[felson]

I think PTjvs is dead on. Also, this effect is strongest when the blocks of hands are very small. If the block is just one hand in length, then (in a 10-handed game) around 90% of your sample points will be <= 0, and about 10% will be greater than zero. As the block size gets larger, the median block value tends towards the mean. You can see this reflected in the plots, which shift to the right as the block size gets larger.