1) Introduction

DaVinci Keno keeps the Classic Keno engine—pick n numbers from 1–80, draw 20 without replacement—and layers a wild-substitution system themed around “masterpiece” tiles. After or before the draw depending on cabinet, one or more wilds are designated. When a wild condition is satisfied, a wild can stand in for one of your unhit spots or promote a base result into a higher paying tier. Some implementations also attach multiplier stamps to wild-affected rounds. The core effect is to convert near-miss outcomes into hits and, occasionally, mid-tier results into steep tiers.

This chapter documents common DaVinci rules, provides representative paytables, derives expected value (EV) and variance under several wild models, and offers simulation-ready formulas. Graph placeholders are included for wild frequency, RTP vs. spot count, payout histograms, and drawdown profiles. Replace the placeholders with outputs from your simulator and venue-specific tables.

2) Rules & Gameplay

2.1 Core Rules

• Board: 1–80.
• Draws per round: 20 unique numbers without replacement.
• Your selection (“spots”): Choose n numbers; analysis uses 1–10 as standard.
• Base payouts: Published paytable maps hit count K to prizes per spot count.
• DaVinci wilds: One or more wilds are designated by the cabinet. If wild conditions are met, the round’s effective hit count is upgraded (e.g., K’ = K + w up to a cap) or a special payout ladder is used.
• Stake: 1 credit per base round unless the cabinet requires an extra credit to activate wilds. Verify cost; it changes EV.

2.2 Common DaVinci Implementations

1. Single Wild, +1 Upgrade: One wild token is available each round. If the base result is a near-miss (at least one of your picks unhit), apply +1 effective hit: K’ = min(K+1, n). Some cabinets restrict upgrades to paying tiers only.
2. Wild Pool, Up to +2: Two wild tokens may apply. Each can fill one unhit pick, up to a cap: K’ = min(K + W, n) with W ∈ {0,1,2} determined by cabinet odds.
3. Patterned Wilds: Specific “masterpiece” tiles are flagged as wild if they appear in the 20 drawn balls. If at least one flagged tile is drawn and you are within one or two hits of a pay tier, upgrades apply by +1 or +2 subject to caps.
4. Wild With Multiplier: When a wild triggers an upgrade, a separate multiplier (e.g., 2×) may apply to the promoted payout. This increases tail weight and variance.

2.3 Round Walk-Through (Single Wild, +1)

1. Select n spots. Stake 1 credit (plus wild-side-bet credit if required).
2. Draw 20 numbers. Count base hits K; compute pay(K).
3. Wild check: if your cabinet allows a +1 substitution and K<n, promote to K’ = K + 1 with cabinet probability p_w(K,n) or deterministically if “always-on”.
4. Resolve payout ladder at K’. Apply any multiplier if the wild rule includes it.
5. Net = payout − total stake.

2.4 Design Implications

DaVinci wilds tilt mass from non-paying or low-paying tiers into higher tiers. Compared with Fireball’s “single number equals my missing pick,” DaVinci often models wilds as tokens that always or sometimes upgrade near-misses regardless of the identity of any single board number. This yields smoother elevation of outcomes with parameterizable frequency and magnitude.

3) Paytables

Many DaVinci cabinets reuse Classic ladders and layer wild upgrades on top. Others publish integrated tables where payouts already include wild math. Below are representative Classic ladders for reference; substitute your venue’s tables 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 Wild Costing and Caps

• Free wilds: Wilds always active at listed tables; stake is 1 credit.
• Side-bet wilds: Wilds activate only with an extra credit; evaluate incremental EV.
• Caps: Typical cap is +1 or +2 upgrades. Some cabinets prohibit upgrading into the jackpot tier. Confirm caps.
• Multipliers: If a wild also multiplies the promoted payout, note the distribution of multipliers and any caps.

4) Mathematics of DaVinci Wilds

4.1 Base Hit Distribution

With n spots and a 20-from-80 sample without replacement:

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

4.2 Wild-Upgrade Models

We formalize two generic models that cover most cabinets.

Model A — Always-On +1 Wild

If K<n, upgrade deterministically by +1. Effective hits K’ = min(K+1, n). No multiplier.

E[payout]_A = Σ_{k=0}^{n-1} P(K=k) · pay(k+1) + P(K=n) · pay(n)
EV_A = E[payout]_A − stake_total
    

Set stake_total = 1 for free wilds or 1 + side_bet for costed wilds.

Model B — Probabilistic Wild, +1 or +2 with Caps

On a round with K<n, a random number W ∈ {0,1,2} upgrades hits with probabilities p_0(k,n), p_1(k,n), p_2(k,n) that may depend on K and n. Effective hits:

K’ = min(K + W, n)

Expected payout:

E[payout]_B = Σ_{k=0}^{n} P(K=k) · [ p_0·pay(k) + p_1·pay(min(k+1,n)) + p_2·pay(min(k+2,n)) ]
EV_B = E[payout]_B − stake_total
    

4.3 Wild With Multiplier (Optional)

If a triggered wild also applies a multiplier M with distribution P(M=m) when W≥1, then for the promoted branch replace pay(·) by m·pay(·) and average over m. This thickens the right tail sharply.

4.4 Variance

DaVinci shifts mass from k to k+1 or k+2. Variance effect depends on the table shape near those tiers. For low spots, upgrades mostly convert non-pays to small pays, often reducing variance. For higher spots, upgrades can push into steep tiers, often increasing variance. Exact variance:

Var[payout] = Σ_i p_i x_i^2 − (Σ_i p_i x_i)^2

where i indexes the mixture over k and wild outcomes. Use simulation for realistic caps and multiplier mixes.

