# Penny Keno

## Introduction

Penny Keno is a format of playing multi-card keno I saw at the Swinomish casino in Anacortes, Washington, in July, 2023. It is basically regular keno, except the player buys 110 to 220 cards \$0.01 games at once. The game conveniently gives the player 12 patterns to choose from in the way his cards are arranged.

## Rules

1. All individual bets are \$0.01.
2. The player will pick one of the following patterns: K,E,N,O,C,A,S,H,F,D,I,coverall.
3. Depending on the pattern, much the card will be daubed in about 20 different groups, identified by various letters (not to be confused with the design of the card, which is usually also a letter).
4. These groups will be combined together or sometimes stand alone as a single card for form a multitude of cards. The types and number of each type of card are shown below.
5. As usual, the game will draw 20 numbers without replacement from a range of 1 to 80. If a number chosen on one of the player's cards match the random draw of the game, that will count at a "catch."
6. The player will be paid according to the number of picks and catches on each card and the pay table below.

The following is the pay table for Penny Keno. Note there is no column for picking 7 or 9 because the game never arranges groups of picks of those sizes.

### Penny Keno Pay Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 8 Pick 10
0 0 0 0 0 0 0
1 0 0 0 0 0 0
2 0 0 0 0 0 0
3 0.5 0 0 0 0 0
4   2.25 0 0 0 0
5     11.5 1 0 0
6       33 1 0
7         15 1
8         550 10
9           500
10           10000
Return 69.38% 68.93% 74.17% 73.52% 71.64% 71.48%

The following table shows how many of each group size is pre-daubed on each pattern.

### Penny Keno Number of each Group Size

Pattern Group
of 1
Group
of 2
Group
of 3
Group
of 4
Group
of 5
Group
of 6
Group
of 8
K 0 13 8 0 0 0 0
E 0 10 0 10 0 0 0
N 0 13 8 0 0 0 0
O 0 6 0 4 0 2 3
C 0 11 10 0 0 0 0
A 0 11 0 16 0 0 0
S 0 0 21 0 0 0 0
H 1 5 15 0 0 0 0
F 0 12 8 0 0 0 0
D 4 11 8 0 0 0 0
I 0 0 16 0 0 0 0

## K Pattern

The K pattern consists of the following groups:

• 13 groups of 2
• 8 groups of 3

There are 21 different groups and 50 numbers daubed. Here are the various cards the player is buying:

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

This results in 182 cards purchased. The overall return is (8*69.38% + 78*68.93% + 104*74.17%)/182 = 71.92%.

## E Pattern

The E pattern consists of the following groups:

• 10 groups of 2
• 10 groups of 4

There are 20 different groups and 60 numbers daubed. Here are the various cards the player is buying:

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

This results in 220 cards purchased. Since all cards are pick-6, the return is that of the pick-6, which is 73.52%.

## N Pattern

The N pattern consists of the following groups:

• 12 groups of 2
• 12 groups of 3

There are 24 different groups and 60 numbers daubed. Here are the various cards the player is buying:

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

This results in 210 cards purchased. The overall return is (66*68.93% + 144*74.17%)/210 = 72.52%.

## O Pattern

The O pattern consists of the following groups:

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

There are 15 different groups and 64 numbers daubed. Here are the various cards the player is buying:

• 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 results in 115 cards purchased. The overall return is (19*68.93% + 96*71.64%)/115 = 71.19%.

## C Pattern

The C pattern consists of the following groups:

• 11 groups of 2
• 10 groups of 3

There are 21 different groups and 52 numbers daubed. Here are the various cards the player is buying:

• 110 pick-5 cards — 11*10=110

This results in 110 cards purchased. The pick-5 return is 74.17%.

## A Pattern

The A pattern consists of the following groups:

• 11 groups of 2
• 5 groups of 4

There are 16 different groups and 42 numbers daubed. Here are the various cards the player is buying:

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

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

## S Pattern

The S pattern consists of the following groups:

• 21 groups of 3

There are 21 different groups and 63 numbers daubed. Here are the various cards the player is buying:

• 210 pick-6 cards — combin(21,2)=210

This results in 210 cards purchased. The pick-6 return is 73.52%.

## H Pattern

The H pattern consists of the following groups:

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

There are 16 different groups and 46 numbers daubed. Here are the various cards the player is buying:

• 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 the following groups:

• 12 groups of 2
• 8 groups of 3

There are 20 different groups and 48 numbers daubed. Here are the various cards the player is buying:

• 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 consists of the following groups:

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

There are 23 different groups and 50 numbers daubed. Here are the various cards the player is buying:

• 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

There are 16 different groups and 48 numbers daubed. Here are the various cards the player is buying:

• 120 pick-6 cards — combin(16,2)=120

The pick-6 return is 73.52%.

## Coverall Pattern

The Coverall pattern consists of the following groups:

• 16 groups of 5

There are 16 different groups and 80 numbers daubed. Here are the various cards the player is buying:

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

The pick-10 return is 71.48%.

## Summary

The following table summarizes the return of each pattern. As you can see, the highest return is on the C pattern at 74.17%.

### Penny Keno Return Summary

Pattern Bet Return
K \$1.90 71.92%
E \$2.20 73.52%
N \$2.10 72.52%
O \$1.15 71.19%
C \$1.10 74.17%
A \$2.20 73.52%
S \$2.10 73.52%
H \$1.10 72.98%
F \$1.70 71.91%
D \$2.10 69.05%
I \$1.20 73.52%
Coverall \$1.20 71.48%