Comments on: Making the Best Choice

By: Brian

Brian — Fri, 07 Mar 2008 13:20:00 +0000

Interesting BUT if we are concerned with the $ value rather than the number of times rounds they won out then I think Colley wins.
I accumulated the $ values taken by each method over the number of trials and ran this a large number of times. Colley won out on the $ value almost every time.

By: Bruce Reistle

Bruce Reistle — Wed, 11 Aug 2004 21:03:00 +0000

Hey there, long time listener, first time caller.

I started this problem and compared my results with the other posters, when it occurred to me that we're all doing it wrong. The object is not to determine which method prevails more often, but rather which method yields the greatest prize.

I ran 20,000 reps of both methods, including the Paulos scenarios where the first three are automatically rejected, the first four are automatically rejected,...,the first n are automatically rejected.

I found the best method to be to skip the first two and then start the bidding. The Paulos method yields slightly higher returns when either two or three are automatically rejected, ties when four are rejected, then loses after that.

In terms of winning percentage, skipping two, three, four, or five yields a higher percentage than loses after that.

I wouldn't take a bullit defending my numbers, but they seem reasonable enough and I'm convinced we want to win more money, not more often.

If anyone wants to see the code or the results let me know.

By: Prasanna

Prasanna — Sat, 22 May 2004 03:00:00 +0000

Paulos method is far more effective.

Amidst around 390 data, Paulos selection method returned around 90% better results.

I am sending the workbook. You can run the recorded macro by keeping the cursor at cell M4 & pressing Ctrl and "q".

By: Dick

Dick — Fri, 21 May 2004 17:01:00 +0000

Andy, I went back and looked up that Paulos thing. After the first 37%, he says to pick the one that’s better than all previous ones. So what you said is correct, greater than the maximum. He doesn’t really say if the last one is the default, but I think that’s a valid assumption. Email the workook to me, if you don’t mind.

By: Andy Miller

Andy Miller — Fri, 21 May 2004 15:37:00 +0000

According to the Workbook that I made (using the logic from my above post, and assuming that either person would pick the last envelope if they had not already chosen one), I came up with the following results based on several thousand runs:

Paulos would "win" nearly half the time (around 47%).
Colley would "win" only about a quarter of the time (roughly 24-27%).
They would tie nearly a quarter of the time (again, roughly 27%).

Therefore, I would definitely have to agree with Paulos' method.

I can submit the Excel file if you'd like.

By: Andy Miller

Andy Miller — Wed, 19 May 2004 23:04:00 +0000

In your comment about Paulo's method, you state that "Paulos proves that you should reject the first 37% of the choices and take the best one after that. Slightly different from just rejecting the first."

If we were given each envelope individually, then how could we determine if it was the "best one after that"? Should we accept the first one that is greater than the maximum of the content of the first four envelopes?