Does the chance of catching a Pokémon change with each throw?

Question

In GamePress's article about Catch Mechanics, they describe how the capture chance is calculated for each ball thrown. At the end of the article they say this...

Catch Success and Failure

Finally, the server generates a Random Number between 0% and 100.0%. If Final Capture Chance is greater than this random number, the Pokémon is caught. If Final Capture Rate is less than this random number, the Pokémon breaks out and possibly flees.

How the capture rate is calculated is explained well in article, however, what I don't understand is when the Random Number is chosen. Is a value chosen with each throw, each encounter, each spawn?

So basically, I can modify the Final Capture Chance by giving a Razz Berry, throwing a different type of ball, and/or throwing the ball when the target circle is smaller/larger. But if the Random Number is 100%, and it never changes for that Pokémon. Then I don't have much chance of ever catching the Pokémon. However, if the Random Number changes with every throw, then I always have a chance to catch it with the next ball (assuming it doesn't run away).

Answer 1

Based on the quote you provided, where it says:

If Final Capture Rate is less than this random number, the Pokemon breaks out and possibly flees.

This indicates that this random number must be generated for each throw.

Many times now, I have attempted to capture Pokemon with Pokeballs, getting Great or Excellent throws, then failing, but then throwing a Pokeball with no accuracy bonus, and catching the Pokemon. If the random number did not change with each throw, these cases would be impossible.

Answer 2

The Random Number is generated once for each throw, the chance of catching a Pokémon does not change with each throw, except with things that explicitly do so like the Razz Berry.

Answer 3

It's pretty much like two dices.

You have a fixed capture rate based on the Pokémon species and its level, the ball you're throwing at it and whether or not a Razz Berry effect is applied. This value will not change, if you keep using Razz Berries (if used at all) and the same Pokéballs.
However, it is increased by throwing curve balls and/or landing nice/great/excellent throws.

The sum of that is your Final Capture Rate, the first dice on the table. So basically the chance changes by what you do. And only by that. If you land the same throws with the same balls the chance will not change. Ever. (For that particular Pokémon that is.)

The random number is your other dice. With each throw you roll your 2nd dice, and if it's higher (or equal)... Gotcha. Regardless of the amount of rolls the first dice will still lie there, only affected by the variable bonuses.

So it would be like this:
You throw the ball...

1. Thrown ball hits the Pokémon
2. Pokémon rolls its dice (capture rate + bonuses = Final Capture Rate = first dice)
3. You roll your dice (random number = second dice)
4. If you land a greater (or equal) roll the Pokémon is yours, otherwise it breaks out and you start over again (unless it flees).