1) Introduction

Power Keno keeps Classic Keno’s core—choose spots, draw 20 without replacement—and layers a single leverage point: if the 20th ball drawn matches one of your picks, then any win in that round is multiplied by 4×. The trigger depends on the last ball only. If you do not win on base hits, the 4× has no effect. When you do win and the final ball is favorable, outcomes jump sharply. This produces end-of-round suspense and a volatility signature different from Cleopatra’s free-game bursts or Caveman’s egg multipliers.

This chapter formalizes rules, provides representative paytables, and derives expectation from the joint event “round pays” ∧ “last ball is one of your spots.” We decompose EV and variance, show how spot count changes both hit rates and trigger probability, and deliver strategy templates. Graph placeholders and simulation tables are included for you to replace with measured results from your own engine.

2) Rules & Gameplay

2.1 Core Rules

• Board: 1–80.
• Draw: 20 unique numbers without replacement. Order matters only for the last ball multiplier.
• Spots: Choose n numbers (analysis typically uses 1–10).
• Base payouts: As per published paytable for your spot count.
• Power trigger: If the 20th ball is one of your n numbers and you have a paying base result, the payout is multiplied by 4×.
• Stake: 1 credit per round unless multi-credit or multi-card play is enabled.
• No free games or wilds: Power Keno’s only modifier is the 4× last-ball condition.

2.2 Round Walk-Through

1. Select n spots and place 1 credit.
2. Draw 20 numbers. Compute base hits K and map to pay(K).
3. Check the 20th ball. If it is among your picks and pay(K)>0, set payout to 4×pay(K); else pay pay(K).
4. Net = payout − 1.

2.3 Design Implications

The trigger does not change whether a round pays; it scales the amount if the final ball is favorable. This creates conditional volatility: the same base paytable, but a subset of wins are quadrupled. Unlike Cleopatra, which clusters value across extra rounds, Power concentrates value within a single round’s finish.

3) Paytables

The base table is identical in spirit to Classic Keno. Power Keno overlays a 4× multiplier only when the last-ball condition is met and the round is paying. Example tables are pedagogical; substitute your venue’s numbers for exact EV.

3.1 Example 4-Spot Base Paytable

3.2 Example 6-Spot Base Paytable

3.3 Example 8-Spot Base Paytable

3.4 Practical Notes

• Only paying outcomes can be multiplied. Zero-pay rounds remain zero regardless of the last ball.
• Because the last-ball event is independent of base hit count before seeing the draw, a simple decomposition is possible for EV.

4) Mathematics of Power Keno

4.1 Base Hit Distribution

With n spots and 20 draws from 80 without replacement:

P(K = k) = [C(n, k) * C(80 - n, 20 - k)] / C(80, 20)

4.2 Last-Ball Event Probability

Before any draw, each of the 80 numbers is equally likely to occupy the 20th position. With n chosen numbers:

P(last ball is one of my picks) = n / 80

This holds irrespective of the first 19 balls’ identities.

4.3 EV Decomposition

Let pay(k) be the base payout for k hits. Define:

• EV_base = Σ_k P(K=k)·pay(k)
• EV_pay>0 = Σ_k:pay(k)>0 P(K=k)·pay(k)
• p_last = n/80

A round that pays is multiplied 4× with probability p_last. So expected payout per round:

E[payout]
  = EV_base + (4−1)·p_last·EV_pay>0
  = EV_base + 3·(n/80)·EV_pay>0
    

Expected net per 1-credit stake:

EV_total = E[payout] − 1

If you only know EV_base and the probability of any pay, Ppay = Σ_{k:pay(k)>0} P(K=k), but not the pay-weighted EV_pay>0, you can approximate with EV_base·p_last_scaled. Exact calculation uses EV_pay>0.

4.4 Variance

The multiplier applies conditionally. Let I be the indicator that last-ball is favorable. Then payout is pay(K)·[1 + 3·I·1{pay(K)>0}]. Variance expands by:

Var[payout] = E[payout^2] − (E[payout])^2

The cross-term involves E[ pay(K)^2 · I · 1{pay(K)>0} ] = p_last · E[ pay(K)^2 · 1{pay(K)>0} ]. Exact closed-form is algebraic but unwieldy; simulation is recommended.

