Model bottle-reveal-1. Virtual-credit prototype. Not a certification or real-money approval.
| Multiplier | Bottles |
|---|---|
| 0× | 15 |
| 0.24× | 2 |
| 0.48× | 1 |
| 0.96× | 1 |
| 1.92× | 1 |
Exact multivariate hypergeometric enumeration without replacement; aggregate return / aggregate wagers. Extra and combined assume buy whenever offered and sufficiently funded. Extra metrics conditioned on a purchase. Distributions use gross return / total cost; SD and maximum gross use original base bet.
| Metric | Base 5 | Extra 3 | Combined |
|---|---|---|---|
| expectedReturnPerBaseBet | 0.96000000 | 0.57603715 | 1.53600000 |
| expectedWagerPerBaseBet | 1.00000000 | 0.60003870 | 1.60000000 |
| rtp | 0.96000000 | 0.96000000 | 0.96000000 |
| hitFrequency | 0.80630805 | 0.60091595 | 0.94891641 |
| netWinFrequency | 0.35932663 | 0.34315939 | 0.44914861 |
| returnSDPerBaseBet | 0.91223266 | 0.75225636 | 1.03207344 |
| netSDPerBaseBet | 0.91223266 | 0.72984923 | 1.17417353 |
| maxGrossPerBaseBet | 3.84000000 | 3.36000000 | 3.84000000 |
| maxProbability | 0.00006450 | 0.00087725 | 0.00361197 |
| maxGrossPerTotalWager | 3.84000000 | 4.80000000 | 3.84000000 |
| Band | Base | Extra | Combined |
|---|---|---|---|
| 0 | 19.36920% | 39.90840% | 5.10836% |
| (0,1) | 44.69814% | 25.77566% | 49.97678% |
| [1,2) | 19.73684% | 13.72767% | 30.59598% |
| [2,3) | 13.86739% | 11.60292% | 12.85475% |
| [3,4) | 2.32843% | 6.86577% | 1.46414% |
| [4,5) | 0.00000% | 2.11959% | 0.00000% |
For every observed five-bottle history H with remaining sum S, E[extra return|H]=B*S*3/(15*100), price=B*S*3/(15*96). Thus E[extra return|H]=0.96*price. For any purchase decision measurable from revealed history (including balance), E[total return]=0.96*E[total cost]. Minimum and maximum wager-weighted theoretical RTP are both 96%, provided all paid reveals eventually settle, no rebates/caps/rounding change the model and hidden prizes are not leaked. The mean of per-round return/cost ratios is NOT RTP.
| Pack | Observed RTP | Standard error | z-score vs 96% |
|---|---|---|---|
| base | 95.91402% | 0.06448 percentage points | -1.333 |
| extra | 95.89903% | 0.08598 percentage points | -1.174 |
| combined | 95.90840% | 0.05159 percentage points | -1.776 |
Exact results enumerate all compositions with integer combination weights. The simulation confirms, but does not replace, the proof. Hit frequency means any positive gross return; it does not mean net profit. Volatility is the standard deviation, not a marketing label.
Sources: operator.json, server/domain.mjs and tools/math-report.mjs. Regenerate with npm run math. Full conditional states: math-report.json.