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. Links below.

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