Doug’s MATLAB Video Tutorials

October 27th, 2009

Puzzler: Ultimate Frisbee- call it!

 I play a fair amount of Ultimate Frisbee® between lunch across the street at Cognex and playing with Boston Ultimate Disk Alliance. Games of Ultimate start with the two teams flipping two Frisbees in the air and calling “Same or different” My team was trying to figure out which is the most likely outcome.

I made a convincing argument, but I am curious what kind of persuasive MATLAB-based ‘proofs’ can be made. I am offering a MATLAB t-shirt to the most persuasive entry. Use published MATLAB files, GUI’s, MATLAB script or function, whatever you think will be most convincing. Contest ends this time next week.

frisbeeflip.jpg

Assumptions: The Frisbees (or coins) are either ‘heads’ or ‘tails’. The coins may or may not be ‘fair’ (i.e. they might be heads 80% of the time!), however the odds of heads versus tails for the two coins is the same for both coins. Send entries to hull@MathWorks.com (no .rar files please!) (Here is the result of this now closed contest)

Frisbee® is a Registered Trademark of © 2004 Wham-o Inc. All Rights Reserved.

By Doug Hull

19:31 UTC | Posted in Level: Basic, Topic: Puzzler | Permalink |

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3 Responses to “Puzzler: Ultimate Frisbee- call it!”

  1. Marcial Medina replied on October 28th, 2009 at 01:59 UTC :

    Is better than I don´t say to much with me happend the same… lol and I love to play too !

  2. Oliver Woodford replied on October 28th, 2009 at 09:31 UTC :

    Let p be the probability of “heads”, so (1 - p) is the probability of “tails”. The probability of same is therefore (p^2 + (1-p)^2) and the probability of different is (2*p*(1-p)). We can plot those over p = [0,1]:

    p = (0:0.001:1)'; plot(p, [p.^2 + (1-p).^2, 2*p.*(1-p)]); legend Same Different

    From this you’ll see that the probability of same is always greater than or equal to the probability of different, so it’s the better call to make.

  3. Oliver Woodford replied on October 28th, 2009 at 09:34 UTC :

    Sorry, Doug. I only just noticed your “email me with solutions” request. I hope I haven’t spoilt it for anyone else.

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