I wish I could come up with something delightfully clever to say before I leave; but my mind is drawing blanks.

At the end of the day, I guess there isn't very much to say in the first place, something I noted awhile back, a pretty long time ago.

Drawn out goodbyes with friends and family is somewhat unnecessary, seeing as I will be back before the turn of the year. True, things might never be much the same again, but, not much.

But to those whom I have missed out, in thoughts or action, to those who meant something to me in the past, and for that reason, if for nothing else, will continue to mean something to me in the future, to those with whom I have shared a smile along the doorways, a drink in company, or a heartfelt thought, but whom I have never had the occasion to see again - goodbye, and godbless.

This blog is starting to degenerate into a convenient space for the co-authors to post thoughts they are too lazy to properly articulate, in the guise of a discussion. Am pretty sure that if we thought about it carefully, there would not be two sides to it - I could go on but I think our current fixation on the same problem is somewhat unhealthy.

I am leaving for the UK in three days time, a fact that, blissfully, has yet to sink in. That's okay, because I will have lots of time during that interminably long flight there for it to sink in. That is also the reason why I have yet to start on the Maths booklet i received sometime last month - it would make my trip somewhat less boring, hence procrastination is justified (QED).

Am not really in the mood to do anything these couple of days, 'cept to sit around and wait. Its sort of like waiting out a class you are stuck in, really, although the reversal of my current situation constitutes somewhat cruel irony.

woot im back.

to my split personality and faithful readers, here's my take on why its half.

Based on the assumption that the host has no prior knowledge of what is behind each door (i.e. he does NOT know where the car is), and discounting the scenario where he opens the door with the car, i argue that the probability for the contestant now switches to half.

Since the host does not know where the car is, by opening one door, he is effectively resetting the problem for the contestant - one that has only has two options instead of three. Consider this, in the original Monty Hall problem, there is a 2:1 ratio of scenarios whereby the host opens door B in favour of switching. But in this variant, it is a 1:1 ratio.

I know this isn't the most convincing of answers, i've still yet to find out figure out how the host's knowledge (or lack of) affects the problem, but i do know (intuitively) that it has something to do with the ratio of scenarios. I understand that this "variant" is rather far-fetched, as it discounts the probability that the host opens the door with the car (1/3 chance!!), hence it is rather lacking still..
I'll be back with more substantial reasoning, dont worry.


On a lighter note, im back!! Yes i know i've been MIA for a long while, many thanks to my split personality who has almost staked a claim for full ownership of this blog. i've been doing alright in the land of the conscripts, enjoying (or rather, trying to) National Slavery. No matter, 13 more months and im gone.

Am quite sure that the previous example would result in a 2/3 probability in favour of switching even if the host doesn't know. The thing is, the host effectively has one choice, because if he will always have another chance to choose the correct, empty door before the curtains are open, which is practically similar to prior knowledge (sort of...heh).

Thing is, assuming that he chooses the right door on his first try, then the situation is practically similar to him stumbling onto the right answer, sans curtain. The answer my friend suggested seems to imply that the different instances in which the i)host gets it correct on the first try, and ii) the host gets it correct on the second one, will give different odds for the player.

It may be well to argue that the knowledge for case ii) might change the odds.

In case i) the host is 2/3 certain that the other unopened door has the prize, whereas in case ii) the position of the prize door would be known to the host. However, I have yet to grapple with how this affects the player, since he could not possibly know that.

Am getting unnecessarily worked up.

Sorry for appearing to be perpetually stuck on the same problem, but my split personality brought it up - I didn't have a choice. Anyway, for the benefit of those new here, I am referring (again!) to the Monty Hall problem.

My friend argues that switching gives you fair odds if the host doesn't know what is behind the door. I have yet to wrap my brain around this slightly counter-intuitive claim; I do not claim that he is wrong, only that there is a fairly problematic hypothetical situation. Anyway, it is entirely probable that I may have left out something somewhere, so thoughts are appreciated.

Assume there is a host and three doors, one of which contains the prize, only that this time, he is behind drawn curtains. It is not known whether the host has prior knowledge of what lies behind the doors. The game is rigged such that if the host doesn't know, the instances where he opens the prize door are not revealed to the player. So, (assuming there is a case in which the host has knowledge, and one in which he doesn't) in both cases, the instances revealed to the player is when he makes his initial choice and the host opens an empty door.

Am unsure whether there would still be a difference in the outcomes of switching between the two cases. Would be very, very surprised if there is.

My hols weren't supposed to end this way.

Actually, in an ideal world, they weren't supposed to end at all.

Source : xkcd.com


I am getting lazy. I know.