I Hate To Lose

 

Down to Lytes Cary Manor (National Trust), about half an hour’s drive from home. A walk through the grounds, damp and gooey clay, the odd mud pool on the path down to the river. Overcast skies. No sign of that unshielded fusion reactor, so dangerously close at 160 million kilometres.

“Do you think we'll see anyone else?” Clare asked, (the car park had been almost full).

“No,” I said confidently, thinking that the wise visitor would have stuck to the house and immediate gardens, and then made a fast retreat to the tea room.

I got the impression that she'd said, or thought, that we would see around six people.

Halfway round our circuit, just after we had admired the bridge, a man passed us. We exchanged greetings. It was 12.15 pm.

“I always think that we should say good afternoon only after lunch,” she said. (We had said good morning).

“That’s my view too,” I said, though my mind was more on the fact we had, now, met somebody.

“I think there is a better way to think about this,” I said, “something a little less binary. When I said we wouldn’t see anyone else, I really meant we should see zero-ish people. I had in mind a distribution. One is very close to zero, so on balance I'm still right about this.”

She looked at me in disbelief.

Soon afterward, in the distance, we spotted two other walkers. That made a total of three, as we headed back towards the tea room for our hot chocolates.

“OK,” I said, “We’re really talking about two binomial distributions here. Divide our walk into, say, n = 12 equal time slots and assume the probability of encountering another walker in each of these time slots is p. We’re really disagreeing about the value of p.

“In my view p was about one twelfth, which means I should have perhaps expected on average to meet just one person. You said we’d meet six people so for you p is one half - twelve times one half is six.”

They do look like rabbits. The tea room is in the manor house, top left

It was hard to see if she was following the argument as her attention seemed fixed on the weeds growing in the adjacent field, which looked like a crowd of rabbits.

"Now, our standard deviations are different: for me, using the formula sqrt(npq) n = 12; p = one twelfth;  it's just under one - while for you with p = a half, it’s around 1.73, the square root of three.

"So seeing three people for me is two standard deviations out - while for you it’s only 1.73 sds.

“Although technically this aligns more to you, I think morally we’d have to call it a draw.”

She turned to me and said, “Even when you lose you hate to lose.”