Counter-Intuitive Probability Puzzle: Random Walkers Meeting On A Grid

Alice and Bob start at opposite corners of a 5x5 grid. Alice moves up/right randomly and Bob moves down/left randomly. What is the chance they meet? What happens for an nxn grid? As n goes to infinity, the answer is interesting and involves pi! Watch the video for the solution. My blog post for this video: https://wp.me/p6aMk-57D Links for asymptotic formula https://en.wikipedia.org/wiki/Binomia... https://en.wikipedia.org/wiki/Central... https://en.wikipedia.org/wiki/Stirlin... http://math.stackexchange.com/questio... http://planetmath.org/asymptoticsofce... If you like my videos, you can support me at Patreon:   / mindyourdecisions   Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter:   / preshtalwalkar   Facebook:   / 168446714965   Google+: https://plus.google.com/1083366085665... Pinterest:   / preshtalwalkar   Tumblr:   / preshtalwalkar   Instagram:   / preshtalwalkar   Patreon:   / mindyourdecisions   Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 27 reviews) https://www.amazon.com/gp/product/150... "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/152... "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. https://www.amazon.com/gp/product/151... "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/151... "Math Puzzles Volume 3" is the third in the series. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/151... "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.7/5 stars on 10 reviews) https://www.amazon.com/gp/product/151... "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150... "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/150...