4.5 Worked Examples (Illustrative)

Example 1 — Always-On +1, 6-Spot

With the representative 6-spot ladder and stake 1 credit, compute P(K=k) for k=0..6, then:

E[payout] = Σ_{k=0}^{5} P(K=k)·pay(k+1) + P(K=6)·pay(6)

Compare to Classic. Expect mean increase and a variance shift dependent on ladder slopes at 1–5 hits.

Example 2 — Probabilistic +1/+2

Suppose, for n=8, cabinet parameters yield p_2 = 0.02, p_1 = 0.18, p_0 = 0.80 for k≤6, and reduced upgrade rates when k≥7. Substitute into Model B. The small p_2 materially affects the right tail due to steep 7→9 and 8→10 transitions.

5) Graphs & Charts

Replace src paths with generated images.

6) Strategy Insights

6.1 Objectives and Spot Count

• Time on device: 3–5 spots with always-on +1 wild. Frequent conversions from 1→2 and 2→3 stabilize the slope.
• Balanced peaks: 6–7 spots with +1 and rare +2. Mid-tier promotions create meaningful spikes without extreme droughts.
• High variance: 8–10 spots with +2 allowed and optional multipliers. Rare promotions into steep tiers drive session outcomes.

6.2 Side-Bet Economics

• Compute incremental value: ΔEV = EV_with_wild − EV_without_wild − extra_stake.
• If ΔEV < 0 but you prefer fewer near-misses, quantify the entertainment cost per 100 rounds.

6.3 Caps and Restrictions

• Top-tier cap: If promotions into jackpot are disallowed, wilds mainly lift mid-tiers. Variance moderates.
• Paying-only promotion: Wilds that require pay(K)>0 behave like conditional multipliers and reduce smoothing at the low end.

6.4 Paytable Sensitivity

Steep ladders magnify upgrade impact. A +1 from 4→5 can dwarf a +1 from 1→2. Map ladder slopes before choosing spot count and wild mode.

6.5 Bankroll Policy

• Unit size: Plan 200–300 rounds for the chosen variance. If side bet is required, treat total stake per round accordingly.
• Stop-loss: Pre-commit to a drawdown threshold. Wilds do not have memory.
• Locking: After a large promoted hit, skim profit and revert to base unit.

6.6 Practical Templates

• Low-variance DaVinci: 4-spot, always-on +1, no multipliers, 300 rounds.
• Balanced DaVinci: 6-spot, +1 common, +2 rare, 250 rounds.
• Aggressive DaVinci: 8–10 spots, +2 enabled, occasional multipliers, 200 rounds.

7) Simulation Results

Simulation captures upgrade logic, caps, and multipliers exactly. Run 500k–1M rounds per configuration. Record seeds, spot count, base table, wild model, caps, multipliers, and any side-bet cost.

7.1 Methodology

• Draw 20 numbers; compute base K and pay(K).
• Apply wild model:
  • Always-on +1: set K’=min(K+1,n) if K<n.
  • Probabilistic +1/+2: sample W∈{0,1,2} by p_w(k,n); set K’=min(K+W,n).
  • Multipliers: if wild applied, multiply by sampled M subject to caps.
• Payout = pay(K’) or M·pay(K’). Net = payout − (base stake + side bet if any).
• Aggregate RTP, standard error, variance, upgrade rates by k, payout histograms, drawdown quantiles, cumulative return percentiles.

7.2 Qualitative Expectations

• RTP: Increases relative to Classic if wilds are free; may still rise with costed wilds if upgrades are frequent.
• Variance: Decreases for low spots with +1; increases for high spots with +2 and multipliers.
• Drawdowns: Shallower in smoothing regimes; deeper but with sharper recoveries under aggressive regimes.

7.3 Example Output Tables (Placeholders)

8) Case Studies

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

Always-on +1 wild. Many 1→2 and 2→3 promotions slow losses and produce a steady cadence. Session high often comes from a promoted 3→4 hit.

8.2 Balanced DaVinci (6-Spot, 250 Rounds)

+1 common, +2 rare. Promotions 3→4 and 4→5 drive momentum. Bankroll alternates between flat segments and clear steps on promoted rounds.

8.3 Aggressive DaVinci (8–10 Spots, 200 Rounds)

Probabilistic +2 and optional multipliers. Many dead rounds. When promotions chain into steep tiers, session flips quickly. Risk controls required.

8.4 Operator Variations

Caps on promotion into the top tier moderate variance. Multipliers on promoted tiers increase tail risk. Verify details; small rule changes move EV and risk notably.

9) FAQ

9.1 Can I influence when wilds apply?

No. Wild triggers follow cabinet rules and RNG. Pick geometry and UI layout do not affect wild odds.

9.2 Do wilds stack?

Only if your cabinet permits multiple tokens or +2 promotions. Otherwise at most +1.

9.3 Are wilds worth a side bet?

Compute ΔEV for your table. If negative, enable only if you value the smoother session feel.

10) Summary & Takeaways

• DaVinci Keno adds wild-substitution that promotes near-misses into paying tiers.
• Model upgrades as always-on +1 or probabilistic +1/+2 with caps and optional multipliers.
• Mean and variance depend on ladder slopes, promotion frequency, and costs. Verify cabinet rules before planning.
• Use simulation for exact RTP and drawdown behavior.
• Pick spots to match time-on-device, balance, or tail hunting goals.