estate" will get rid of queries with "rent", but not get rid of "commercial property". In this option "+ buy + residential real estate" get rid of the "rent" and the commercial sector, but options with "buy a residential trailer" or "buy a residential garage" are likely.
I hope I have written everything clearly. Ask questions if it's not clear.