Always Swap!

Over a large enough sample, the active agent should always benefit by three to two. Over as many as a hundred goes, the active agent should get the pound coin about 60 times. The passive agent only receives it 40 times.
Choice 1 of an envelope from three represents a chance of 33.33% (recurring - one third) of being correct.
Then the referee removes an envelope.
If the active agent does not swap, the chance remains at 33.33%. By swapping after the removal of a disc, the active agent is making a choice at 50% chance.
The effect of that is to transfer the 33.33% choice to the passive agent. The passive agent loses out, statistically, the difference working in the active agent's favour.
50% to 33.33% is roughly three to two, 16.67% being the difference and 16.67*3=50.01 and 16.67*2=33.34. This is the true explanation.


Adrian Worsfold

Pluralist - Liberal and Thoughtful