Duck Picnic

"Three ducks - Ada, Bert, and Coco - are watching two picnic blankets.

At the same moment, each duck must choose one blanket to run to.

The blankets have crumbs as follows:

Blue blanket: 12 crumbs. Red blanket: 24 crumbs, but it is farther away, so any duck going there loses 6 crumbs worth of energy.

If several ducks go to the same blanket, they split that blanket’s crumbs equally.

So:

If k ducks go to Blue, each Blue duck gets 12/k. If k ducks go to Red, each Red duck gets 24/k−6.

Each duck only cares about ending with as many crumbs as possible.

All three ducks are equally clever. None of them can see the others’ choices before choosing. They all use the same rule:

Run to Red with probability p, and run to Blue with probability 1−p.

Find the value of p.

Give your answer as a decimal rounded to 3 decimal places."

The contest ended at 8:16 p.m. AEST on Thursday 2nd July. All submissions will be unofficial .