The assumption that generally fails to get communicated is that the host will always give you an option to switch. You can only do proper statistical analysis

The assumption that generally fails to get communicated is that the host will always give you an option to switch. You can only do proper statistical analysis of the situation if know what the host will do under any given set of conditions. Otherwise you have to consider the possibility that you'll have the option of switching iff your first choice was the correct one -- in which case you obviously should never switch.