pgebet: high odds vs low odds

The impact of betting odds might not be immediately apparent. Surprisingly, a 120% Return on Investment (ROI) with odds around 1.25 signals greater player skill than odds around 5.00. Betting on outcomes with lower probabilities (higher odds) inherently carries more risk (assuming equal stakes) due to increased susceptibility to random fluctuations.

Put simply, returns become more volatile. For instance, at odds of 5.00, achieving a return between 95% and 105% yields approximately 19 to 21 winners. In contrast, at odds of 1.25, achieving returns between 98.75% and 101.25% results in roughly 79 to 81 winners. Betting on higher odds entails taking greater risks for potentially higher rewards.

pgebet delves into the impact of betting odds by scrutinizing the standard deviation of profits and losses across betting histories. For equal stakes, the standard deviation can be approximated by the following expression:

\[ \text{Standard Deviation} = \frac{o – r}{o \cdot r} \]

Here, \( o \) represents the average odds of the betting history, and \( r \) represents the player’s actual return. The standard deviation for bets at odds of 5.00 is over four times greater than that for bets at odds of 1.25. Assuming an expected return of 100% (purely based on luck), the t-score can be calculated as follows:

\[ \text{T-Score} = \frac{\sqrt{n}}{100} \]

Where \( n \) represents the number of bets. Hence, with equivalent betting and return histories, the t-score is more than eight times smaller at odds of 5.00 compared to odds of 1.25.

It’s crucial to note that exceptionally high returns from betting on higher odds (common in markets like horse racing) don’t necessarily denote superior predictive prowess on the player’s part. In such scenarios, the same luck yields a substantially higher proportion of returns.

Hence, solely considering proportional returns when comparing betting histories (a common practice when ranking tipsters) is fundamentally misleading. The t-score, accounting for betting odds, offers a method to evaluate earnings quality above expectations, while factoring in risk elements.