“A bird in the hand is worth two in the bush.” This is genuinely good advice, and worth remembering. At least for myself, I often forget it – I’m a dreamer, and I’ve gotten caught losing the sure thing because of the better longshot more than once in my life.
But that got me thinking. It’s good advice… for values 1 & 2. But I don’t think the formula can be extrapolated linearly.
Here’s what I mean: At certain values, increased upside is better than certainty because the certain option may not be enough no matter what.
Imagine you have until 5 PM today to buy a car at auction or it’s going to someone else, and you really want that car. You need 10,000 more to buy it. If someone offers you $5,000 cash or the ability to flip a coin for either $0 or $10,000, which would you take?
Normally – take the five grand! It’s the certain option, and the expected value of the coin flip is five grand anyway (the average between the two possible options). But in this case, $5k doesn’t get you what you actually want – the car – so you might as well take the only option where you might get it.
Also, the folksy truism assumes that it’s always X in the hand, 2X in the bush. But what if it were 5x? 10x? How many birds in the bush are worth one in the hand? Would you rather take a guaranteed thousand dollars or a coin flip for zero or a hundred thousand?
And here’s the caveat to the caveat: At a certain value, marginal utility diminishes. If you offered me a choice between [A: $1,000] or [B: Flip a coin for either $0 or $100,000], I’d absolutely choose B. The expected value is much higher (being $50,000), and I don’t *need* a thousand dollars to where the certainty is more important than the upside. But! If you offer me a choice between [A: $10,000,000] or [B: Flip a coin for either $0 or $1,000,000,000], I would choose A, hands down. Sure, the upside of B is way higher. But A – with no chance involved – would completely change my life. Ten million dollars would represent such a radically different change in my available resources that I’d be crazy to gamble that on the chance for more, even if it were a lot more.
And consider still that I’ve been talking about coin flips – 50/50 odds. But in real life, it could be 60/40, or 15/85, or whatever.
So here’s the deal, then: Whether or not a bird in the hand is worth some in the bush depends a lot on how badly you need one bird, how much good just one bird will do you, how many birds are in that bush, and how likely you are to catch them.
Start with the truism, sure. But consider carefully.