Full Report
Roulette is an over the board game that is similar to Wheel of Fortune. Since these are spun by hand of the person running the board, the author asked "is this good randomness?" In the game, there are 54 small segments: 1, 2, 5, 10, 20, 40, 1x and 2x. Players bet on a number that the wheel will land on. For payouts, the player gets the money bet * segment + 15. If it lands on a multiplier, the players winnings are multiplied by that amount. The author did an analysis on which numbers were landed on, which segment was landed on and a few other pieces of information. From there, the author looked at the randomness of these values to see if they could gain an edge. The author noticed that the particular numbers on the board did not have random probabilities for being landed on for the turn being performed. They did analysis on the expected amount of money outputted from this as well. For example, position 29 had a 2.15% probability instead of the expected 1.851% probability. The strategy is pretty simple. Wait for the 40 number to be the in the relative 29th position. If not, then don't bet. Using this strategy would take a while but would yield results with a 90% probability. This means that the house edge could be overcome but exploiting the lack of randomness on spins.
Analysis Summary
# Main Topic
Exploitation of non-randomness in an over-the-board game (Roulette variant) to overcome the house edge.
The core finding is that the physical process of spinning the game wheel does not produce truly random outcomes, allowing for the calculation of probabilities higher than expected for certain segments based on the wheel's position.
## Key Points
- The game uses 54 segments (e.g., 1, 2, 5, 10, 20, 40, 1x, 2x).
- Analysis revealed that the probability of landing on specific numbers deviated significantly from the theoretically expected random probability.
- **Specific Finding:** Position 29 showed a landing probability of 2.15%, significantly higher than the expected random probability of 1.851%.
- The core leverage involves observing the wheel's position and the segment located there.
## Threat Actors
- **N/A.** The context describes an analyst/player exploiting an inherent flaw in a game mechanism rather than a malicious threat actor targeting systems or data. The "actor" is a player seeking an edge in gambling.
## TTPs
- **Observation and Analysis:** Monitoring the physical state of the game (wheel position) across multiple spins.
- **Statistical Modeling:** Calculating empirical landing probabilities for specific positions versus theoretical probabilities.
- **Exploitative Strategy:** Betting only when a known advantageous position coincides with a desirable segment (waiting for the '40' number to be in the relative 29th position).
## Affected Systems
- The physical "over the board game" mechanism (a specific variant of Roulette/Wheel of Fortune).
- The systems/victims affected are the operators or house managing the game, as the expected house edge can be overcome.
## Mitigations
- **For the Game Operator:** Redesigning the physical spinning mechanism to ensure true randomness in segment landing probabilities.
- **For Players:** The strategy outlined yields a 90% probability of success, implying the risk relies on the operator not yet fixing the physical randomness issue.
## Conclusion
The analysis demonstrates a feasibility study for exploiting physical imperfections in a mechanical system. By rigorously quantifying the bias in landing probabilities related to the spin position, a strategy was developed that increases the probability of winning significantly, effectively undermining the intended mathematical edge of the game operator. The primary recommendation for the game operator would be an immediate engineering review and recalibration of the physical spinner mechanism.