تسحب صديقتي بطاقة لعب من دون أن تغش.

The verb تسحب comes from سحب, whose basic idea is pulling or drawing out.

In a card context, تسحب بطاقة means to draw a card. So although the verb can literally mean pulls, the natural English translation here is draws.

Here تسحب is the non-past, third-person feminine singular form, so it means she draws.

That matches the subject صديقتي = my female friend.
A useful thing to know: the written form تسحب can also mean you (masculine singular) draw, but the context here makes it clearly she draws.

Because Arabic very often uses verb–subject–object order, especially in neutral statements.

So تسحب صديقتي... is a very normal structure in MSA.
You could also say صديقتي تسحب..., but that puts a bit more focus on my friend.

The base word is صديقة = female friend.
When you add the suffix ـي meaning my, it becomes صديقتي = my female friend.

The reason you hear t is that the final ة (taa marbuuTa) is pronounced like t when another ending or suffix follows it. So:

• صديقة = ṣadīqah
• صديقتي = ṣadīqatī

Arabic does not have a separate word for a/an.

Instead, a noun is indefinite simply by not having الـ. So بطاقة لعب can mean a playing card even though there is no separate word for a.

Yes. بطاقة لعب is an iDaafa (construct phrase), literally something like a card of play/game.

That is how Arabic often expresses combinations that English might translate with an adjective or a compound noun. So:

• بطاقة لعب = a playing card

In this structure:

• the first noun is بطاقة
• the second noun is لعب

Because بطاقة is the first term of an iDaafa, and the first term of an iDaafa does not take tanwīn.

If the phrase is fully vocalized, it would be:

• بِطاقةَ لَعِبٍ

Here بطاقةَ is the direct object of تسحب, so it is accusative, but it still has no tanwīn because it is in iDaafa.

In an iDaafa, the second noun is put in the genitive case.

So if fully vocalized, it is:

• لَعِبٍ

That is why the phrase is structurally بطاقةَ لعبٍ.

من دون means without, and أن introduces a following verb.

So من دون أن تغش means without cheating or more literally without her cheating.

This is a very common Arabic pattern:

• من دون أن + verb
• without doing ...

Because Arabic often uses أن + imperfect verb after expressions like من دون.

Also, أن puts the following imperfect verb into the subjunctive. So the fully vocalized form is:

• تَغُشَّ

In normal everyday writing, short vowels are usually omitted, so you just see تغش.

By itself, in unvocalized Arabic, تغش could be read as either she cheats or you (masculine singular) cheat.

But the context removes the ambiguity. Since the sentence is about صديقتي, the intended meaning is she cheats.

Yes. بدون أن and من دون أن both mean without and both are widely understood.

In MSA, من دون أن often sounds a bit more formal or classically written, while بدون أن is also very common and natural.

A fully vocalized version is:

تَسْحَبُ صَدِيقَتِي بِطَاقَةَ لَعِبٍ مِنْ دُونِ أَنْ تَغُشَّ

A rough transliteration is:

tasḥabu ṣadīqatī biṭāqata laʿibin min dūni an taghushsha

This shows several things clearly:

• تسحبُ = non-past feminine singular
• بطاقةَ = accusative object
• لعبٍ = genitive, because it is the second term of the iDaafa
• تغشَّ = subjunctive after أن