We have seen a counterintuitive solution to the particular hide-and-seek game in which a signal (light) comes up at a fixed probability from one of the locations should one choose to hide there. Here is how one should hide, given the chance of the signal from the very location.
Let’s develop some intuition over the message from the plot. When there is no signal from one of the locations (the house), it becomes a normal hide-and-seek, and the person who hides must choose both places randomly at a 50:50 chance. On the other hand, when there is a signal from the house, the seeker can use it to her advantage, as some of the uncertainty over hiding behind the house gets eliminated by the presence of a signal and can search the other place more often. Once you understand the seeker’s mind, the hider must choose the house more often to counter the opponent.
The extreme case is when the probability of the signal is 99.99%, where the seeker can almost ignore the house and concentrate on the bushes. And that’s what the seeker will do, as seen in the plot below.
