All rivers are one outers

Imagine if you will a battle of the blinds. I raise with AKK6 single suited from the SB. Villain defends with who knows what in the BB. Flop comes KQ2 rainbow. I lead for pot, villain re-pots, I shove, villain calls. I show top set, villain shows 226J for bottom set and needs either running hearts or the case deuce. Turn puts out a three of diamonds and the river produces the you-know-what.

At times like these I try to remember all the times that I sucked out a one outer. Of course good players don't get themselves in the situation where they need to catch a one outer, right? Well it happens, both ways...though it seems to always happen the other way more often. And it stings when it does. But I always try to keep things in the math perspective. After 80K hands there are bound to be one outers along the way. And then it occurred to me that ALL rivers are one outers. The odds of the river being the jack of diamonds are the same as the three of clubs or the ace of spades. Now whether that card makes someone's hand or not is another question and whether or not that is the ONLY card that can make someone's hand is a different situation still. It's actually a pretty rare occurrence that there is even a scenario where someone only has exactly one out much less hit it.

So the hand is an interesting study in probabilities and notable for its rarity. Still sucks though.