Development of Push Gaming - an approach to mathematics and balance

Development of Push Gaming - an approach to mathematics and balance

1. Basic principles of mathematical design

Target RTP: a range of 94-97% is set, depending on the subject and position of the game in the portfolio.
Payout Frequency and Size Balance: The combination of small frequent winnings and rare large prizes forms the desired volatility profile.
Uniqueness of the mechanic: each new function (Cluster Pays, Reel Split, Collect) receives its own "multiplier" and weight in general mathematics.

2. Calculation of volatility and hit-frequency

Volatility is defined as the variance of payments:

• Standard deviation of payments from the average payment.
• Breakdown of the profile into clusters: basic payments, cascades, bonus rounds.
• Hit-frequency is calculated as the proportion of spins paid ≥ rate.

For medium-low volatility, target hit-frequency ≈ 25-30%.
For high-voltage slots, the target hit-frequency ≈ 15-20%.

3. Building a Mathematical Model

1. Script Generator:

• Python scripts generate millions of random spins at given character weights.
• Key metrics are calculated: average payout, max win, bonus frequency.
2. Balance calibration:
• Adjust the probability of symbols, multipliers, and bonus triggers.
• Iterative process: A new simulation is performed after each calibration.
3. Final stability test:
• Sessions of 10 million spins to identify rare borderline cases.
• Check for phase shifts of "dry" series and their compliance with the permissible limit (not more than 1% of spins in a row without winning).

4. Bonus mechanic integration

Cluster Pays + Reactive Multipliers:
• Each stage is assigned a rising factor × n with a maximum limit (usually × 20- × 25).
• The probability of starting a cluster cascade ≥ 0.5% for highly volatile, ≥ 1.5% for medium games.
Collect & Progress Bar:
• Collector symbols receive a weight of 0.8-1.2% per spin, filling the scale guarantees a bonus round.
• The number of steps to the bonus varies from 15 to 25 depending on volatility.
Reel Split:
• Probability of separation of drums into mini-sections is 0.3-0.7% per spin.
• The size of the mini-reels and the stakes preserve the general mathematics of RTP.

5. Simulation and user testing

Automated simulations: Continuous run on cloud to monitor metrics in real time.
A/B tests: the internal focus group runs demos, testing the subjective perception of the "dynamics of payments."
Gaming sessions: Testers run Autoplay series with different Stop-Loss/Take-Profit settings, capturing bonus frequency and maximum drawdown.

6. Certification and Audit

External auditors (iTech Labs, eCOGRA, GLI):
• Check the RNG and mathematical model for compliance with the declared RTP and uniformity of distribution.
• Recertification after each major patch or mechanics update.
• Regular audit: frequency - at least once a year for each release.

7. Adapting to the Australian market

Local rate limits: forming max rates up to AUD 100 for high rollers and up to AUD 1 for beginners.
Statistics display in AUD: all Stop-Loss/Take-Profit metrics, bets and winnings are calculated in AUD.
Post-release monitoring: Collecting anonymous Australian player session metrics to adjust parameters in the following updates.

Conclusion:
• The Push Gaming methodology combines a rigorous scientific approach to calculating RTP, volatility and hit-frequency with multiple simulations and user testing. The integration of innovative mechanics goes through the calibration of scales and external audits, and adaptation to the Australian market ensures compliance with local requirements and maximum comfort for players.