WEBVTT

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Somebody offers you a hundred houses.

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You will see them one at a time,

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in a random order, and each time
you must say yes or no on the spot.

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Say no, and that house is gone for good.

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Here is the kind part.

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You do not need the best of the hundred.

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Any of the ten best
would make you perfectly happy,

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and that single change turns
a famously hard problem into an easy one.

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Let me build a scale to measure this on.

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Give every house a score,

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and hand the scores one to a hundred
out to the hundred houses, one each.

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So a hundred is the best house
there is, and one is the worst.

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They arrive in a random order,
so they land anywhere along it.

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The first house scores forty two.

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The second scores sixty eight,
better, and both are already gone,

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because you turned them down.

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One warning about this picture.

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We are outside the story,
so we can read the scores.

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The buyer cannot.

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All the buyer can ever do is hold
two houses side by side and say

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which of them is better.

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Now the target. The ten best houses
are the ten highest scores, ninety one up

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to a hundred, so winning means landing
under this brace at the top of the scale.

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Compare that with the famous version,

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where nothing
but the very best house will do.

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That target is a single point,
and everything else is failure.

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The known answer is to look

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at thirty seven houses, buy nothing, then
take the first one that beats them all.

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It wins about thirty
seven times in a hundred.

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Now widen the target to ten points
and keep that very same strategy,

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cutoff and all.

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Whenever it buys a house, the house it
buys is one of the ten best better than

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ninety eight times in a hundred.

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Making sure it buys at all
is the only job left over.

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Here is one journey through
a hundred houses, seen from outside.

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Along the bottom,
the order they arrive in.

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Up the side, their scores,

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with the ten best of them
inside the red band at the top.

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I will not draw all hundred houses.

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I will draw one thing instead:

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the best score seen so far.

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That line can only climb,

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and every step in it is a house
that beat everything before it.

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There are only five or six
of those steps in a random hundred,

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and they thin out as you go,

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because beating the best of fifty is far
harder than beating the best of five.

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Now the strategy, in three lines.

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One: let the first thirty seven
houses go past, whatever they are,

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and buy nothing at all.

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Two: take the best score
among those thirty seven.

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Here it is, ninety three,
at house twenty six.

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That score is now your bar.

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Three:

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from house thirty eight onward,
buy the first house that clears the bar.

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And that is the whole rule.

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Look for a third of the list,

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then take the first house that beats
everything you saw while you were looking.

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Watch it run.

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House forty one is pleasant enough.

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House forty nine scores eighty seven,
better than almost anything you have seen,

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and you must let it go,
because it does not clear the bar.

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Then house fifty eight
scores ninety seven.

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That clears the bar,
so you buy it and stop.

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And look where it landed, inside the band.

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It is the fourth best
house of the hundred.

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The very best house of all,

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the one scoring a hundred, turns
up much later, at house eighty four.

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You never see it, and it
does not matter in the slightest.

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You were not trying to find it.

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Two things could have gone wrong, and both
are about where that dashed line stands.

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Stop looking after five houses

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and the bar would sit at sixty eight, low
enough for an ordinary house to clear it.

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Look at ninety
and the bar would be a hundred,

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which nothing left could ever beat.

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So why is a bar built from only
thirty seven houses good enough?

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Let me take the climbing line away
and mark the ten best houses instead.

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There they are.

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Ten houses inside the band, landing
anywhere, because the order is random.

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Now count how many arrived
in your first thirty seven.

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Exactly one, the ninety
three that set your bar.

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One is all you need,
and that is the secret.

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Each of these ten, on its own,

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has a sixty three percent
chance of landing after the line.

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For your bar to miss the band,
every single one of them has to.

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Sixty three percent, ten times over,
is about one chance in a hundred.

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The ten crowd each other slightly,

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so the true figure is smaller still, about
one chance in a hundred and thirty five.

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Which means the bar you built out
of thirty seven houses is itself one

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of the ten best, ninety
nine times in a hundred.

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And here is the step
that turns that into a promise.

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Suppose the bar is inside the band.

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The band runs from the bar
up to the top of the scale,

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so every score above the bar
is inside the band as well.

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So any house clearing
the bar is one of the ten best.

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Not probably.

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Certainly.

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The only way this rule hands you
a bad house is if the bar itself

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missed the band, and that is the one
chance in a hundred and thirty five.

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Which leaves exactly one weakness,
and it is not about buying badly.

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It is about never buying at all.

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Here is a different hundred
houses, in a different order,

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and this time the luck runs the other way.

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The best house in the whole
set, the one scoring a hundred,

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arrives at house twelve,
while you are still only looking.

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So the best of your first
thirty seven is a hundred,

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and your bar sits
at the very top of the scale.

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Nothing can clear it.

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You watch the remaining sixty three houses
go past, turn every one of them down,

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and reach the end of the list
having bought nothing at all.

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And this is no freak.

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The best house of the hundred
is equally likely to be anywhere,

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so it lands inside your looking
window thirty seven times in a hundred,

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and every one
of those runs ends empty handed.

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Here is the cure,
drawn as a second picture.

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Along the bottom, the order again.

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Up the side, how many houses you
are willing to have above the one you buy.

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At first you accept nothing
but the best you have seen.

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As the list runs out you relax.

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After fifty, the second best
of what you have seen will do,

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then the third, and near the end
you take almost anything decent.

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Why is that safe?

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The second best of fifty houses
misses the top ten only if nine or ten

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of the ten best hid in the second half.

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That is like ten coin flips
coming up almost all heads,

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about eleven chances in a thousand.

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Relax that way all the way down the list,

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and the rule nearly always buys, and what
it buys is nearly always in the top ten.

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Better than ninety eight times
in a hundred, and that is the promise.

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So here is the whole
strategy, in four lines.

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Look at the first thirty
seven houses and buy nothing.

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Set the bar at the best of them.

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Then buy the first house that clears it.

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And as the list runs out, let
the bar come down, one place at a time,

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so you never reach the end with nothing.

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That is the whole of it.

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You cannot know which house is the best.

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But you can spend a third

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of your search learning what good looks
like, and then have the nerve to stop.