W-34/70 is the prototypical tetraploid (4 sets of chromosomes) lager yeast strain. It has two sets of S. cerevisiae chromosomes and two sets of S. eubayanus chromosomes. However, it also suffers from aneuploidy. Aneuploidy is a condition where an organism does not have a total number of chromosomes that is evenly divisible by the haploid cell count (i.e., one full set of chromosomes, which is 10 chromosomes when discussing yeast) due to chromosome addition or deletion. Down Syndrome is an example of chromosome addition aneuploidy in humans. People who have Down Syndrome have a full or partial extra copy of chromosome number 21. Wolf-Hirschhorn syndrome is an example of chromosome deletion aneuploidy in humans. It is caused by partial deletion of chromosome 4.
As an aside, scientists used to believe that the Saaz (e.g., Carlberg Bottom Yeast No. 1) and Frohberg (e.g., W-34/70) families of yeast strains were the result of two different hybridization events up until very recently. However, a research team at Carlsberg labs proved that the two families of yeast strains are more than likely from the same hybridization event due to carrying identical genetic translocations. A translocation is the exchange of genetic material between nonhomologous chromosomes (i.e., chromosomes that are not part of a chromosome pair). What is really interesting about this discovery is that the Saaz family of lager yeast strains are triploids that contain one set of S. cerevisiae chromosomes and two sets of S. eubayanus chromosomes. The S. eubayanus genetic admixture is what gives lager yeast its cold tolerance; hence, Saaz strains are more cold tolerant than Frohberg strains.