1) Introduction

Caveman Keno augments Classic Keno with a simple but powerful feature: egg multipliers. At the start of each round, the game designates a small number of “egg” positions on the 80-number board. If enough of those egg numbers are among the 20 drawn balls, your win for that round is multiplied, often by 2×, 4×, or 8× depending on how many eggs you hit. The base combinatorics remain unchanged—players still choose n spots; the game draws 20 numbers without replacement—yet the egg layer increases volatility and introduces right-skewed outcomes.

This chapter formalizes rules, presents representative paytables, and derives multiplier probabilities from first principles. We decompose expected value into base and multiplier contributions, quantify variance, and provide strategy templates for low-, mid-, and high-volatility play. Graph placeholders are included for hit-distribution curves, multiplier-hit rates, payout histograms, RTP by spot count, and drawdown profiles. Replace placeholders with generated images from your simulator to publish production pages.

2) Rules & Gameplay

2.1 Core Rules

• Board: Numbers 1–80.
• Draws per round: 20 unique numbers sampled without replacement.
• Your selection: Choose n spots (typical analysis uses 1–10).
• Base payouts: Determined by the paytable for your spot count.
• Egg placement: At the start of the round, the machine designates E egg numbers on the 1–80 board. Commonly E = 3.
• Multiplier condition: If exactly x of the E egg numbers appear among the 20 drawn balls, your round’s payout is multiplied by a factor M(x). Typical schedule:
  • Hit 0–1 eggs → M=1× (no bonus)
  • Hit 2 eggs → M=4×
  • Hit 3 eggs → M=8×
  Some cabinets use M={2×, 4×, 8×} or similar. Always confirm the schedule.
• No free games: Unlike Cleopatra, the bonus expresses only as a multiplier on the current round’s payout.
• Stake: 1 credit per base round unless you choose multi-credit play.

2.2 Round Walk-Through

1. Select n spots and place a stake.
2. Machine highlights E egg positions on the board.
3. Draw 20 numbers. Count hits K between your picks and drawn balls.
4. Compute base payout pay(K) from the paytable for your spot count.
5. Count egg hits X among the drawn balls. Apply multiplier M(X) to your base payout.
6. Net = M(X) × pay(K) − stake.

2.3 Design Implications

Eggs increase variance by adding multiplicative weight on the right tail of the distribution while leaving loss-rounds overwhelmingly unaffected. The feel shifts from Classic’s steadier cadence to a stop-and-surge profile where occasional egg hits amplify already-good rounds.

3) Paytables

Caveman uses standard Classic Keno paytables for the base payout; multipliers apply on top. Below are representative, pedagogical examples. Replace with your venue’s tables for precise EV and volatility.

3.1 Example 4-Spot Base Paytable

Egg multipliers multiply the payout shown above when eggs hit.

3.2 Example 6-Spot Base Paytable

3.3 Example 8-Spot Base Paytable

3.4 Typical Egg Multiplier Schedule

Some venues use 2×/4×/8×. Always verify.

4) Mathematics of Caveman Keno

4.1 Base Hits

With n player spots and 20 draws without replacement from an 80-number population, base hits follow the hypergeometric distribution:

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

4.2 Egg-Hit Probability

Let E be the number of eggs placed (commonly 3). Eggs are chosen uniformly from the 80-board before the draw. During the 20-ball draw, the number of eggs that appear among the 20 is X. Conditional on the egg set, the draw is uniform, so X is hypergeometric with population 80, success states E, sample size 20:

P(X = x) = [C(E, x) * C(80 - E, 20 - x)] / C(80, 20),   x = 0..min(E,20)

For E=3, X ∈ {0,1,2,3}. Eggs are sparse, so X ≥ 2 is rare, which concentrates multiplier mass in the tail.

4.3 Joint Structure and Independence Notes

The base hit count K and the egg hit count X are both functions of the same 20-draw outcome, so they are dependent in a strict sense. However, Caveman multipliers do not depend on which player numbers are matched by eggs; they depend only on egg appearances among the 20 balls. The payout is M(X) × pay(K). To compute E[ M(X) × pay(K) ] exactly, sum over the joint distribution of (K, X). In practice, two simplifying approaches are common:

• Simulation: Directly sample rounds, compute both K and X, and average M(X) × pay(K).
• Approximation: When eggs are few and independent of the player’s picks, treat X and K as approximately independent for EV purposes, i.e. E[M(X) × pay(K)] ≈ E[M(X)] × E[pay(K)]. This slightly over- or under-estimates EV depending on paytable shape but is often close.

4.4 Expected Multiplier

The expected multiplier per round is:

E[M] = Σ_x P(X=x) × M(x)

For E=3 and schedule {1× for x=0,1; 4× for x=2; 8× for x=3}, compute P(X=x) from the E=3 hypergeometric and plug in.

4.5 Expected Return (EV) per Round

If using the independence approximation:

EV ≈ E[M] × EV_base - stake

where EV_base = Σ_k P(K=k) × pay(k). For exact EV, simulate or enumerate the joint states of drawn sets and evaluate M(X) × pay(K) directly.

4.6 Variance

Variance grows because the random factor M(X) scales base payouts. Using the independence approximation:

Var[M×pay(K)] ≈ E[M^2]E[pay(K)^2] − [E[M]]^2[E[pay(K)]]^2

Exact variance is best from simulation due to dependency and the discrete, heavy-tailed nature of payouts.

