This ternary approach doesn't actually average 3/2 comparisons per level:
- First third: 1 comparisons
- Second third: 2 comparisons
- Third third: 2 comparisons
(1+2+2)/3 = 5/3 average comparisons. I think the gap starts here at assuming it's 50% of the time because it feels like "either you do 1 comparison or 2" but it's really 33% of the time because "there is 1/3 chance it's in the 1st comparison and 2/3 chance it'll be 2 comparisons".
This lets us show ternary is worse in total average comparisons, just barely: 5/3*Log_3[n] = 1.052... * Log_2[n].
In other words, you end up with fewer levels but doing more comparisons (on average) to get to the end. This is true for all searches of this type (w/ a few general assumptions like the values being searched for are evenly distributed and the cost of the operations is idealized - which is where the main article comes in) where the number of splits is > 2.
Oh yeah!
If you sort of squint this idea does work in cases where the cost of comparison is dominated by the cost of going down a level. And that leads you to things like b-trees where fetching a page from disk is expensive but doing the comparisons within that page is basically free.