Я веду счёт в дартсе.

Веду is the 1st person singular form of the verb вести — to lead, conduct, keep.

So:

• я веду = I keep / I lead / I am keeping
• ты ведёшь = you keep
• он/она ведёт = he/she keeps

In this sentence, вести счёт is a fixed expression meaning to keep score.

This verb is also a bit irregular, so it does not follow the simplest verb patterns. That is why you get веду, not something more predictable like вещу or вестиу.

Вести счёт is a common expression meaning:

• to keep score
• to keep track of the score
• sometimes more generally, to keep count

So in Я веду счёт в дартсе, the idea is not literally I lead the score, but rather I am the one tracking the points / score in a darts game.

This is a good example of a phrase that should be learned as a whole:

• вести счёт = to keep score

Счёт can mean several related things, depending on context:

• count
• score
• bill
• account

Here it means score.

In sports and games, счёт often refers to the numerical result:

• Какой счёт? = What’s the score?
• Вести счёт = to keep score

So in this sentence, счёт is the thing being tracked.

The correct spelling is счёт, with ё.

However, in normal Russian writing, ё is often replaced with е, so you may also see:

• счет

Even when it is written счет, it is still usually understood and pronounced as счёт in this meaning.

For learners, it is helpful to remember:

• счёт is pronounced with yo
• the stress is on that vowel: счёт

So if you see счет, be aware that it may still mean счёт.

Because Russian uses в + the prepositional case to mean in something.

Here, в дартсе means:

• in darts
• in the game of darts

The noun дартс changes form after в:

• дартс = darts
• в дартсе = in darts

So this is a normal case change:

• Я играю в дартс. = I play darts.
• Я веду счёт в дартсе. = I keep score in darts.

Notice that different meanings of в can require different cases.

Good question — this is something learners often notice.

In Russian:

• играть в дартс uses в with the accusative
• в дартсе uses в with the prepositional

Why?

Because the meanings are slightly different:

• играть в дартс = to play darts
  Here в is part of the pattern for playing a game.
• в дартсе = in darts / in the context of darts
  Here в means in or within that activity.

So even though English uses darts in both cases, Russian treats them differently.

Not always.

Russian often drops subject pronouns when the verb form already makes the subject clear. Since веду already means I keep, you could say:

• Веду счёт в дартсе.

That can still mean I’m keeping score in darts if the context is clear.

However, Я may be included:

• for clarity
• for emphasis
• when contrasting with someone else

For example:

• Я веду счёт, а ты бросаешь. = I’m keeping score, and you’re throwing.

So Я is perfectly natural, but not always required.

It can mean either one, depending on context.

Russian present tense often covers both:

• a general/habitual meaning: I keep score
• a right now/current meaning: I am keeping score

So:

• Я веду счёт в дартсе could mean
  I keep score in darts
• or
  I’m keeping score in darts

If you need to know which one is meant, context will usually tell you.

Yes. Russian word order is fairly flexible.

The neutral order here is:

• Я веду счёт в дартсе.

But you could also say:

• В дартсе я веду счёт.
• Счёт в дартсе я веду.

These versions shift the emphasis a bit:

• В дартсе я веду счёт emphasizes in darts
• Счёт в дартсе я веду emphasizes the score

English usually relies more on word order, but Russian often uses word order to show focus or emphasis rather than basic grammatical roles.

No, but it is a very natural and common way.

Other possible expressions include:

• считать очки = to count points
• подсчитывать очки = to tally points
• записывать счёт = to write down the score

But вести счёт is especially good when you mean to keep track of the score during the game.

So for a learner, вести счёт is probably the best basic phrase to remember.

A simple pronunciation guide would be:

Ya vi-DU shchyot v DAR-tsye

A few useful notes:

• веду is stressed on the last syllable: ве-ДУ
• счёт has one stressed syllable and sounds like shchyot
• дартсе is stressed on дар: ДА́РТСЕ

The consonant cluster in счёт can feel difficult at first, so learners often need a little practice with that word.