How to Use This Tool
  • Enter the amount you expect to win in the "$ Won" field.
  • Enter the amount you expect to lose in the "$ Lost" field.
  • Enter the probability of winning as a decimal in the "Win Percent" field. For example, for a 50% chance of winning, enter 0.5.
  • The "Results" section will display the expected value of the bet, the odds against winning, the risk to reward ratio, and the breakeven win percentage.
  • In the "Monte Carlo Simulation" section, enter your initial bankroll, the number of tries, and the number of simulations you want to run.
  • The tool will run the specified number of simulations and display the percentage of simulations that went bust (i.e., the bankroll hit zero).
  • The chart will display the results of each simulation, with the bankroll after each try on the y-axis and the number of tries on the x-axis. Simulations that went bust are shown in red.
  • To highlight the importance of a big enough bankroll to withstand variance, try using a high number of tries (e.g., 1000) and a win percentage slightly above 0.5 (e.g., 0.55). This will show that even with a positive expected value, you can still go bust if you don't have a large enough bankroll to withstand the variance.
  • To demonstrate the concept of risk of ruin, try using a high number of tries (e.g., 1000) and a win percentage below 0.5 (e.g., 0.45). This will show that even with a large bankroll, you can still go bust in the long run if your expected value is negative.
  • To illustrate the effect of bet sizing on your bankroll, try using different amounts for "$ Won" and "$ Lost" while keeping the win percentage and number of tries constant. This will show how increasing your bet size can increase your risk of ruin, even if your expected value is positive.
  • To show the impact of win percentage on your expected value and risk of ruin, try using different values for "Win Percent" while keeping the other inputs constant. This will show how a higher win percentage can increase your expected value and decrease your risk of ruin.
Expected Value Calculator
Results

The probability of winning is 0.5 or 50%

The odds against hitting the target are 1.00:1.

The R:R ratio is 0.91:1 so in general this seems like a favorable bet.

The breakeven win percentage is 0.4762 or 47.62%.

The EV is $5.00.

Monte Carlo Simulation

The percentage of simulations that went bust is 0%.