[Grammar] (that) that? omission of that?

[atssarbia]

I'll bet that made her mad!

Is the sentence like this sentence?

I'll bet (that) that made her mad!

 

[Raymott]

I'll bet that made her mad!

Is the sentence like this sentence?

I'll bet (that) that made her mad!

Yes, that's exactly what it is. But it's not necessarily changed to avoid two thats.
"I'll bet [that] this made her mad!" is a similar construction.

 

[2006]

I'll bet that made her mad!

Is the sentence like this sentence?

I'll bet (that) that made her mad!

You can omit the first "that".

Do you think (that) he will go?