Are the algorithms for picking between 2 numbers randomly a lot less computer intensive than the algorithms for picking almost any number randomly?
In principle yes, but in practice probably not; both of them are likely to be extremely fast.
You can randomly choose between two numbers by generating a random bit.  That is extremely fast in practice.
You can't &quot;pick almost any number randomly&quot;.  Instead, all you can do is sample from a distribution. The time it takes to sample from a distribution depends on the specific distribution you have in mind.  However, for most cases commonly encountered, this too is very fast.  For instance, if you want to pick uniformly at random an integer from a particular range, that can be done in a standard way by generating some random bits and then using them to select an integer; it will be very fast in practice.
So, while picking between two numbers might be quicker, both operations are likely to be so fast that it's not clear it is worth worrying too much about which is faster.
If you want to understand why this is the case, I suggest you study algorithms for picking a random number and for sampling from various distributions; that will give you a concrete understanding.