Penny Keno

Introduction

Penny Keno is a variation of multi-card keno that I experienced at the Swinomish casino located in Anacortes, Washington, in July 2023. In this version, players can buy between 110 and 220 cards for just $0.01 each. Additionally, the game provides players with 12 different patterns to select how their cards are arranged.

Rules

1. All individual bets are $0.01.
2. Players can choose from the following patterns: K, E, N, O, C, A, S, H, F, D, I, and coverall.
3. Based on the selected pattern, varying numbers on the card will be marked across approximately 20 different groups, each represented by distinct letters (this should not be mixed up with the card design, which typically features a letter as well).
4. These groups can either be combined or exist separately as individual cards, contributing to a diverse range of card possibilities. The types of cards and how many of each are detailed below.
5. As is customary, the game draws 20 unique numbers from a pool of 1 to 80 without repetition. When a number from one of the player's cards matches a number drawn in the game, that counts as a 'catch.'
6. Winnings are based on how many catches and selections are made on each card in accordance with the pay table provided further down.

Below is the pay table specific to Penny Keno. Note that there is no entry for selecting 7 or 9 numbers because the game does not feature those sized groups.

The table that follows illustrates how many cards are automatically marked for each pattern size.

Click here for larger version of image.

K Pattern

The K pattern comprises the following groups:

• 13 groups of 2
• 8 groups of 3

In this game, there are 21 distinct groups with a total of 50 numbers marked. Here are the various cards that can be purchased by players:

• 8 pick-3 cards — combin(8,1)=8
• 78 pick-4 cards — combin(13,2)=78
• 104 pick-5 cards — 13*8=104

The total comes to 182 cards bought. The expected return is calculated as (8*69.38% + 78*68.93% + 104*74.17%)/182 = 71.92%.

E Pattern

The E pattern consists of these groups:

• 10 groups of 2
• 10 groups of 4

This setup includes 20 distinct groups with 60 numbers marked. Here are the cards available for the player to buy:

• 220 pick-6 cards — combin(6,3)+10*10 = 120+100 = 220

This results in a purchase of 220 cards. Given that all cards consist of pick-6 combinations, the return reflects that of the pick-6 game, which stands at 73.52%.

N Pattern

The N pattern comprises the following groups:

• 12 groups of 2
• 12 groups of 3

Within this pattern, there are 24 different groups and 60 numbers marked. Here are the various cards available for purchase:

• 66 pick-4 cards — combin(12,2)=66
• 144 pick-5 cards — 12*12=144

This totals to 210 cards acquired. The overall expected return is (66*68.93% + 144*74.17%)/210 = 72.52%.

O Pattern

The O pattern includes the following groups:

• 6 groups of 2
• 4 groups of 4
• 2 groups of 6
• 3 groups of 8

In this case, there are 15 different groups and 64 numbers marked. Here are the cards one can buy:

• 19 pick-4 cards — 4+combin(6,2)=19
• 96 pick-8 cards — combin(6,4)+combin(6,2)*4+6*2+3=15+15*4+6*2+6+3=15+60+12+6+3=96

This leads to 115 total cards purchased. The overall return is calculated as (19*68.93% + 96*71.64%)/115 = 71.19%.

C Pattern

The C pattern consists of these groups:

• 11 groups of 2
• 10 groups of 3

This pattern includes 21 unique groups and 52 marked numbers. Here are the available cards for players to purchase:

• 110 pick-5 cards — 11*10=110

This results in a total of 110 cards bought, with a pick-5 return of 74.17%.

A Pattern

The A pattern encompasses the following groups:

• 11 groups of 2
• 5 groups of 4

It features 16 different groups with 42 numbers marked. Here are the cards that players can buy:

• 220 pick-6 cards — combin(11,3)+11*5 = 165 + 55 = 220

This results in 115 cards purchased. The pick-6 return for these cards is 73.52%.

S Pattern

The S pattern consists of these groups:

• 21 groups of 3

There are 21 unique groups and 63 numbers marked in this pattern. Here are the various cards available for purchase:

• 210 pick-6 cards — combin(21,2)=210

This leads to 210 cards bought, with a pick-6 return of 73.52%.

H Pattern

The H pattern comprises the following groups:

• 1 groups of 1
• 5 groups of 2
• 15 groups of 3

In total, there are 16 different groups with 46 numbers marked. Here are the cards available:

• 25 pick-4 cards — combin(5,2)+1*15 = 10+15=25
• 85 pick-5 cards — 5*15 + 1*combin(5,2) = 75+10 = 85

The overall return is (25*68.93% + 85*74.17%)/110 = 72.98%.

F Pattern

The F pattern consists of these groups:

• 12 groups of 2
• 8 groups of 3

There are 20 unique groups, and 48 numbers are marked. Here are the various cards offered for purchase:

• 8 pick-3 cards
• 66 pick-4 cards — combin(12,2) = 66
• 96 pick-5 cards — 12*8=96

The overall return is (8*69.38% + 66*68.93% + 96*74.17%)/170 = 71.91%.

D Pattern

The D pattern includes the following groups:

• 4 groups of 1
• 11 groups of 2
• 8 groups of 3

It features 23 different groups with 50 numbers marked. Here are the cards available for players to buy:

• 56 pick-3 cards — 8+4*11+combin(4,3)=8+44+4=56
• 154 pick-4 cards — combin(11,2)+4*8+11*combin(4,2)+combin(4,4) = 55+32+66+1 = 154

The overall return is (56*69.38% + 154*68.93%)/210 + 69.05%.

I Pattern

The I pattern consists of the following groups:

• 16 groups of 3

This pattern contains 16 groups with 48 marked numbers. Here are the cards available for purchase:

• 120 pick-6 cards — combin(16,2)=120

The pick-6 return is 73.52%.

Coverall Pattern

The Coverall pattern comprises these groups:

• 16 groups of 5

In this case, there are 16 groups and a total of 80 numbers marked. Here are the cards players can buy:

• 120 pick-10 cards — combin(16,2)=120

The pick-10 return is 71.48%.

Summary

The following table provides a summary of the overall return for each pattern. Notably, the C pattern offers the highest return at 74.17%.

Written by: Michael Shackleford