Der Würfelwurf bestimmt die Ereigniskarte.

Der is the definite article the for a masculine singular noun in the nominative case. Here, Würfelwurf is the subject of the sentence, so it takes der.

• der Würfelwurf = the dice roll
• nominative = the thing doing the action

So Der Würfelwurf is the thing that bestimmt something.

Würfelwurf is a compound noun:

• Würfel = die / dice
• Wurf = throw / roll

Together, Würfelwurf means dice roll or more literally die throw.

German very often combines nouns into one longer noun like this.

Because German commonly forms compound nouns by writing them as a single word.

So instead of something like dice throw as two separate words, German usually makes:

• Würfel
  • Wurf → Würfelwurf

This is extremely common in German:

• Haus
  • Tür → Haustür
• Spiel
  • Karte → Spielkarte
• Ereignis
  • Karte → Ereigniskarte

Bestimmt is the conjugated form of the verb bestimmen, meaning to determine.

The subject is Der Würfelwurf, which is third person singular, so the verb must match it:

• ich bestimme
• du bestimmst
• er/sie/es bestimmt

Since der Würfelwurf is grammatically like he/it, the correct form is bestimmt.

Ereigniskarte is a feminine noun, so its definite article is die.

Here it is the direct object of the sentence, the thing being determined:

• Der Würfelwurf = subject
• bestimmt = verb
• die Ereigniskarte = object

For feminine nouns, the definite article is die in both the nominative and accusative, so the form does not change here.

You can tell from both word order and articles/case.

In this sentence:

• Der Würfelwurf comes before the verb and is the subject
• die Ereigniskarte comes after the verb and is the direct object

So the structure is:

• Subject
  • Verb
    • Object

That is the normal basic order in a simple German main clause.

Because all nouns are capitalized in German.

That is a standard spelling rule, not something special about this sentence.

So:

• der Würfelwurf
• die Ereigniskarte
• das Spiel
• die Karte

all have capital letters because they are nouns.

It is another compound noun:

• Ereignis = event
• Karte = card

So Ereigniskarte literally means event card.

Again, German builds this as one word rather than two.

Yes, that is also possible.

It means roughly the same thing:

• Der Würfelwurf = the dice roll
• Der Wurf des Würfels = the roll/throw of the die

The original version with Würfelwurf is more compact and very natural in German because compound nouns are so common.

The ü is a sound English does not have exactly. It is made with the tongue position of ee but with rounded lips.

A rough guide:

• Würfel sounds somewhat like VEER-fel, but with rounded lips on the first vowel
• Wurf sounds a bit like voorf, but again not exactly

A few pronunciation notes:

• W in German sounds like English v
• ü is not the same as u
• wurf has a short, crisp ending with f

So Würfelwurf is roughly VUER-fel-vurf, but that is only an approximation.

In this compound, Würfel is the dictionary form used inside the noun, and you do not need to read it as a separate plural in the sentence.

The whole word Würfelwurf functions as one singular noun:

• der Würfelwurf

So even though Würfel can mean die or cube, inside this compound the important thing is that the complete noun is singular and takes singular agreement:

• Der Würfelwurf bestimmt ...

Yes. Bestimmen has several related meanings, including:

• to determine
• to decide
• to define
• sometimes to appoint

In this sentence, the natural meaning is to determine: the dice roll decides which event card applies.