The Coin Flip Game that Stumped Twitter: Alice HH vs Bob HT

Who is more likely to win after 100 flips? Alice, who scores for every Heads-Heads, or Bob who scores for every Heads-Tails? An intuitive answer involving a dog on a soccer field is presented. See my new follow up video on this problem    • Counterintuitive Coin Flips meet Deep Neur...   Link to python code: https://colab.research.google.com/dri... Link to written version of proof: https://publish.obsidian.md/nicam/Fun... 0:00 Twitter’s Alice Heads-Heads vs Bob Heads-Tails coin flip problem 1:06 Histograms for individual scores 2:12 Extra points for TT makes them indistinguishable 3:17 The answer 5:12 Intuition by Soccer Game and Dog Analogy 7:38 Why is the coin flip game like the soccer analogy 9:40 Markov chain for the game Score Difference X_t and Last Coin C_t 13:28 The Victory Point Function 14:38 Value Functions 16:05 Recursion Relation Update Rules for the Value Function 18:35 Computer plot of value functions 23:47 Why Bob has an advantage explained with value functions 28:30 Conclusion