What is the mass (or density) of the average Jenga block?
Well, it looks like that per Hasbro, an official Jenga set is made of Alder, which apparently has a density of 0.38 g/cc, which when combined with the dimensions of a standard Jenga block from this answer of 1.5cm x 2.5cm x 7.5cm, gives us an average of 10.6875g per block for a 28.125cm&sup3; block. 

The margin of error on both the density (one site I found had a range from 0.4&ndash;0.7 &times;10&sup3; kg/m&sup3;, or 0.4&ndash;0.7g/cm&sup3;) and the dimensions of the block due to manufacturing tolerances are enough to be considered significant, so I'd add a nice fudge factor to that before running further calculations.