Cutting The Pie, And Choosing

One cuts, the other chooses…

As the youngest of 6, portions and portion control was always a big topic around the house.

The end to all arguments was simple – one of you divides it in half, the other picks.

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The most even split

If you’ve cut it so that one side is bigger, you can expect that piece to be taken first.

So clearly if you’re doing the dividing, it’s in your own best interest to make the split as even as possible.

Choosing sides

It’s often good to be the chooser. All the pressure is on the divider – if you can pick the larger piece. That means you have to be able to evaluate positions and figure out which is “better”.

(and you don’t get all day to do this – speed is critical as well)

Gaming theory

And this is perhaps one component to games as well.

One player gets to go first, and then the other can respond. If the first has divided things evenly, there may not be an advantage to one position or the other.

But it still takes skill and analysis.

The uneven cut

But consider this… What if I cut things so that the thinner piece is slightly larger. Your analysis now has to consider the length and width, but also the thickness.

What if the one has a larger layer of fudge in the middle?

If I do this well, you might pick the inferior piece.

If you pick well, I might get stuck with the inferior piece.

Uneven, but evenly balanced

So perhaps I’ll make the one with the extra fudge slightly smaller in volume.

If you pick the fudge, I get more of the cake. If you pick the larger cake, I’ll enjoy the fudge.

And in a game this can be even more useful. I’ll divide things so that one side will have an advantage with one strategy, the other side will have a different advantage. There may not be any specific advantage to the choice you make.

Except that I’ve already planned a couple different strategies to work with each side’s advantage. And you might not have those in mind.

A bit of a challenge

The creamier piece of pie, the advantageous position within the simulation – it’s a fair setup.

You divide, I’ll pick.

Next time I’ll divide and let you pick.

Whoever does it better gets a little bit of satisfaction…