The name trifolium literally means 3 leaves in Latin, and most clovers do indeed have only 3 leaves. But some clovers end up with 4 leaves. And these are the ones celebrated to give the finder good luck. Why are they so hard to find? To understand that we have to take a look at their genetics.. the blueprint that makes up life.
The genome, the entirety of the blueprints that makes up the organism, is pretty unique in this case. White clover has an allotetraploid genome, it has 1 copy of 2 different genomes! Each one of those genomes are diploid (2), this it has 4 gene copies! How does this happen? Well, in this case it is suspected that Trifolium occidentale and T. pallescens crossed. The resulting offspring kept both genomes to become T. repens. Because of this it has been difficult to map the genome and tease apart which genes control which traits.
Thankfully, there have been a few studies that have shed some light on this subject. It turns out that the progenitor of the Trifolium genus had 5 leaflets and the number of leaflets has decreased over evolutionary time to become 3 leaflets. But the 3+ leaflet is still a genetic possibility. At least one multifoliate gene has been discovered. This gene is a recessive gene that is not only inherited (about 1 out of every 10,000) but can be activated by environmental conditions. Four leaf clovers like it hot, studies have shown there are more 4 leaf clovers in the summer than winter, and more in the greenhouse than outside during winter.
As Saint Patrick's Day occurs in March, this is not the ideal time to be searching for that "lucky" four leaf clover. Come back in June, when the days are warmer, to increase your odds!
Ford and Claydon Inheritance of multifoliate leaves in white clover. Agronomy Society of New Zealand Special Publication No 11. 167-170 http://www.grassland.org.nz/publications/nzgrassland_publication_646.pdf
Griffiths et al 2013. An integrated genetic linkage map for white clover (Trifolium repens L.) with alignment to Medicago. BMC Genomics 14:388 http://bmcgenomics.biomedcentral.com/articles/10.1186/1471-2164-14-388
Gustine and Huff 1998. Genetic variation within among White Clover populations from Managed Permanent Patures of Northeastern USA. Crop Science 39:524-530 https://dl.sciencesocieties.org/publications/cs/abstracts/39/2/CS0390020524
Tashiro et al 2010 Leaf Trait Coloration in White Clover and Molecular Mapping of the Red Midrib and Leaflet Number Traits. Crop Science 50:1260-1268 http://parrottlab.uga.edu/parrottlab/Publications/Tashiroetal2010.pdf