Could not find play-services-basement.aar

jcenter() has had mirrors of some libraries (I guess they are doing intentionally) that should originally available through google() or maven() repositories. When gradle build works, for any library that is used in the project the first place to look for is the repository that is listed first in repositories {.. When the jcenter() mirror does not have the release (e.g com.google.android.gms:play-services-ads:15.0.1 for my case) your gradle is looking for, the build fails with such error.

So, jcenter() should be listed at the last place in repositories {.. parts as below.

   buildscript {
    ext.kotlin_version = '1.2.50'
    repositories {
        google()
        maven {
            url 'https://maven.google.com/'
            name 'Google'
        }
        jcenter()
    }...

and

  allprojects {
    repositories {
        google()
        jcenter()
    }
  }

This is crazy!!! I faced the same issue. The builds were working fine and then suddenly started to fail with the same issue. I tried the suggestions above but it didn't work for me. Finally, this is what worked for me:

Update to latest firebase dependencies:

implementation 'com.google.firebase:firebase-core:16.0.4'
implementation 'com.google.firebase:firebase-ads:17.0.0'

also, the ads services:

implementation 'com.google.android.gms:play-services-ads:17.0.0'

Note: with play-services-ads:17.0.0, it mandatory to add the following in the Manifest file, otherwise application crashes on opening.

<application>
    <!-- Sample AdMob App ID: ca-app-pub-3940256099942544~3347511713 -->
    <meta-data
        android:name="com.google.android.gms.ads.APPLICATION_ID"
        android:value="[ADMOB_APP_ID]"/>
</application>