Epistemic status: aye lmao, tell me I’m wrong—IDC: benstubbing(at)gmail(dot)com
Mistakes in previous years have included, but not been limited to: a devil-may-care attitude to declamatory statements and an inability to count, in French, up to the number two. It may be that, each year, the real coolest things I learned were the things I learned after I said I learned cool things that I hadn’t learned.
When he presented a guest lecture to the Treasury on the topic of economic shocks, I asked Alan Bollard, former Treasury Secretary & Governor of the Reserve Bank, what was the most probable economic shock scenario that New Zealand’s current institutional setup is least prepared for and why hasn’t this been fixed? Without hesitation, Bollard said foot & mouth disease was still the one that kept him up at night.
Suppose tomorrow's weather forecast shows a 40 percent chance of rain and I offer you this bet:
If it rains, I'll pay you $2
If it stays dry, you pay me $1.
These are 2:1 ("two-to-one") odds: you risk $1 to win $2. Should you take this bet? There are three questions to consider.
First, are the odds favourable? If you believe what the forecast says (i.e., that the chance of rain is 40 percent) then the odds implied by your belief are 1.5:1, meaning that minimum bet you should be willing to accept is:
If it rains, I'll pay you $1.50
If it stays dry, you pay me $1
At these 1.5:1 odds, a 40 percent chance of rain makes the bet exactly break even. Any better odds—like the 2:1 I'm offering—create a favorable opportunity.
Second, what’s the expected value? With a 40 percent chance of winning $2 and a 60 percent chance of losing $1, you’d expect to make 20 cents on average each time you took this bet. Expected value is different from favourable odds: you could have favourable odds but tiny expected gains, or unfavourable odds but positive expected gains if the payoff is large enough.
Third, is the size right? A $1 bet might be trivial, but what if I offered the same odds on a $10,000 bet? Even with favourable odds and positive expected value, the size of the bet matters. This is something that Paul Samuelson understood well.
When they were junior fellows together at Harvard, the physicist Stanislas Ulam told future Nobel economist Paul Samuelson that he considered a coward to be…
Someone who will not bet when you offer him 2:1 odds and let him choose his side
To which Samuelson retorted that a better definition would be
Someone who will not make a sufficiently small bet when you offer him 2:1 odds and let him choose his side