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Jun 23, 2011

What Are the Odds? Flipping a Flying Disc, Bowl, Cat

Statisticians like to talk about flipping coins, especially fair coins, which have an equal chance of being heads or tails. But what about flipping other things? In particular, as an Ultimate Frisbee player, I want to know what the odds are for a flying disc. Maybe knowing the odds will give me an advantage since a disc flip is used to determine which team starts on offense.

How do I figure out the answer? Flip a disc 10 times? 100 times? 1,000 times? Or study up on physics? If I flip a disc 100 times, what kind of answer do I need to be confident that the odds are not really 1:1 like a coin?

I'll tell you what I know in my Discovery 2008 session on Presentation Quality Graphics on June 16 at 4:15 p.m., but first tell me what you know. Post comments with theory and guesses on the chances of the following items landing as pictured. Two are filled in for you in the table below.

Bonus question: If I flip the same item twice, what are the odds of same versus different results?

Flying disc?
Jar lid?
Metal bowl?

Community Member

Bob wrote:

While my cat flipping experience is severely limited, I do suspect that you would not get more than one chance at a "fair flip."

Perhaps landing on "Heads" (versus heads up) might get you another chance, but you would have to move fast. A second attempt after "tails" might be cause for a compression bandage...

Community Member

Greg wrote:

Has anyone else noticed that the "Flip a quarter" question has gotten considerably more complicated since it was first used in chapter one of nearly every statistical textbook?

Heads probability remains at 50%, but the options for the other side have grown from the formerly simple option of Tails (as represented by the eagle)....

Since 1999 the other side can be a "Delaware", "Pennsylvania"- up to 47 states so far :) (pause here for laughter)

Modelling the non-head outcomes would be an interesting exercise.

Community Member

Andrew wrote:

The way to beat any biased coin is to flip it twice. The person calling it has to either pick Heads then Tails or Tails then Heads. If the same side comes up both times you have to redo it. The probably of heads then tails will always be the same as tails then heads. [Prob(Heads)*(1-Prob(Heads))]

I believe I learned this from Innumeracy.

Community Member

Ashley wrote:

Flipping two frisbees is fairer than flipping one. The system of flipping two frisbees is better than flipping one, since it accounts for small inaccuracies in either disc.

Community Member

Flipping Results from Discovery 2008 Talk - JMP Blog wrote:

[...] didn't get any guesses on the odds of flipping various items from my Flipping Odds post. Instead, the commenters went directly to the question of interest, which is how does the chance [...]