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Math reports

Twin Charge: math report

Engine’s report for Twin Charge: return, volatility, the payout distribution, every mode and every validation check.

OverviewGoblin Gold MineWild ShabangTwin Charge
RTP96.70%Mean payout 0.97x
Max win25,000xEvery mode
Volatility12.29Medium · std dev 12.2943
Hit rate40.20%1 in 2.49 spins
Zero rate59.80%Spins that pay nothing
Min payout0.00xLowest outcome
Outcomes99,936In the lookup table
ReportVersion 10Engine math summary

Outcome breakdown

Every base-game spin, in three groups

59.8%38.1%
No win 59.8%Win below bet 38.1%Bet back or more 2.1%

One spin in 2.49 pays something. One in 47.6 returns the stake or more.

Between any win2spins

Average

Longest dry run13spins

1-in-1,000 chance

Between profits47spins

Average

Longest losing run320spins

1-in-1,000 chance

Hit-rate distribution · Base game

Payout distribution

Every payout band, how often it lands and how much of the return it supplies.

Share of RTP by payout band

Multiples of the bet · hover a column for detail

0%10%20%30%0.1–11–22–55–1010–2020–5027.89%50–100100–200200–500500–1k1k–2k2k–5k5k–10k10k–20k20k+
Payout bandDistinct payoutsLandsPer spinRTP shareShare of return
No win (under 0.1x)11 in 1.6759.880%0.00%
0.1x to 1x91 in 2.6338.023%6.04%
1x to 2x101 in 1,228.210.081%0.12%
2x to 5x301 in 438.130.228%0.77%
5x to 10x501 in 330.150.303%2.26%
10x to 20x1001 in 267.450.374%5.22%
20x to 50x3001 in 173.550.576%18.86%
50x to 100x4971 in 255.510.391%27.89%
100x to 200x7761 in 985.750.101%13.01%
200x to 500x6721 in 1,274.440.078%21.26%
500x to 1,000x2521 in 120,508.360.00083%0.57%
1,000x to 2,000x1101 in 387,230.080.00026%0.33%
2,000x to 5,000x431 in 1,607,097.290.000062%0.18%
5,000x to 10,000x71 in 16,252,707.010.0000062%0.05%
10,000x to 20,000x31 in 38,701,260.880.0000026%0.03%
20,000x and above11 in 25,000,053.440.0000040%0.10%

Game modes

All modes

Engine rates volatility per mode. Costs are multiples of the base bet.

ModeCostAt a $1 betVolatilityRTPHit rateB/E
Base game1x$1.00Medium96.70%40.20%2.1%
Ante5x$5.00Low96.70%43.20%6.2%
Bonus100x$100.00Low96.70%100.00%27.5%
Super Bonus200x$200.00Low96.70%100.00%43.3%
Feature Spins400x$400.00Low96.70%99.97%35.6%
All In500x$500.00Low96.70%91.44%15.0%
Death1,000x$1,000.00Low96.70%99.98%36.0%

Engine validation

Compliance and bet tiers

Engine validates every title before release: the base mode must pass seven compliance checks, then each bet tier tests the game against risk limits.

Compliance · base mode7 of 7 passed
  • Cross-mode RTP consistency

    RTP across all modes stays within the allowed variance. Expected ≤ 0.50%.

    0.00%
  • Base mode cost

    The cheapest mode is the 1.0x base game. Expected = 1.00x.

    1.00x
  • Base mode standard deviation

    Base-game standard deviation stays within limits. Expected ≥ 0.60x.

    12.29x
  • Bet level validator

    A valid three-star bet-level template exists. Expected: valid template.

    500max_1cent
  • RTP range

    Return to player sits inside the allowed band. Expected 90.0% to 96.70%.

    96.70%
  • Cost multiplier

    A mode’s cost multiplier stays under the cap. Expected ≤ 50,000x.

    1x
  • Max payout multiplier

    The largest win stays under the cap. Expected ≤ 1,000,000x.

    25,000x
2-star tierCaps reduced

Bet template 100max_1cent

Max exposure15,000,000 → 10,000,000
Max bet cost100,000 → 50,000

Reason: Risk limit (CVaR) and tail probability

3-star tierFull caps

Bet template 500max_1cent

Every constraint within limits.

When a mode exceeds a tier’s limit, Engine lowers that tier’s caps instead of blocking the game. Values over a limit come from high-cost modes, noted in the table below.

Full constraint report
Constraint2-star value2-star limit2-star3-star value3-star limit3-star
Tail probability ≥ 5,000x
Over the 2-star limit in All In
0.03340.0100Over0.03340.0500Within
Tail probability ≥ 10,000x
Over the 2-star limit in All In
0.00980.0050Over0.00980.0100Within
Tail probability ≥ 25,000x4.0e-80.0020Within4.0e-80.0050Within
Tail probability ≥ 50,000x0n/aWithin0n/aWithin
Tail probability ≥ 100,000x0n/aWithin0n/aWithin
Risk limit (CVaR, per stake)261.2700.0Within261.2700.0Within
Risk limit (CVaR, absolute)
Over the 2-star limit in All In
21,375.720,000.0Over21,375.750,000.0Within
Expected tail liability (40x)0.703n/aWithin0.703n/aWithin
Expected tail liability (10,000x)0.294n/aWithin0.294n/aWithin
Expected tail liability (sum)0.7041.300Within0.7041.500Within
Expected tail liability (absolute)1633,000Within16310,000Within

n/a means the limit was not legible in the captured report.

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