Comments on: A Drunkard’s Walk Through Baseball Stats

By: A Drunkard’s Walk Through Baseball Stats < It’s all about the trends

A Drunkard’s Walk Through Baseball Stats < It’s all about the trends — Fri, 29 May 2009 11:22:07 +0000

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By: Brian B

Brian B — Fri, 03 Apr 2009 03:11:10 +0000

Glen, you’re right of course. The odds do not “reset.”. But they are also dependent on perspective. For instance, Monty knows what is behind each curtain, right? So to him, the odds of the curtains with duds behind them are precisely 0% that they will have season tickets. How can the odds of those curtains get “better” just because we change perspective to someone who knows less than Monty? Too much focus on the numbers distorts reality. It’s fun though!

By: Glenn

Glenn — Fri, 03 Apr 2009 01:51:43 +0000

All that math gave me a headache. I don’t understand it all but no matter how clueless I am I’d hesitate to call Marilyn Von Savant an idiot. I’d rather call David in NYC an idiot.

By: Mike

Mike — Thu, 02 Apr 2009 18:51:14 +0000

“Itâ€™s a 1-in-3 chance to start, but once Curtain 3 is out of the loop, the odds have to redistribute. No?”

No. Curtain 3 isn’t out of the loop just because you know what’s behind it.

Suppose there were no reveal. That is, you choose Curtain 1, and then Monty — without opening any curtains — tells you you can switch your choice to take BOTH Curtain 2 and Curtain 3. Of course you would switch, because that gives you a 2/3 chance of winning instead of a 1/3 chance.

After Monty opens Curtain 3 and reveals nothing, now Curtain 1 (your choice) has a 1/3 chance, which Curtain 2 has a 2/3 chance. The odds do not “reset”.

By: Dave

Dave — Thu, 02 Apr 2009 18:32:06 +0000

My challenge to those who think it’s 50-50 is to actually play the game. Get a friend, play this game with playing cards. Have your friend be Monty Hall – he must know where each card is and always choose a non-winning card to show you.

I guarantee it won’t take too many versions of the game before you decide it’s always in your best interest to switch.

By: Pete R

Pete R — Wed, 01 Apr 2009 13:27:43 +0000

Is there any point in adding yet another comment? Probably not, but here goes.

The key is the assumption: “Monty ALWAYS opens a curtain that he knows has nothing there.”

Say you replace that with “Monty doesn’t know where the prize is. He’s just opening a curtain at random.” Then it’s 50/50- and the same applies even if there are a million curtains, although then he would be unlikely to find 999,998 empty curtains.

Or if you replace it with “Monty is trying to help you win- he will offer a switch only if you were wrong”, then you definitely switch.

Or, if you assume “Monty is trying to make you lose. He only offers a switch if he knows you had guessed right”, then you definitely don’t switch.

If someone offers you the chance to play this game, the tricky bit is working out which of the four assumptions (if any) is correct.

By: Richard Aronson

Richard Aronson — Tue, 31 Mar 2009 19:58:52 +0000

First, the painful stuff. Joe, this is far from the best paragraph you ever wrote: I have no great for it. But I want to know how it works. For instance, while reading The Drunkardâ€™s Walk, I became fascinated by this formula the author used to explain probability in a seven-game series. He used various statistical tools that I immediately that I immediately had to try myself. The first sentence should include a noun, e.g. “I have no great talent for it.” The last sentence repeats “that I immediately”.

As for the math, this is how bridge players might approach the Monty Hall problem. In fact, it’s analagous to “The Principle of Restricted Choice” which yields the same resulting odds (2:1 to switch) but I won’t detail here; you can go to: http://acbl-district13.org/artic003.htm or Google it if you’re interested. There are six possible outcomes before you pick:

Prize is behind A. Monty exposes B.
Prize is behind A. Monty exposes C.
Prize is behind B. Monty exposes A.
Prize is behind B. Monty exposes C.
Prize is behind C. Monty exposes A.
Prize is behind C. Monty exposes B.

Because Monty is never going to expose the winning prize, your choice did not matter. He is always going to pick a loser that you did not pick (unless you REALLY offended him, in which case he might not allow you to switch). There were always two possible curtain opens for any pick, and four other choices. Thus, whatever you picked (two outcomes) there were four other outcomes, even though he exposes the one you know to be wrong. Four to two is good odds; you should switch.

By: Wickethewok

Wickethewok — Tue, 31 Mar 2009 15:49:09 +0000

The Monty Hall problem, Hall of Fame voting, and Derek Jeter’s defense? Very few combinations of topics will get you as many comments.

Anyway, a similarly fun “paradox” is the boy/girl problem: http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

By: Wade

Wade — Tue, 31 Mar 2009 15:13:26 +0000

Not sure if this link has been provided, but it’s a nice simulator of the problem stated.

http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html

You can do up to 100 trials at a time and tell it to stick, switch, or alternate.

By: Ryan JL

Ryan JL — Tue, 31 Mar 2009 07:14:56 +0000

I guess I am late to the party, but I have tried to explain the Monty Hall thing many times and I usually have the most success when I break it down very simply:

If you play the game 100 times and never switch, you will only win when you picked right initially. Since that is only going to be the case around 33 times, you would have won around 67 times had you switched (the only other choice.)