Пускай первый дротик оказался промахом, ты не промахнёшься снова.

Not really. Here пускай is being used in a concessive sense, meaning something like:

• even if
• granted that
• let it be that
• suppose

So Пускай первый дротик оказался промахом means something like Even if the first dart was a miss or Granted that the first dart missed.

Russian пускай can also mean let in commands, but that is not the main sense here.

Yes, they are very close. In many sentences they can be swapped:

• Пускай...
• Пусть...

Both can mean let or even if / granted that, depending on context.

The difference is mostly stylistic:

• пусть is more neutral and common
• пускай can sound a bit more conversational or expressive

So this sentence could also be written as:

• Пусть первый дротик оказался промахом, ты не промахнёшься снова.

Because the first part is a subordinate clause introduced by пускай.

Structure:

• Пускай первый дротик оказался промахом = concessive clause
• ты не промахнёшься снова = main clause

So the sentence works like:

• Even if X, Y
• Although X, Y

Russian normally separates that kind of clause with a comma.

Because оказаться often takes the instrumental case when it means to turn out to be.

Pattern:

• оказаться кем? чем? = to turn out to be what?

So:

• дротик оказался промахом = the dart turned out to be a miss

Here:

• промах = nominative form
• промахом = instrumental singular

This is very normal after verbs like:

• быть
• стать
• оказаться

especially when describing what something or someone turned out to be.

Оказался means turned out to be or proved to be.

So:

• первый дротик был промахом = the first dart was a miss
• первый дротик оказался промахом = the first dart turned out to be a miss

Оказался adds a sense of result or discovery. It sounds a little more dynamic, as if the throw happened and the result became clear.

Also, оказался is the past masculine singular form, agreeing with дротик.

Yes. Дротик is the usual word for a dart, such as a dart thrown in a game.

It is historically related to a smaller-forming suffix, so it can feel like a small dart / little projectile, but in modern usage it is simply the normal word for dart.

So learners do not need to treat it as especially cute or emotional here. In this sentence it just means dart.

Промахнёшься is:

• 2nd person singular
• future
• from the verb промахнуться
• perfective
• reflexive form with -ся

So it means:

• you will miss

Why does it look like a present-tense form? Because in Russian, perfective verbs do not have a true present meaning. Their non-past forms usually express the future.

So:

• ты промахнёшься = you will miss
• ты не промахнёшься = you will not miss

Yes. This is a nice piece of wordplay.

• промах = a miss, an error
• промахнуться = to miss

So the sentence uses the same root twice:

• оказался промахом
• не промахнёшься

That gives it a neat rhetorical effect, a bit like English:

• The first throw was a miss, but you won’t miss again.

So the Russian is elegant because the noun and verb echo each other.

Yes, it could be omitted.

Russian often leaves out subject pronouns when the verb form already shows the person:

• не промахнёшься снова already means you won’t miss again

Including ты makes it more direct and personal. It can add:

• emphasis
• encouragement
• contrast

So:

• не промахнёшься снова = neutral
• ты не промахнёшься снова = you won’t miss again

It sounds more like someone reassuring or motivating another person.

Russian word order is flexible, so снова can move around more than again usually can in English.

Here, putting снова at the end makes it sound natural and gives a slight emphasis to again:

• ты не промахнёшься снова

Other placements are possible, for example:

• ты снова не промахнёшься
  This can sound different, and depending on context may suggest again you won’t miss, which is not the same idea.

So in this sentence, final снова clearly means:

• you won’t miss again

Yes. It has a reassuring, motivational tone.

It basically says:

• So what if the first attempt failed? You won’t fail again.

The first clause admits a mistake, and the second clause encourages the listener. That is why the sentence feels more expressive than a plain factual statement.

Yes. Depending on context, a natural English translation could be:

• Even though the first dart was a miss, you won’t miss again.
• Even if the first dart missed, you won’t miss again.
• Granted that the first dart was a miss, you won’t miss again.

The exact English wording depends on tone, but the Russian idea is concessive: the first failure does not stop the expected success afterward.