fun88: Analyze betting using Monte Carlo method

How to Perform Monte Carlo Simulation in Excel

Monte Carlo methods offer a practical way to obtain numerical outputs through repeated random sampling. This approach is particularly valuable for bettors who may not be well-versed in complex statistical testing methods, as it doesn’t require advanced mathematical knowledge.

Applying Monte Carlo Simulation to Sports Predictions

fun88 has explored the application of Monte Carlo simulation in sports predictions, using the example of forecasting the outcome of a Formula One championship.

Analyzing Betting Performance

Suppose we have a dataset containing 1,521 bets and a profit margin of 0.76% from fixed-amount bets. How do we determine if this performance is typical or influenced by luck?

To assess this, we compare the results to expectations. Implicit in this approach is estimating the fair betting odds for each bet, from which we derive the expected value. For instance, if fair odds are 2.00 and the bookmaker offers 2.10, the expected value is 5% or 1.05 (2.10/2.00).

Fair odds of 2.00 imply a 50% win rate. For 100 such bets, with 50 wins yielding €1.10 profit each and 50 losses resulting in a loss of €1 each, the net profit is €5 (or a 5% income on €100 wagered). Similarly, if fair odds are 3.00 and the bookmaker offers 3.50, the expected value is 16.67%.

Running Monte Carlo Simulation in Excel

Executing a Monte Carlo simulation in Excel is relatively simple:

1. Calculate the expected win rate for each bet, represented as a decimal between 0 and 1 (the reciprocal of fair odds).
2. Use Excel’s RAND function to generate a random number between 0 and 1 for each bet.
3. Determine the outcome of each bet by comparing the random number to the expected win rate. If the random number is lower, the bet wins (profit equal to the odds); otherwise, it loses (-1 profit).
4. Calculate the overall profit by summing profits and losses from all bets. For fixed-amount bets, divide the total profit by the number of bets.
5. Utilize Excel’s data table function to refresh the specified number of simulated random numbers.

By following these steps, bettors can gain valuable insights into their betting performance and make informed decisions.