teban ni yotte, tukau kaado ga tigau.

手番 means a player's turn or turn order in a game.

So in this sentence, it refers to which turn it is or whose turn it is. That is why the sentence is talking about how the card used changes depending on the turn.

It is a game-related word, and it is more specific than just 番, which can mean turn more generally.

Here, 〜によって means depending on..., according to..., or based on....

So:

• 手番によって = depending on the turn

This pattern is often used when something changes based on some condition.

Examples:

• 人によって考え方が違う。
  = Ways of thinking differ depending on the person.
• 場所によって値段が違う。
  = Prices differ depending on the place.

In your sentence, it sets up the condition: the turn changes which card is used.

Because 使うカード is a relative clause in Japanese.

Japanese puts descriptive clauses before the noun they modify. So:

• 使うカード = the card that is used / the card you use

Literally, it is something like:

• [use] card

This is very normal Japanese word order. There is no relative pronoun like that, which, or that you use. Japanese just places the verb phrase directly before the noun.

Other examples:

• 食べる物 = the thing you eat
• 昨日見た映画 = the movie I saw yesterday
• 彼が書いた本 = the book he wrote

Yes, it is omitted, which is very common in Japanese.

In 使うカード, the sentence does not explicitly say who uses the card. The subject could be understood from context as:

• you
• the player
• one
• or whoever is relevant in the game situation

So 使うカード can naturally mean:

• the card you use
• the card the player uses
• the card used

Japanese often leaves out information that is obvious from context.

Because 違う is not used like a normal transitive verb with を here.

In this sentence:

• カードが違う = the card is different / the cards differ

The particle が marks the thing that is different.

A useful way to think about it is:

• 違う often behaves like to differ / to be different

So Japanese says:

• Aが違う = A is different

Examples:

• 色が違う。 = The color is different.
• 答えが違う。 = The answer is different.

So 使うカードが違う means the card(s) used are different, not to differ the card.

The が marks 使うカード as the thing that is doing the differing, or more naturally, the thing that is different.

Structure:

• 手番によって = depending on the turn
• 使うカードが = the card(s) used
• 違う = are different

So the sentence is built around X が 違う:

• X is different
• X differs

This is a very common pattern in Japanese.

Because this sentence is written in plain style, which is common in:

• explanations
• game rules
• casual writing
• dictionary-style statements
• notes and instructions

So:

• 違う = plain form
• 違います = polite form

The polite version would be:

• 手番によって、使うカードが違います。

Both are correct. The difference is just tone and level of politeness.

Usually 手番によって is better here.

Why? Because によって clearly expresses variation depending on a condition. The sentence is about how the card changes based on the turn.

• 手番によって、使うカードが違う。
  = The card used differs depending on the turn.

If you used で, it would not express that same depending on meaning as naturally.

So for this kind of sentence, where the result changes according to something, 〜によって is the standard choice.

It can be understood as either, depending on context.

Japanese nouns usually do not mark singular vs. plural unless necessary. So カード could mean:

• the card
• cards

That means 使うカードが違う could be interpreted as:

• the card you use is different
• the cards you use are different

The surrounding context, especially the rules of the game, tells you which is more natural.

The comma helps separate the condition from the main statement:

• 手番によって、 = depending on the turn,
• 使うカードが違う。 = the card used is different.

It makes the sentence easier to read, especially because 手番によって is an introductory phrase.

The comma is helpful, but not always absolutely required. You may also see:

• 手番によって使うカードが違う。

with no comma. Both are natural.