The Monty Hall Math Problem Solution (Part 2)

[BigDan]

This is the answer to the question in part one.

Yes, you should change your guess! By taking the opportunity to change your guess you double your odds of success from 1/3'rd to 2/3'rds! It goes against all instinct, but it is true. When you had a choice of three holes, you had a 1/3 chance of being right. I KNEW which holes contained the clad coins, and removed one of them from the equation.

Here's the hard part, you may think you have a fifty/fifty chance now. You don't. Nothing changed with your original odds. BUT, if you take the offer of changing your pick, you are taking advantage of my knowledge. By taking one of the three variables away, I am allowing another right answer in your favor.

It's like this. You had a 1/3 chance. I gave you another 1/3 chance of being right. That's 2/3'rds.

If you don't believe it, get a partner and play at it with cards. One ace and a couple other of anything. Have them set it up, try to pck the ace. They then remove one of the other. See how often your pick is right...1/3 of the time, compared to how often the ace is the other card left...2/3rds. It's just...weird, but true.

 

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[mrs.oroblanco]

HUH?

That makes no statistical sense. For me, I screw up when I DON'T go with my first gut feeling.

B

 

[spartacus53]

Bigdan,

firstly, let me say I enjoy your posts. I like something that will make you think, but in this case I will stick to my original reply of "no"

Reason??

I was only wrong once in my life and that was back in 1977 when I thought I was wrong.

I rest my case

 

[mrs.oroblanco]

- That's cute, Spartacus53! That's a nice play on words from the old adage (I once thought I was wrong, but I was mistaken)

It is, however, still just basic math statistics. And one of the reasons why compulsive gamblers think they have the odds figured out, and one reason why lottery players buy many tickets - to up the odds, when, in reality, it doesn't do.

B

 

[BigDan]

For those that don't believe

I urge you to test it. I was right there with you...until it was proven to me. You don't even need help to see how this works. (But it's more fun)

Take three cards, and ace and two of anything else. Mix 'em up, spread them out in front of you. Guess at which one is the ace. Without help, just take one of the other two away. If by circumstance it happens to be the ace you have to start over. (Remember in the "test" someone knows the location of all the coins...they wouldn't remove the one you are after.) If it isn't the ace, now you've duplicated the scenario all by yourself.

Should you change your original guess? YES! I promise that 2/3'rds of the time, the ace is NOT the card you selected. Although it seems like black magic...it is all in the other person knowingly removing 1/3 of the variables.

 

[spartacus53]

Dan, don't go crazy on me, I was only joking and understand the principle behind it. Silly me, I just like to have a little fun.

 

[BigDan]

No Problem. Too late on the crazy...did that long ago.