Viktor Nacht: Coin Toss Bias Theory (Link)

[Viktor Nacht]

Toss Out the Toss-Up: Bias in heads-or-tails

[Don Schlesinger]

I went to elementary school with Percy Diaconis. He is a gifted magician and mathematician, who, as you might know, did some studies, years back, on shuffles.

But, I am flabbergasted to read that a penny spun on its edge lands tails 80% of the time. I'm going to do some experiments; I can't believe that this would be true.

Don

[Don Schlesinger]

Just for fun, I just spun a penny on its edge 50 times. Result: 27 heads, 23 tails.

80% tails is utterly preposterous. Makes you wonder why you should believe the rest of the story.

Don

[Fuzzy Math]

> Just for fun, I just spun a penny on its
> edge 50 times. Result: 27 heads, 23 tails.

> 80% tails is utterly preposterous. Makes you
> wonder why you should believe the rest of
> the story.

> Don

18 tails, 7 heads, then I was forbidden to do anymore trials with other people in the house. Hmph.

[ET Fan]

> Just for fun, I just spun a penny on its
> edge 50 times. Result: 27 heads, 23 tails.

> 80% tails is utterly preposterous. Makes you
> wonder why you should believe the rest of
> the story.

On page 401 of Concrete Mathematics, Second Edition by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik; Addison-Wesley, 1994, the authors state ""Con artists know that p \approx 0.1 when you spin a newly minted U.S. penny on a smooth table. (The weight distribution makes Lincoln's head fall downward.)"

So maybe your penny isn't new enough, or your table smooth enough?

ETF

[Norm Wattenberger]

Since their is no such thing as an unbiased coin; it would seem obvious that it is very slightly more likely to land on the same side as you found it. As you say, 80% is nutty.

But, there is something that I've wondered about in coin tosses that are caught. It's too fast for the mind to register it conciously, but the mind can probably see the reflections of light as it spins and may tend to catch the coin on an even number of half spins. I've noticed that if I spin an irregularly shaped object I tend to catch it in the same manner the great majority os times even though the spin rate is too fast for me to conciously see.

[Don Schlesinger]

> So maybe your penny isn't new enough, or
> your table smooth enough?

Nothing in the article said it had to be new, and mine wasn't. I'll try it again with a new one, when I get one, and will report my findings.

Don

[Viktor Nacht]

[Norm Wattenberger]

OK, I will now release the extensive research that I have performed on Craps. Craps can be beaten. The process is very simple in concept; although not everyone has the ability. First, you need to slow time during the roll. This is critical. After the dice have hit the back wall, examine them in slow motion to determine if they are about the end as a seven. If so, adjust Planck?s Constant. An even 7 x 10-34 joule-second will do. This will cause the dice to roll past the seven.

Now not everyone has this ability. So, you need to discern the players skilled in this manner. This is very simple. When you approach the table, state in a firm but not too loud voice ?Has anyone here seen Timothy Leary today?? The person that instinctively answers yes is your shooter.

Cautionary note: There is a one in 10,000 chance that adjusting Plank?s Constant will cause the Universe to wink out of existence. But then, you won?t seven out anyhow.

[Don Schlesinger]

Got a brand-new 2004 penny. Spun it on my smooth, dining-room table top. Decided ahead of time to do another 50 spins. Each spin lasted several seconds.

Results: 26 heads, 24 tails. I reject categorically the notion that this would ever approach anything near 80-90% tails. The premise is preposterous.

I invite others to duplicate my experiment. Report your results here. I'll bet no one even comes close to getting 40 tails out of 50 (80%). The whole thing sounds like an urban legend to me.

Don

[Cacarulo]

I can't get the article.

Cac

[Norm Wattenberger]

[Coug Fan]

> I invite others to duplicate my experiment.
> Report your results here. I'll bet no one
> even comes close to getting 40 tails out of
> 50 (80%). The whole thing sounds like an
> urban legend to me.

> Don

With such a small sample size, someone may very well get 40 out of 50 on one set of 50 trials. After all, I have lost 40 out of 50 BJ hands before, even though the expectation is to only lose a little over 25.

You are no doubt correct that the author is overstating the impact of weighting bias, but I think we would need a much larger sample size before we could "prove" this to any real degree.