Here's what I don't get. I've played a lot of Hearts for many years - thousands of games I'm sure. The number of times I've played a low heart, and the trick has gone 2H, 3H, 4H, 5H seems way out of probable reality. But the number of times I've seen all four players play the any of the same value card (e.g. 6C, 6D, 6H, 6S) is once. Why is the probability of 2H, 3H, 4H, 5H any lower than any 4 same value cards? In my naiveté it seems that in both cases, the probability calls for 4 players to have a specific card at the same time. Can anyone explain it to me like a 4 year old?
The reason H2,H3,H4,H5 is more likely than H6,S6,C6,D6 is simply the rules of the game. If a heart is led, it is mandatory to play a heart if possible, so most tricks contain four of the same suit, and a trick with one of each suit is extremely rare. When you add in the requirement for all four to be of the same rank, your second example is vanishingly improbable. This boils down to the fact that a card game is not a random selection of available cards (except when my partner is choosing an opening lead, of course).