1 - The Saint Petersburg Paradox

2 - The other Saint Petersburg Paradox

  • N = 1 \(BEV = ((3000 + 1000)^{95} * (3000)^{5})^{1/100}) = 12,081\)

  • N = 100 \(BEV = ((1.18)^{95} * (0.27)^{5})^{1/100}) = 1.098\)

3 - The Eternal Return

3.1 - Dice with Schrodinger’s Demon

\[EV = (-0.5+0.05+0.05+0.05+0.05+0.5)/6 = 0.033\]

After 300 rolls: \(1.033^{300} = 18,713\)

3.2 - Dice with Nietzsche’s Demon

if the following rolls: 3 -> 6 -> 1 -> 5 -> 4 -> 2 \(EV = 1 * 1.05 * 1.5 * 0.5 * 1.05 * 1.05 * 1.05 = 0.912\)

4 - Ergotic vs. Non-Ergotic Situations