Expected Value :-

For a European roulette even-money bet:- • Probability of win = 18/37 • Probability of loss = 19/37

EV = P(WIN)(+1)P(LOSS)(-1) = 18/37 - 19/37 = -1/37 = -0.027

This implies a house edge of ~2.7%.

Monte Carlo simulations in this project empirically confirm convergence of the average profit per bet to the theoretical expected value.

Simulation Validation:-
	•	Ran large-scale Monte Carlo simulations (10⁴+ independent trials per configuration)
	•	Observed that empirical average profit converges to the theoretical expected value (−1/37) as the number of simulations increases

This confirms that the simulation correctly models the underlying probabilistic process.

Strategy Comparison Insight

Two betting strategies were evaluated using Monte Carlo simulation: • Flat Betting • Martingale

Key observations: • All strategies retain the same negative expected value dictated by the game odds • Martingale redistributes risk by increasing variance and ruin probability,without improving expected return.

Key takeaway: In negative-EV games, betting strategies can only reshape risk and variance, not create positive expected value.