Calibrating With Cards

In this post, I’ll try to bring to­gether two things I en­joy: ra­tio­nal­ity and magic. Like Hazard, I’ve also prac­ticed close-up magic for a good amount of time now. After re­cently see­ing Tyler Alter­man make a Face­book post about es­ti­ma­tions and Sys­tem 1, it oc­curred to me that there are a few cal­ibra­tion ex­er­cises you can do with a deck of play­ing cards. The three ex­er­cises be­low are all var­i­ants of cut­ting/​ma­nipu­lat­ing a deck of cards, and then try­ing to in­tuit some­thing about the deck.

This serves three pur­poses:

  1. Get a feel for your Sys­tem 1:

    1. The goal of the fol­low­ing three ex­er­cises is to see how good your gut is at es­ti­mat­ing un­cer­tainty (hint: prob­a­bly bet­ter than you think!)

  2. Im­prove cal­ibra­tion:

    1. Th­ese ex­er­cises all al­low for some room for er­ror. You can set your con­fi­dence in­ter­vals and see how quickly you can get cal­ibrated us­ing first prin­ci­ples.

  3. Prac­tice cool party tricks:

    1. While I don’t in­tend for this to be a full-on magic tu­to­rial, the ex­er­cises I out­line are build­ing blocks for magic tricks, and even demon­strat­ing your su­per-cal­ibra­tion (af­ter get­ting good) might be im­pres­sive.

Below are the three ex­er­cises. If you have a deck of cards handy, you can tag along!

Cut Estimation

The sim­plest ex­er­cise is as fol­lows:

  1. Lift up a packet of cards.

  2. Es­ti­mate how many cards you’ve picked up.

  3. Count to check how many you ac­tu­ally picked up.

You have a few ob­vi­ous refer­ence points. The en­tire deck is 52 cards, and you can eas­ily tell if you’ve lifted up more or less than half (and this re­curses). With a lit­tle prac­tice. I’ve found that my gut is pretty good at this sort of thing. I’ll ask my­self how many cards, and there will be a num­ber that feels right. It’s usu­ally quite close.

Things to pay at­ten­tion to:

  • When your Sys­tem 2 es­ti­mate con­flicts with your Sys­tem 1 gut an­swer of how many cards you cut off.

  • Whether you are sys­tem­at­i­cally over or un­der­es­ti­mat­ing the amount.

Re­peat­ing The Cut

This is similar to the first one:

  1. Cut to a card.

  2. Re­place the pack on the deck.

  3. Cut to the same card again.

Things to pay at­ten­tion to:

  • When you try to cut to the card a sec­ond time, how quickly does your gut know that you got it right or wrong?

  • What does it feel like to “know” that the pack of cards in your hand is not the same size as the first time?

  • If you know you got it wrong, do you know if you cut too much or too lit­tle? And by how much?

Riffle Peek

This one is some­thing I’ve just started play­ing with re­cently, and it’s a mildly su­per­hu­man feat to get down right.

  1. Name a card. Any play­ing card.

  2. Riffle through the cards, watch­ing the cor­ners (where the num­ber and suits are) flip to­wards you, and look for the card you named.

  3. Us­ing the in­for­ma­tion in 2, cut to where you saw the card.

This is difficult. It’s par­tially an es­ti­ma­tion task be­cause you need to know ap­prox­i­mately where through the deck you saw the card, i.e. half-way, at the end, etc. To start, you can go slow, such that you can see each card as it slips off your thumb.

This gets harder the faster you riffle through the cards. To ramp up the difficulty, riffle faster, such that you can only get a frac­tional peek at each card’s cor­ner.

Things to pay at­ten­tion to:

  • How does your vi­sual ex­pe­rience of watch­ing the cards differ when you aren’t look­ing for a par­tic­u­lar card vs when you are? Does any­thing jump out at you? Are there false pos­i­tives?

  • How many riffles through the deck does it take for you to glimpse the card? (I don’t always see it on the first pass through the deck my­self.)

  • What is the vi­sual ex­pe­rience of try­ing to differ­en­ti­ate be­tween two similar cards (e.g. Ace of Hearts vs Ace of Di­a­monds)?

I think the above three ex­er­cises are fun learn­ing ex­pe­riences and a way to check in with your gut feel­ings through a medium many peo­ple may not have tried be­fore. With enough prac­tice, you can hit very lev­els of ac­cu­racy on these tasks, de­spite them seem­ing just a lit­tle im­pos­si­ble.

If you do de­cide to give these a go, let me know how it turns out!