You are reading a single comment by @mashton and its replies.
Click here to read the full conversation.
London Fixed Gear and Single-Speed is a community of predominantly fixed gear and single-speed cyclists in and around London, UK.
This site is supported almost exclusively by donations. Please consider donating a small amount regularly.
@mashton
Oops, I meant six:
Mather is in box 1.
Six scenarios, with comments:
i) You pick 1, host opens 2. You should not change.
ii) You pick 1, host opens 3. You should not change.
iii) You pick 2, host opens 1. Will not happen.
iv) You pick 2, host opens 3. You should change.
v) You pick 3, host opens 1. Will not happen.
vi) You pick 3, host opens 2. You should change.
So, it appears that there are two scenarios in which you should change and two in which you should not, ergo it doesn't matter, right?
Not quite. Scenario's i) and ii) offer the host a choice of which box to show you. Therefore over a series of such events, i) will occur half the time and ii) will occur half the time. contrast this with iv) and vi). Given your choice of box, the host has no choice about which box to show you. So over a series of events of you picking box 2, scenario iv) will always happen. Similarly for you picking box 3 and scenario vi).
Because of the argument above, you need to weight scenarios iv) and vi) as twice as significant as scenarios i) and ii). Ergo, you should change.
A more formal way of making the above argument is to draw out eighteen scenarios, each equally likely - basically the six above, but times 3 for changing the box that the Mather is in.
Drawing a probability tree helps as well, but my ASCII art is not up to it.