4.5 Worked Example (Illustrative)

Suppose a representative 6-spot table yields EV_base = 0.47 credits and EV_pay>0 = 0.49 credits. With n=6, p_last = 6/80 = 0.075:

E[payout] = 0.47 + 3 * 0.075 * 0.49
          ≈ 0.47 + 0.11025
          ≈ 0.58025
EV_total  ≈ −0.41975 credits per round
    

Numbers are illustrative, not universal. Real values depend on your paytable.

5) Graphs & Charts

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6) Strategy Insights

6.1 Objectives and Spot Count

• Time on device: 3–5 spots with supportive mid-tiers. You’ll see more paying rounds, so more opportunities for 4× to matter.
• Balanced peaks: 6–7 spots. Paying rounds are less frequent than low-spots, but when they occur with a favorable last ball, spikes are meaningful.
• High variance: 8–10 spots. Most rounds pay zero; when pays occur and the last ball hits, outcomes jump dramatically.

6.2 Paytable Sensitivity

Power multiplies paying results only. Tables that shift mass into small but frequent pays increase the chance that 4× is applied, while tables with steeper tops make the rare 4× events very large. Choose according to variance tolerance.

6.3 Bankroll Policy

• Unit size: Target 200–300 rounds for the chosen volatility.
• Stop-loss: Define a maximum drawdown. Power’s spikes should not tempt escalation after losses.
• Locking: After a 4× amplified win, skim profit and reset unit.

6.4 Misconceptions

• “Saving” the last ball: False. The last position is random among 80 numbers.
• Ordering picks for the last ball: Irrelevant. Only identity of the 20th ball matters, not pick order on the UI.
• Hot/cold last balls: Noise under fair RNG.

6.5 Practical Templates

• Low-variance Power: 4-spot, 1 credit, 300 rounds. Frequent small pays, occasional 4× boosts.
• Balanced Power: 6-spot, 1 credit, 250 rounds. Noticeable spikes when last ball aligns with mid-tier pays.
• Aggressive Power: 8–10 spots, 1 credit, 200 rounds. Long droughts, rare but dramatic 4× turns.

7) Simulation Results

Simulation validates decomposition and quantifies variance. Run 500k–1M rounds per configuration. Record seeds, paytables, and spot counts.

7.1 Methodology

• For each round: draw 20 numbers; compute K and pay(K).
• Check 20th ball ∈ picks. If yes and pay(K)>0, set payout = 4×pay(K) else payout = pay(K).
• Aggregate RTP, standard error, variance, payout histogram, last-ball favorable rate, drawdown quantiles, cumulative return percentiles.

7.2 Qualitative Expectations

• RTP: Matches EV_base + 3·(n/80)·EV_pay>0 − 1 within sampling error.
• Variance: Higher than Classic due to conditional spikes.
• Drawdowns: Longer plateaus than Cleopatra but steeper step-ups when 4× aligns with pays.

7.3 Example Output Tables (Placeholders)

8) Case Studies

8.1 Low-Variance Power (4-Spot, 300 Rounds)

With 4 spots, base pays appear often enough that some will coincide with a favorable last ball. The session shows many modest results and occasional 4× enlargements. Bankroll slope is shallow with intermittent steps.

8.2 Balanced Power (6-Spot, 250 Rounds)

Fewer paying rounds than 4-spot, but mid-tier pays exist. When the last ball aligns, step-ups are significant and define the session. Player experience alternates between quiet runs and sharp boosts.

8.3 High-Variance Power (8–10 Spots, 200 Rounds)

Most rounds pay zero. A paying outcome is rare. When it arrives and the last ball is favorable, the 4× creates dramatic impacts that can flip the session. Suitable only for players who accept long droughts.

8.4 Operator Variations

Some cabinets adjust top-tier pays in Power to target an RTP band. Always verify tables. Small changes in mid-tier pays can shift both EV and feel due to the conditional 4×.

9) FAQ

9.1 Does the last-ball 4× apply to non-paying rounds?

No. Only paying results are multiplied.

9.2 Can I influence the last ball?

No. Each number has 1/80 chance to be last; with n picks, the favorable probability is n/80.

9.3 Is higher spot count always better in Power?

No. It increases last-ball probability linearly but also changes base hit distribution and variance. Evaluate against your objective.

10) Summary & Takeaways

• Power Keno multiplies paying rounds by 4× when the 20th ball is one of your picks.
• Trigger probability is n/80; only paying outcomes benefit.
• EV = EV_base + 3·(n/80)·EV_pay>0 − 1. Variance rises from conditional spikes.
• Pick spot count and paytable to match preferred volatility.
• Use simulation to capture variance and drawdown profiles accurately.