Monty Hall

[andrewducker]

[Poll #1770413]

Explanation

I have known what the answer was for ages, but for some reason it only "clicked" in my head today. You can blame sarahs_muse for triggering it.

Comments

[chuma.livejournal.com]

It it only unintuative to you. I suggest if you want me to take you seriously from this point on you start linking me to some sort of reference online which actually backs up your way of thinking. Something that isn;t just a friend of yours on LJ but an actual statistical reference. Mainly as at this stage I think you are probably trolling rather than just being stupid.

[theweaselking.livejournal.com]

If you don't believe me, simulate it. Or take a look in the comments of xkcd, where I originally got it.

One of the correct answers is here.

And the short version is Bayes' Theorem and the sum of an infinite series.

(rather than sum the infinite series, a more elegant solution: Consider the two die rolls as simultaneous. If the first is a 6 (6/36 of the time), Bob loses. If the first is not a 6 and the second is a 6 (5/36) of the time, Bob wins. If neither is a 6, the test repeats.

Therefore, you can view this as an infinite loop with 11 possible exits, 6 of which are Sue wins and 5 are Bob wins. Given that SOMEONE wins, we see that Bob wins 5/11 of all games.)

If you don't like that, then yank out your geometric progression rules and sum the infinite series the hard way. I'll wait, you'll get 5/11.


Now: You've already shown that, for any game, the odds of Bob winning in turn 2 are 5/6*5/6*5/6*1/6: not-6, not-6, not-6, 6. That's 125/1296.

So, the odds of him winning in ANY game in turn 2, divided by the percentage of games he wins, gives you (125/1296) / (5/11).

Which is 275/1296.

275/1296 of Bob's wins will come in turn 2, which means that, for any given game where Bob wins, the odds of his win happening in turn 2 are about 21%.

Mainly as at this stage I think you are probably trolling rather than just being stupid.

You're demonstrably, aggressively wrong about the dino babies, the pub coins, and Bob and Sue, and you're calling *me* stupid because of it. You have no leg to stand on with accusations of "trolling"

[chuma.livejournal.com]

See other comment save me repeating myself.