Editing Monte Carlo Methods (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Pi Estimator' (Calculating Pi by throwing 'Random Darts'):'''
<syntaxhighlight lang="python">
import random

def estimate_pi(num_darts):
    """
    Throws darts at a 1x1 square. A circle fits inside.
    The ratio of hits in the circle / total darts = Pi / 4
    """
    hits = 0
    for _ in range(num_darts):
        x = random.random()
        y = random.random()
        # Distance from center (0.5, 0.5)
        if (x-0.5)**2 + (y-0.5)**2 <= 0.25:
            hits += 1
            
    pi_est = 4 * (hits / num_darts)
    return pi_est

# 100 darts (Low accuracy)
print(f"Pi with 100: {estimate_pi(100)}")
# 1,000,000 darts (High accuracy)
print(f"Pi with 1,000,000: {estimate_pi(1000000)}")
</syntaxhighlight>

; Monte Carlo Landmarks
: '''The Manhattan Project''' → The first real use of Monte Carlo to "Simulate Neutron Diffusion" inside the first Atomic Bomb, because "Human math" couldn't handle the complexity.
: '''Value-at-Risk (VaR)''' → The standard risk measure in Banks: "What is the maximum amount we can lose in 1 day with 99% certainty?" (Calculated using 10,000 Monte Carlo simulations).
: '''Ray Tracing''' → How modern "Video Games" and "Movies" create realistic light. They "Shoot random rays of light" (Monte Carlo) into a scene and see what they hit.
: '''AlphaGo''' → The AI that beat the Go champion. During the game, it would "Play 10,000 random games to the end" from every possible move to see which one "Usually" wins.
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