Strange Wagers

In a recent Veritasium video, Derek Muller can be seen accosting Australians in the street and giving away money (almost) and they turn him down. The video itself is really interesting and you should watch it and see if you feel the same was as the people he's talking to. 

The strange feature this highlights is that the human mind is woefully inadequate when it comes to assessing probability and risk. Even though the arithmetic for assessing whether or not his bet is straightforward enough to be carried by an elementary school students who has a decent handle on fractions, there are instincts at work behind your eyes consistently pushing you away from the right answer.

One of the most interesting secrets in magic involves exploiting people's inability to accurately assess risk. Risk is not linearly additive (when you put two risks together, you don't wind up with one single risk which is twice as big) so it runs afoul of our mental bookkeeping.

There are a surprising number of tricks which either derive their method (or at least their drama and impressiveness) from disguising risk. Most magic tricks require a chain of events to unfold in exactly the right way in order to work. One weak link - one mistake - and the whole thing allegedly falls apart. It turns out not to be as true you would at first believe. When you see a trick where there are lots of choices — he could have opened the book to a different page, he could have thought of a different number, he could have chosen a different key to the locked box —that means there are lots of chances for things to go wrong. In reality what that usually means is that most of those choices don't matter; they don't affect the outcome of the trick in any meaningful way. On top of that, a little bit of acting can make just about any risk seem slightly larger than it actually is

There was a great Canadian sleight of hand performer, Martin Nash, who famously said:

If you want to perform miracles, you have to be willing to take risks.

The British impossibilist David Berglas said something similar but he's not Canadian, so there.

Unfortunately, they only way around this cognitive shortcoming seems to be formal training. You need to sit down with a teacher or a textbook and have someone walk you through the math step by step (this could be something like a statistics or a finance course). Then the most important part is to put the instinct on hold and to thoughtfully work through the math so you don't accidentally deceive yourself.*


*Unless you're in the audience at a magic show, then by all means let your intuition run wild. That's what we're here for.