Пускай жеребьёвка определила очерёдность, я буду вести счёт.

Here пускай means something like let or have ... in English.

So the idea is:

Let the draw decide the order; I’ll keep score.

A very close synonym is пусть.

• пусть is more neutral and standard
• пускай is a bit more conversational

This is the trickiest part of the sentence.

If you want a straightforward let ... decide meaning, many native speakers would more naturally say:

Пускай / пусть жеребьёвка определит очерёдность.

So yes: определит is the form many learners would expect, and it is the safer form to use yourself.

The given определила is understandable, but it sounds less standard in this type of sentence. It can feel colloquial or slightly loose, as if the speaker treats the deciding as a completed preliminary step, or almost like fine, let the draw have decided the order.

So for active use, remember:

• most natural: пусть жеребьёвка определит очерёдность
• the version with определила is more unusual

Because it agrees with жеребьёвка, which is a feminine singular noun.

In the past tense, Russian verbs show gender in the singular:

• masculine: определил
• feminine: определила
• neuter: определило

So:

жеребьёвка определила = the draw determined

Жеребьёвка means a drawing of lots, a random draw, or a procedure used to decide something by chance.

Depending on context, it could be:

• drawing lots
• a random draw
• the toss

In games or competitions, it often means the random procedure used to decide who goes first or in what order people act.

Очерёдность means order, sequence, or the order in which people do something.

In this sentence, it means the order of turns or participation.

So:

• определить очерёдность = to determine the order
• очерёдность игроков = the players’ order
• очерёдность ходов = the turn order

Yes, it is the direct object, so it is in the accusative case.

The verb определить takes a direct object:

определить что? → очерёдность

But nouns like очерёдность often look the same in the nominative and accusative, especially inanimate feminine nouns of this type ending in -ость.

So the case changes grammatically, but the form stays the same.

Вести счёт is an idiom meaning to keep score.

Literally:

• вести = to lead, to conduct, to carry on
• счёт = count, score

But together, the natural meaning is:

вести счёт = keep score / keep track of the points

Because вести is an imperfective verb.

In Russian, the future of an imperfective verb is normally formed with быть + infinitive:

• буду вести
• будешь вести
• будет вести, etc.

So:

я буду вести счёт = I will keep score

This sounds natural because keeping score is an ongoing activity, not a single completed act.

If you used a perfective verb instead, the meaning would change and could sound more like I will begin to keep score rather than simply I’ll be the one keeping score.

Yes, it could be omitted.

Russian often leaves out subject pronouns when they are clear from the verb form. So:

Буду вести счёт
would also be possible.

Here я is probably included for emphasis or contrast:

Let the draw decide the order; I’ll keep score.

So the sentence neatly divides responsibilities:

• the draw decides the order
• I keep score

Because the sentence contains two clauses:

• Пускай жеребьёвка определила очерёдность
• я буду вести счёт

Russian uses a comma to separate them in this kind of structure.

In English, you might naturally say:

• Let the draw decide the order, and I’ll keep score
• Let the draw decide the order; I’ll keep score

Russian commonly uses the comma here.

Yes, they are important for pronunciation.

• жеребьёвка
• очерёдность
• счёт

The letter ё is pronounced yo.

In many ordinary Russian texts, ё is often written as е, so you may also see:

• жеребьевка
• очередность
• счет

But the pronunciation is still with ё, and for learners it is very helpful when the dots are written.

Yes, in some contexts пускай can have a concessive sense, something like:

• granted
• even if
• let it be that

That is one reason this sentence may feel a little less straightforward than the more standard:

Пусть жеребьёвка определит очерёдность, я буду вести счёт.

So if this sentence sounds slightly unusual to you, that is a reasonable reaction. The clearest learner-friendly version would usually be with определит rather than определила.