Predicting Random Events Accurately 60% of the Time?

[Anerystos]

Let me just think out loud for a moment about the cards.

You have a set of five cards. One is drawn, and you make a guess. Your chance of getting it right is 0.2. A second is drawn; if you know what the first one was, your chance of predicting the second is 0.25. Your chance of getting the third is 0.3º, the fourth is 0.5 and the fifth 1 (because you can eliminate the other four). I haven't done the arithmetic, and I'm not sure I can be bothered, but it seems to me that the expectation value is that you'll get about three right purely by guess and elimination. Is that what he meant?

Dave

The arithmetic has been done.

See Epstein, R A: The Theory of Gambling and Statistical Logic.

My memory is that the expected score is about 8.3 out of 25 (eg Zenner cards): the maths is beyond me, but simulation shows that it works.

If anyone wants the reference, I'll get it.

 

[carlitos]

Just ask your classmates to prove it. Seems simple enough.

- Work out the math for 57% likelihood (of predicting Heads / Tails) based on standard distribution
- Make a few bets.
- Flip a coin and count.
- Profit!!

 

[Robin]

Just ask your classmates to prove it. Seems simple enough.

- Work out the math for 57% likelihood (of predicting Heads / Tails) based on standard distribution
- Make a few bets.
- Flip a coin and count.
- Profit!!

Yes, I think that is the way to go. Obviously the professor and the classmates have gotten the wrong end of the stick about something or other.

But my guess is that they would not agree to it. It is often embarrassing to admit you have been wrong about something like this.

I actually started flipping coins and guessing the result. By the time I got to 25 coins I had guessed 60% correctly and was half thinking maybe there was something in it after all.

But by the time I got to 50 coins I was back to 50% accuracy. I haven't done the maths, but I am guessing that even at 100 flips you might get as many as 57% correct guesses.

 

[Robin]

I once claimed to my brother that there was a certain plant that was estimated to have lived since prehistoric times. When he challenged me I went to look for the research and found that I had simply misremembered and that the root system was estimated to have lived only since Roman times.

The great temptation was to simply say that I couldn't find the research and let the matter drop, especially since my brother has a habit of rubbing in silly mistakes like that.

In the end I 'fessed up about my mistake but it was a close decision.

I suspect the professor is in a similar position to this.

 

[GreyICE]

I once claimed to my brother that there was a certain plant that was estimated to have lived since prehistoric times. When he challenged me I went to look for the research and found that I had simply misremembered and that the root system was estimated to have lived only since Roman times.

The great temptation was to simply say that I couldn't find the research and let the matter drop, especially since my brother has a habit of rubbing in silly mistakes like that.

In the end I 'fessed up about my mistake but it was a close decision.

I suspect the professor is in a similar position to this.

Amusingly, you may have been right.

http://news.nationalgeographic.com/news/2008/04/080414-oldest-tree.html

9,500 years is, if not prehistoric, close.

But it's a good story.