Barry
Zeeberg
We quantitatively evaluated the assertion that says if one suit is found to be evenly distributed among the 4 players, the rest of the suits are more likely to be evenly distributed. Our mathematical analyses show that, if one suit is found to be evenly distributed, then a second suit has a slightly elevated probability (ranging between 10% to 15%) of being evenly distributed. If two suits are found to be evenly distributed, then a third suit has a substantially elevated probability (ranging between 30% to 50%) of being evenly distributed. The probabilities for more unbalanced distributions decrease in similar proportion, but these probabilities are quite low to start with, so the further decreases may only rarely be of practical significance.
The full manuscript is available in the inst/pdf folder.