4.7 Worked Example (Illustrative)

Assume E=3 and multiplier schedule {1× for 0–1 eggs, 4× for 2 eggs, 8× for 3 eggs}. Suppose your 6-spot base EV is 0.47 credits per 1-credit stake (from the representative table). If E[M] ≈ 1.12 from the egg distribution (illustrative), then:

EV ≈ 1.12 × 0.47 − 1 = 0.5264 − 1 = −0.4736 credits per round

This is not a claim about actual RTP; it demonstrates mechanics. Real figures depend on your venue’s paytables and egg schedule.

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-tier base pays. Eggs become “nice-to-have” boosts.
• Balanced peaks: 6–7 spots. Mid-tier base hits plus occasional egg multipliers produce memorable spikes.
• High variance: 8–10 spots with aggressive top pays. Expect many dead rounds punctuated by egg-amplified wins.

6.2 Paytable Sensitivity

Multipliers magnify whatever base table you choose. If the base table shifts weight toward top tiers, Caveman will further accentuate tail outcomes. For steadier feel, prefer base tables with modest mid-tier pays.

6.3 Egg Schedule Trade-offs

• Higher multipliers (e.g., 2×/4×/8× vs 1×/4×/8×): Larger E[M] but increased volatility.
• More eggs (E): Raises probability of multiplier hits but can require lower base tables to keep RTP in target.

6.4 Bankroll Policy

• Unit size: Target 200–300 rounds at your volatility level.
• Stop-loss: Pre-commit. Caveman’s droughts can be long before an egg-amplified recovery.
• Lock policy: After a large egg-boosted hit, skim profit and reset to base unit.

6.5 Myths to Ignore

• Eggs can be “aimed”: The egg set and the 20 draws are random. Positioning picks near egg icons on the UI does not change probability.
• Hot/cold eggs: Illusory under fair RNG.

6.6 Practical Templates

• Low-variance Caveman: 4-spot, 1 credit, 300 rounds. Eggs provide occasional 4×/8× spikes.
• Balanced Caveman: 6-spot, 1 credit, 250 rounds. Noticeable spikes from 2–3 egg hits during already-good base rounds.
• Aggressive Caveman: 8–10 spots, 1 credit, 200 rounds. Plan for deep troughs and rare, dramatic step-ups.

7) Simulation Results

Simulation is the cleanest route to exact EV and variance because it captures dependency between base hits and egg hits. Use 500k–1M rounds per configuration. Record seeds, spot count, base paytable, E, and multiplier schedule.

7.1 Methodology

• For each round: randomly choose E eggs on 1–80; draw 20 numbers without replacement.
• Compute player hits K from the draw; compute egg hits X in the same draw.
• Payout = M(X) × pay(K); Net = payout − stake.
• Aggregate: RTP, standard error, variance, egg-hit frequency, payout histogram, drawdown quantiles, cumulative return percentiles.

7.2 Qualitative Expectations

• RTP convergence: Matches analytic EV when measured over large runs.
• Right-tail amplification: Payout histograms show thicker right tails versus Classic.
• Drawdown profile: Deeper and longer troughs; recoveries occur in discrete steps when egg hits align with mid/high base hits.

7.3 Example Output Tables (Placeholders)

8) Case Studies

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

A player chooses 4 spots at 1 credit. The median round pays nothing; 2-hit returns slow losses; 3-hit pays punctuate. When 2 or 3 eggs land in the same draw as a paying 3–4 hit, the session experiences a meaningful step-up. Most rounds do not involve multipliers; the occasional amplified win defines the session high.

8.2 Balanced Caveman (6-Spot, 250 Rounds)

With 6 spots, the player sees enough 3–4 hit results to stay engaged while egg hits occasionally multiply payouts. Bankroll trajectories show longer flat sections than Cleopatra but sharper up-steps when egg hits coincide with mid/high base tiers.

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

The player chases large, egg-multiplied hits. Many rounds pay zero; streaks of losses are normal. When a good base hit aligns with X=2 or 3 eggs, the round produces dramatic returns that can flip the whole session. This style requires higher tolerance for drawdowns.

8.4 Operator Variations

Some venues change E or the multiplier schedule or subtly adjust base paytables. Confirm details; small changes propagate into EV and risk sharply due to the multiplicative nature of the bonus.

9) FAQ

9.1 Do eggs affect which numbers I should pick?

No. Eggs are chosen randomly; your picks do not influence egg placement or appearance probability.

9.2 Are eggs fixed on the UI grid?

No. They are sampled each round. Visual positions on the screen do not create probability seams.

9.3 Does picking numbers “near” eggs help?

No. Eggs are not magnets. Only whether eggs appear in the 20 drawn balls matters.

9.4 Can I estimate multiplier frequency?

Yes. Use P(X=x) with population 80, E eggs, and sample size 20. Then compute E[M] and, via simulation, the exact EV.

10) Summary & Takeaways

• Caveman Keno = Classic Keno + egg multipliers.
• Egg hits follow a hypergeometric law independent of your picks; multipliers amplify paying rounds.
• EV comes from base table × expected multiplier; exact values are best from simulation.
• Variance increases. Expect deeper troughs and sharper recoveries than Classic.
• Choose spot count for your objective: time, balance, or high volatility.