@littmath Cases by the parity of the greatest-numbered box with a present:
even (p > 0.5): Alice or Tie(ONLY if last box is 100)
odd (p < 0.5): Alice or Bob or Tie
To say Alice wins more often, it is sufficient to show p(Tie in even) <= p(Tie in odd). This seems true lol.
@AnthonyLeeZhang The counting argument is interesting. Alphabet of s symbols, (# positions=n-k+1)*s^(n-k) double counts len n words that contain the len k target sequence more than once (say m times), but it double counts it exactly m times since any single target sequence can be the "fixed" one!
So I tried to play destiny 2 last night.. is this how it feels like playing a MMO for the first time? I had like 20 quests that all seem insignificant and nowhere to go.
A double pendulum demonstrates chaos theory, tracing its unpredictable path
The dependence on initial conditions, and sensitivity to variation is one of the fundamental properties of chaos
This is commonly referred to as "the butterfly effect,"