I rewrote a nongrammatical sentence in a casual conversation

Question

So, here’s another problem: how many people do you need in a room for there to be more than likely to have two people with the same birthday?

I tried and rewrote the above sentence as below.

1. how many people do you need in a room for there to be more than likely at least two people with the same birthday?

2. how many people do you need in a room more than likely to have two people with the same birthday?

1. Which sentence is more natural?
2. Considering 'more than likely' is an adverbial phrase meaning 'more likely than not : probably' in Webster dictionary, what is the most natural position of the phrase in the rewritten sentence?

Answer 1

Neither sentence is really correct, I suggest

How many people do you need in a room for it to be more than likely that at least two of them have the same birthday?