Comment by DamnInteresting

Prompt:

You and another LLM are being asked to pick a number between 1 and 10. Whichever gets closest to the real number wins. The other LLM chose 6. What number do you choose?

Response:

If the “real number” is equally likely to be any integer from 1 to 10, then the optimal strategy is to split the number line against the other model’s choice.

The other LLM picked *6*.

The midpoint between 6 and 7 is 6.5.

* If the real number is *1–6*, then 6 is closer (or tied at 6).

* If the real number is *7–10*, then 7 is closer.

If I also pick 6, we tie every time 6 wins.

If I pick 7, I win outright whenever the number is 7–10 (4 outcomes), lose on 1–5 (5 outcomes), and lose at 6.

So:

* Picking 6 → guaranteed tie every time 6 is optimal.

* Picking 7 → gives me exclusive wins for 7–10.

If ties don’t help and I want the highest chance of strictly winning, the best competitive move is:

*7*.

lol