High rates and volatility: calculating risks
1. The concept of volatility and its role
Volatility is the degree to which game outcomes are spread around mathematical expectation (RTP). At high rates, volatility determines how quickly and deeply a bankroll can sink or grow. For a high roller, it is important not only to know the average return value, but also the value of the standard deviation of the payouts.
2. Risk metrics
1. Standard deviation (σ):
2. Coefficient of variation (CV):
3. Max Drawdown:
4. Value at Risk (VaR):
3. Bankroll calculation and risk management
1. Fixed-bet:
2. Kelly Criterion:
3. Risk limit model:
4. Calculation Example for Slot
RTP = 96%, spin σ ≈ 3 β (where β is the average multiplier rate).
β rate = €1,000, N = 100 spins:
To limit the risk to 10% bankroll B = €500,000, the daily loss limit of ≈€50 000 coincides with VaR₀.₀₅, which provides a 95% guarantee of capital safety in one session.
5. Practical recommendations
1. Test run: Before big bets, run 100-200 spins on a fixed beta to empirically evaluate σ and Max Drawdown.
2. Adaptive percentage: lower k after drawdown of more than 20% B, increase only with stable growth.
3. Regular analysis: keep a betting log, record μ and σ for each game, revise the strategy once a week.
4. Diversification: Spread bankroll between different games (slots, roulette, blackjack) to reduce overall CV.
5. Control automation: Use scripts or API tools to track thresholds and instantly block bets when a limit is triggered.
6. Conclusion
The exact calculation of risks at high rates is based on an understanding of volatility and the use of statistical metrics (σ, VaR, CV). A well-built bankroll management system - fixed interest, Kelly's criterion, stop limits and interval raids - allows high-rollers not only to save capital, but also to make the most of the potential of large rates.
Volatility is the degree to which game outcomes are spread around mathematical expectation (RTP). At high rates, volatility determines how quickly and deeply a bankroll can sink or grow. For a high roller, it is important not only to know the average return value, but also the value of the standard deviation of the payouts.
2. Risk metrics
1. Standard deviation (σ):
- For slots: based on spin series σ≈β·√N, where β is the average beta multiplier, N is the number of bets.
- For board games: calculated from possible outcomes (for example, in roulette σ≈√ (p· (1-p))· β).
2. Coefficient of variation (CV):
- $CV = \frac{σ}{μ}$,
- where μ is the average win per bet. The higher the CV, the greater the drawdown should be expected with a series of failures.
3. Max Drawdown:
- Full bankroll decline from peak to bottom per game session; calculated on the basis of historical data or according to the VaR formula (Value at Risk).
4. Value at Risk (VaR):
- $VaR_{α} = μ - z_{α}·σ$,
- where zₐ is the quantile of the normal distribution (for example, z₀.₀₅≈1. 645 for 95%).
3. Bankroll calculation and risk management
1. Fixed-bet:
- rate = k· B, where B is the current bankroll, k = 1-2%. Limits drawdown to a predictable amount.
2. Kelly Criterion:
- $f= \frac{bp - q}{b}$,
- where b is the net odds, p is the probability of winning, q = 1-p. Used carefully (fractional Kelly ≤½).
3. Risk limit model:
- Daily stop loss: 10-15% of B.
- Stop wine: fixed profit target, after which the session closes (5-10% B).
- Interval raids: series of M bets (for example, M = 50), then analysis and break.
4. Calculation Example for Slot
RTP = 96%, spin σ ≈ 3 β (where β is the average multiplier rate).
β rate = €1,000, N = 100 spins:
- μ = (RTP–1)·β = –€40
- σ\_total ≈ 3·€1 000·√100 = €30 000
- VaR₀.₀₅ ≈ –€40 –1. 645· €30,000 ≈ - €49,360 → chance of losing over €49,360 no more than 5%.
To limit the risk to 10% bankroll B = €500,000, the daily loss limit of ≈€50 000 coincides with VaR₀.₀₅, which provides a 95% guarantee of capital safety in one session.
5. Practical recommendations
1. Test run: Before big bets, run 100-200 spins on a fixed beta to empirically evaluate σ and Max Drawdown.
2. Adaptive percentage: lower k after drawdown of more than 20% B, increase only with stable growth.
3. Regular analysis: keep a betting log, record μ and σ for each game, revise the strategy once a week.
4. Diversification: Spread bankroll between different games (slots, roulette, blackjack) to reduce overall CV.
5. Control automation: Use scripts or API tools to track thresholds and instantly block bets when a limit is triggered.
6. Conclusion
The exact calculation of risks at high rates is based on an understanding of volatility and the use of statistical metrics (σ, VaR, CV). A well-built bankroll management system - fixed interest, Kelly's criterion, stop limits and interval raids - allows high-rollers not only to save capital, but also to make the most of the potential of large rates.
