additive.py

#!/usr/bin/env python3

import numpy as np

class Organism:
    def __init__(self, name):
        self.wealth = 30
        self.name = name
        self.alive = True

    def takes_bet(self, q1, q2):
        if not self.alive:
            return False
        elif self.name == "log":
            return 0.5*(np.log(self.wealth + q1) - np.log(self.wealth)) + 0.5*(np.log(self.wealth + q2) - np.log(self.wealth)) > 0
        elif self.name == "growth":
            return (q1 + q2) / 2 > 0
        else:
            return True


organisms = [
    Organism("log"),
    Organism("growth"),
    Organism("yes"),
]

for _ in range(10000):
    # q1, q2 = (1/2, -11/30)
    q1, q2 = (15, -11)
    # q1 = np.random.uniform(-1, 15)
    # q2 = np.random.uniform(-1, 15)

    # offer a positive-EV bet that the log organism is guaranteed to refuse
    # log_org_wealth = organisms[0].wealth
    # q1 = log_org_wealth/2
    # q2 = log_org_wealth*(-11/30)

    outcome = np.random.choice([q1, q2])
    for org in organisms:
        if org.takes_bet(q1, q2):
            org.wealth += outcome
            if org.wealth < 0:
                org.alive = False

for org in organisms:
    print(org.name, org.wealth)

highest = 0
highest_name = None
for org in organisms:
    if org.wealth > highest:
        highest = org.wealth
        highest_name = org.name

print(highest_name, "wins")

multiplicative.py

#!/usr/bin/env python3

# see https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity

import numpy as np

class Organism:
    def __init__(self, name):
        self.log_wealth = 0
        self.name = name

    def takes_bet(self, f1, f2):
        if self.name == "log":
            return np.sqrt(f1 * f2) > 1
        elif self.name == "ensemble":
            return (f1 + f2)/2 > 1
        elif self.name == "guaranteed_win":
            # only take the bet if you are guaranteed to gain money
            return min(f1, f2) > 1
        elif self.name == "test1":
            return f1 + f2 > 1
        elif self.name == "test2":
            return (f1 + f2)/((1.1 + 2) * 0.75) > 1
        else:
            return True


organisms = [
    Organism("log"),
    Organism("ensemble"),
    Organism("yes"),
    Organism("test1"),
    Organism("test2"),
    Organism("guaranteed_win"),
        ]

for _ in range(100000):
    # f1, f2 = np.random.uniform(0, 1.5, size=2)
    # f1, f2 = (1.5, 0.6)
    p1 = np.random.uniform(0, 1.1)
    p2 = np.random.uniform(0, 2)
    p3 = np.random.uniform(1, 2)
    p4 = np.random.uniform(0, 0.7)
    p5 = np.random.uniform(0, 0.2)
    p6 = np.random.uniform(0, 3)

    f1 = np.random.choice([p1, p2, p3])
    f2 = np.random.choice([p4, p5, p6])

    outcome = np.random.choice([f1, f2])
    for org in organisms:
        if org.takes_bet(f1, f2):
            org.log_wealth += np.log(outcome)

for org in organisms:
    print(org.name, org.log_wealth)