There is, I think, an easier way to explain advantage.
In the middle, when you need to roll 11 or more to succeed, that's 50% chance.
Since advantage gives you two shots of making the roll, and you only need to roll 11+ once, the total probability is 75%. In layman's terms, the second roll is only relevant if the first one fails, so the second roll's success rate (50%) is halved by the fact that the first roll is only a failure half the time, and 50% + 25% = 75%.
An increase by 25% is what we gamers would express as a +5 bonus on a d20.
Mathematically, of course, you take the probability of each roll failing, multiply them together (since they are independent) to get the chance of not succeeding; to find out the chance of actually succeeding you subtract that number from 1 (100%). In our example this becomes 1-(0,5x0,5)=0,75.
Now let's investigate the extremes. When you need only to roll a 2, that's 95% chance. This time advantage gives you much less of a benefit, because if you roll 2 or better, you've succeeded already, and you gain nothing from advantage.
This is the reason advantage can't be pinned down to a single number, and this is the insight you need - no actual math needed.
But let's investigate anyway: while the success rate supplied by advantage is 95%, it only applies 5% of the time (the first roll's failure rate). So we reduce the first number by the second (i.e. we multiply them) to get 0,95x0,05. Before we even whip out our calculators, you should see this will be a number close to 0,05, since we are close to calculating 1x0,05. 0,05 is 5% which is equivalent to a +1 bonus. (The real result is 4,75%)
Mathematically, advantage increases our success rate from 0,95 to 1-(0,05x0,05)=0,9975. The increase is 0,0475 which is the 4,75% number above which we'll round up to 5% because that's +1 on a d20
So already we've concluded that advantage can both mean a +5 bonus and a +1 bonus, depending on whether we're right in the middle of the probability curve, or at either end of it.
If you have a +5 attack bonus, and the monster has AC 16, advantage means a whopping +5.
But if the monster has AC 7 (or indeed AC 25), advantage means only +1.
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Now, while you're "only" getting a +1 on your AC 7 attack, don't forget that you almost don't need it, since after all, you will succeed 19 times out of 20 anyway, even without advantage.
Saying this because it's not just so simple as "advantage is sometimes close to worthless". After all, it's only "worthless" when you either don't need it, or when you're hopelessly behind.
Instead I'd say
advantage helps those exposed to pure luck and chance the most. It is when your d20 roll could be reduced to a coin toss advantage carries the most impact.
Advantage is truly a wonderful mechanism
It is far better than statical bonuses, because it levels out the playing field.
Yes, it also leaves the have-nots in the dust, but when has a hero ever had that problem?
The much more common scenario in previous editions was when your hero had a very high chance, and a static +5 would only obliterate any remaining chance at drama or tension, since it would turn a highly likely roll into a statistical certainty.
With a static +5 bonus you can no longer fail at hitting AC 7 (in the example above).
With advantage, you can still roll two ones in a row and thus you can still fail.
Not coincidentally, the chance of that happening is 1 out of 400. Which is, you guessed it, exactly the "missing" 0,25%. The success rate only went up to 0,9975, remember.
This means that advantage is an important part of the entire bounded accuracy concept of 5E.
