Lobster Pots

You run a lobster business. You have six pots and fifty pounds. Every morning you decide how many pots go in the shallow water near the shore, where the catch is small and safe, and how many go out into the deep, where the catch is much better and a bad day destroys them.

A week later, whatever is left is your score.

How a day works

A die is rolled for the forecast. One, two or three means good weather is predicted. Four, five or six means bad.

You place your pots. Then a second die is rolled for the actual weather. If it comes in under the forecast, a current runs. Otherwise the water stays calm.

You must always have six pots, so anything the sea takes has to be bought back the same day. If that puts you in debt, you go into debt.

The decision

Here is the thing the game does not tell you, and the reason it was worth twenty minutes of a maths lesson.

The forecast die is not a mood. It is a probability. A current runs when the second roll lands under the first, so a forecast of F means a current with probability (F - 1) / 6. That is the whole game in one line.

Work the expected value per pot and the picture is flat:

Offshore is only worth it when the chance of a current is under about two in nine. In practice: go deep on a one or a two, and keep everything inshore from three upwards.

The trap on a “good” day

Look at the row for three.

The game tells you good weather is predicted. It is technically right, three is in the good half. But a third of the time a current still runs, and that is already enough to make the deep water a losing bet. Offshore returns 67 pence a pot against inshore’s £2.67.

So the player who listens to the forecast loses money to the player who reads the number behind it. I like that a lot. It is a very small, very cheap lesson about the difference between a label and a measurement, and it is doing it to fourteen year olds with two dice.

The three odd days

Three days behave differently, which is where the rest of the syllabus sneaks in.

Tuesday is a lottery. Pick the sum of two dice and win £100 if you call it. The honest answer is seven, which comes up six times in thirty six, worth £16.67 on average. Any other guess is worse, and two and twelve are worth £2.78.

Thursday is tax day. Eight per cent of your profit so far, and nothing at all if you have not made any. Losing money has never felt so rewarding.

Saturday pays ten per cent interest on a positive balance. The rules let the person running the game decide whether a debt grows on a Saturday too. I have been kind: in this version it does not.

Where it comes from

The version I have built is the one published by the National Math Club at MATHCOUNTS, who are refreshingly honest that they did not invent it either and have never managed to trace where it came from. If you know, they would like to hear from you.

Their original is a classroom game: a teacher with two dice, a room full of students, and a photocopied table. That version is better than this one, because the interesting part is arguing with the person next to you about whether to go deep. This is just the solitaire edition, for when there is nobody to argue with.