Revisting

I posted on Friday about a bias that's fairly common when we don't do the math in statistics.

Now, I don't claim to be a statistician. In fact, it was by far my weakest area of math. I actually didn't start to really "get" it until I could apply it to poker.

So where does a conjunctive fallacy play? Not in the math side of things at all really. If you're just starting to apply things like pot odds and outs to your game, then you're going to do the math far more regularly than someone who has it down as second nature. I still play with people who are amazed that pros can figure out their percentages so quickly (when it's really, REALLY simple math to get an estimate). Once it becomes second nature, you just know.

No, this comes into play with the emotional aspect of the game.

Change the question. You have AA and you get it all-in preflop vs 78s. Which situation is worse?

sssxx
xxsss
xsssx

Yah, they all suck equally as much, but when the cards are coming down one at a time, we tend to get angrier when that flush-completing river comes, or the flush is flopped right out of the gate. Actually, if the flush is flopped, we hold out some narrow hope that we 4-flush or quad up for the win or that the board somehow splits. But when it comes on the turn? Somehow, that feels like it sucks less.

But the x's don't matter, it's the "sss" that kills you, regardless of where it shows up.

The fact is, statements like "Always on the river!" make no sense here. Sure, if you're betting all the way down and can't shake the chaser, it's a different story, but the suited runner-runner is no different than the flopped flush if all the money's already in.

But we get more tilted by the dramatic beat than the forgone conclusion. We hold our breath as the cards come down. This emotional response to something that's mathematically equivalent to being beat any other way just hurts our game in the next hand we play.