Boss rush generation thoughts

'Second' boss room occurs only when coins >= 5 upon starting Necro/Depths II as far as I can tell, no other factors.

Thoughts as to why this could be:
5 coins is the condition for arcades spawning

Assume a single, shared random number generator with seed = RH10K4BX (or whatever the seed is for a particular run)
A random number generator will produce the same 'random' numbers in a row each time
Assume each time a room is built, a random number used to decide which room from the relevant pool should be used
Let r[i] be the ith random number generated
Assume Isaac generates all normal rooms first (i.e, non shop/item room/secret room/etc.), assume after doing so, last value from RNG was r[j].
Assume only special rooms are: Arcade, Boss Rush.
At 5 coins or more: Generate Arcade using r[j+1], generate Boss Rush using r[j+2]
At 4 coins or less: Generate Boss Rush using r[j+1]