Keno Strategies: What the Mathematics Supports

Odds?

No number-selection system changes the probabilities fixed by the pool, draw count and picks.

Probability · P(K=5 | N=70,D=20,s=5)?

70/20 · s=5 · k=5 · P(K=5)=0.12810032% · ≈ 1:780.64

P(K=5 | s=5) · 56/16 ↔ 70/20 ↔ 80/20?

56/16 · s=5 · k=5 · P(K=5)=0.11435106% · ≈ 1:874.5 · 70/20 · s=5 · k=5 · P(K=5)=0.12810032% · ≈ 1:780.64 · 80/20 · s=5 · k=5 · P(K=5)=0.06449247% · ≈ 1:1550.57

Odds

Editorial inference No number-selection system changes the probabilities fixed by the pool, draw count and picks.

NIST · H(N,D,s,k)

Editorial inference Exact-match probabilities follow the hypergeometric model. [1]

S₁ ↔ S₂ · |S|=s

Editorial inference When N, D and s stay fixed, replacing one selected set with another set of the same size does not change the exact-match probabilities.

Editorial inference Number Pool=N · Numbers Drawn=D · Picks Allowed=s · Matches=k

Editorial inference |S₁|=|S₂|=s ⇒ P(K=k | S₁,N,D) = P(K=k | S₂,N,D)

Probability Distribution · 70/20 · s=5

Editorial inference 70/20 · s=5 · k=0 · P(K=0)=17.50605262% · ≈ 1:5.71

Editorial inference 70/20 · s=5 · k=1 · P(K=1)=38.05663614% · ≈ 1:2.63

Editorial inference 70/20 · s=5 · k=2 · P(K=2)=30.76919518% · ≈ 1:3.25

Editorial inference 70/20 · s=5 · k=3 · P(K=3)=11.53844819% · ≈ 1:8.67

Editorial inference 70/20 · s=5 · k=4 · P(K=4)=2.00156754% · ≈ 1:49.96

Editorial inference 70/20 · s=5 · k=5 · P(K=5)=0.12810032% · ≈ 1:780.64

P(K=5 | s=5) · 56/16 ↔ 70/20 ↔ 80/20

Editorial inference 56/16 · s=5 · k=5 · P(K=5)=0.11435106% · ≈ 1:874.5 · 70/20 · s=5 · k=5 · P(K=5)=0.12810032% · ≈ 1:780.64 · 80/20 · s=5 · k=5 · P(K=5)=0.06449247% · ≈ 1:1550.57

Editorial inference Compare configurations only while holding s and the target k fixed; the figures compare probabilities, not prizes or financial return.

Important Notice

Editorial inference Never gamble with money you cannot afford to lose; stop and seek help if playing becomes hard to control.

Probability ≠ Top prize

Editorial inference Probability alone does not state a payout; assessing financial value also requires the stake and the official paytable.

Editorial inference Probability=P(K=k) · Top prize=v(s)

Editorial inference P(K=k) ∈ [0,1] · V = Σ v(k) × P(K=k) · v(k)=∅ ⇒ V=∅

Keno Directory · Blog · Tools

• How Keno WorksStart with the game configuration, choose an allowed set of numbers, wait for the draw, count the matches, and then read the probability for that match count. Exact-match probabilities follow the hypergeometric model.
• History of KenoAcademic research documents gambling and lottery practices in late-Qing China; it does not verify the Keno origin legend. The Nevada Historical Society documents Chinese lottery activity in Reno and the use of the name Race Horse Keno in the 1930s and 1940s.
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