I’ve really enjoyed Scott Sumner’s recent posts. There is a reason we can do bad things about this, but what I want to talk about here is to selectively collect only certain coincidences, making them look much more appealing than they actually are.
This is an example of this phenomenon that I often make myself. Growing up, my family has developed towards the tradition of playing spades – usually my dad and I are on the team against my mother and sister. Sometimes I used my thought-provoking hand, so I (usually) remind myself that the probability of getting this particular mix of 13 cards is exactly the same as the mix of the other 13 cards.
Why did I have this reaction in Som’s hands, but not others (mostly) have this reaction? When I got a hand that seemed unusual in a truly notable way, I tend to have that knee jerk response, which personally influenced what number of tricks I could expect to win. If I got a total of 7 cards, the fact that I was stuck in my hand made my hands unusually strong and I was able to pull out the average number of tricks on Avoba. Or, if the Evary card in my hand is below 7, my hands may be usually weak and I might consider a zero bid. However, I had most of the hands I got had compost to make them look unique immediately. Most of the hands were evenly mixed with black and red cards, suits and cards.
To use extreme cases, consider two possible spades.
Hand 1: Ace of Spades, 7 Hearts, King of Clubs, 2 Diamonds, 10 Spades, 5 Clubs, Jack of Hearts, 3 Spades, Queen of Diamonds, 9 Spades, 6 Hearts, 8 Clubs, 4 Spades. Hand 2: 2 spades, 3 spades, 4 spades, 5 spades, 6 spades, 7 spades, 8 spades, 9 spades, 10 spades, Jack of Spades, Queen of Spades, King of Spades, Ace of Spades.
If I had a first hand, the ID would look at it a bit and start thinking about a lot of tricks I should bid on, but I didn’t think about it again beyond that. If I had a second hand I fell out of the sheath surprised by this one-time Toussandt coincidence and the person who played Spade couldn’t believe it was true. Certainly, if I’m playing a game on Subuone and they get that secondhand item, I think they’re being fooled (or they’re skilled card magicians like the same thing.
Still, each of these hands has exactly the same odds to be dealt with. But the second one feels intuitively unlikely. The first one basically bothers what randomness looks like, while the second one doesn’t. The strength of the first hand is in the normal range and the medium seconds are invincible. That’s why I don’t notice the coincidences of thousands of people in my first hand. The direct probability of that is low for Vray (about 1 in 635 billion people), but the effect of having that particular hand is not for Vray. Every time you’re treated with 13 cards in Spade, you’re witnessing thousands of times fewer subjects than winning a Powerball, which is something we selectively overlook.
(*The total number of 13 cards that can be dealt with is 52! /(13! *(52-13)!) and it becomes a potential move of 635,013,559,600.)
“The odds of X where X is happening is about one in 635 billion people,” and if I take you, you might conclude that it’s reasonable that X can be close to you if it never happens in your life. Still, every time you handle your hand on a spade, there’s one chance in every 63.5 billion people. Very unlikely events happen all the time – but we rarely notice them.
What’s even more surprising is the placement of the decks of certain cards that you shuffle. There’s 52! How to place decks of cards – or, fully written,
80,658,175,170,943,878,571,660,636,856,403,76,975,289,505,440,883,277,824,000,000,000,000,000,000,000,000
The possibilities for unique arrangements that allow you to shuffle decks of cards. (See this for an attempt to explain how heart-worthy this number can hold you in.) Every time you shuffle a deck of cards, you’re almost certain you’re creating an arrangement that doesn’t exist, even without the universe’s heat death. But even knowing that, I never shuffle decks of cards and I will never be floored at the near impossible odds of the arrangement I just created – unless it is distinctive in a sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sub-sum-sum-sum
This is everything I know intellectually, but still, I can’t grasp it instinctively, so it’s as if my knee’s reaction to a particular spade’s hand was unusual. But while there is this knee jerk response in my “System 1” mind, it’s still good to dive into your “System 2” mind and remind you that the mundane things around you are just as miraculously unlike any other.
