Find the highest number satisfying a condition in an infinite range

I wrote the below function for doing a variation of bisection search that I came up with. This can be useful when the higher bound is not known. It assumes that as number increases the result of the condition is also increasing.

For example - find the largest classroom size where the probability of two students sharing the same birthday is less than 0.99.

If I have a function that finds the probability of two students sharing the same birthday based on number of classrooms then I can pass that function and perform a bisection search over an infinite range to find the highest number.

def largest_satisfying_condition(condition):
    lo, hi = 1, 3
    mid = None
    lowest_hi_false = float('inf')
    while lo != hi:
        mid = (lo + hi) / 2
        if condition(mid):
            lo, hi = mid, hi * 2

            if hi > lowest_hi_false:
                #Because any value greater than this will give false result
                hi = lowest_hi_false - 1
        else:
            lo, hi = lo, mid
            if hi < lowest_hi_false:
                #No need to go over this when increasing hi
                lowest_hi_false = hi
    return mid

I wanted to know whether this can be written in a better way - according to either algorithm or Python.

if/else inside the loop doesn't look clean. Consider splitting the code into two parts:

# Find the "good" range

    while condition(hi):
        lo, hi = hi, hi * 2

    # At this point it is known that condition(lo) is True,
    # and condition(hi) is False. A normal bisection search
    # follows.

   return binary_search(lo, hi, condition)

It would be also worthy to factor the setup loop out in its own function.

StackExchange Code Review Q#84510, answer score: 6