Last Updated: August 9, 2019

# 80-Ball Bingo

## Introduction

80-Ball Bingo is a bingo-based game by Rival, which provides games for Internet casinos. It is a simple bingo game played on a 4 by 4 card and with 80 balls. The player plays against the game, not other players, and is paid on the highest paying pattern he covers on each card.

## Rules

1. The player begins by choosing how many cards to play (1 to 100), the bet per card (10¢ - \$1), and the number of balls in the draw (35, 45, or 55).
2. The total amount bet may not exceed \$50.
3. The game is played on 4 by 4 bingo cards, each with 16 random numbers from 1 to 80.
4. The game shall randomly choose the number of bingo balls previously specified by the player.
5. The following table shows the pay table according to the number of balls drawn.

### Pay Table

Event 35 Ball Draw 45 Ball Draw 55 Ball Draw
Coverall 10,000 1,200 55
Frame 1,000 400 5
X 15 2 1
Two lines 15 2 1
One line 2 1 1
Single Diagonal 2 1 1
Four corners 1 1 1
6. The win for one and two lines are for horizontal and vertical lines only. What would be called a "hard way" in a Vegas bingo room. To win for two lines, one line must be vertical and one must be horizontal. This rule is not stated in the game rules. As evidence, I present the following screenshot of a card with two horizontal lines covered, but a win for only one row is highlighted.

## Analysis

The following three tables show the probability and return for all possible events for a 35-, 45-, and a 55-ball draw. Please forgive the only 15 significant digits in the number of combinations. That is the maximum that Excel can handle.

### 35 Ball Draw

Event Pays Combinations Probability Return
Coverall 10000 8,719,878,125,622,740 0.000000 0.001506
Frame 1000 793,238,105,763,171,000 0.000014 0.013700
X 15 47,002,468,397,940,000,000 0.000812 0.012177
Two lines 15 1,670,087,230,521,540,000,000 0.028844 0.432660
One line 2 11,392,710,937,450,700,000,000 0.196763 0.393526
Single Diagonal 2 2,339,744,359,480,040,000,000 0.040410 0.080819
Four corners 1 608,483,251,135,119,000,000 0.010509 0.010509
Loser 0 41,841,789,642,484,500,000,000 0.722648 0.000000
Total   57,900,619,847,453,700,000,000 1.000000 0.944898

### 45 Ball Draw

Event Pays Combinations Probability Return
Coverall 1200 1,388,818,294,740,300,000 0.000024 0.028783
Frame 400 26,251,279,138,350,600,000 0.000453 0.181354
X 2 429,163,923,596,237,000,000 0.007412 0.014824
Two lines 2 8,729,048,304,509,150,000,000 0.150759 0.301518
One line 1 20,563,711,677,724,600,000,000 0.355155 0.355155
Single Diagonal 1 3,403,618,112,099,550,000,000 0.058784 0.058784
Four corners 1 586,839,257,951,780,000,000 0.010135 0.010135
Loser 0 24,160,598,474,139,200,000,000 0.417277 0.000000
Total   57,900,619,847,453,700,000,000 1.000000 0.950554

### 55 Ball Draw

Event Pays Combinations Probability Return
Coverall 55 401,038,568,751,466,000 0.001104 0.060694
Frame 5 2,245,422,778,081,550,000 0.006179 0.030893
X 1 14,863,463,822,459,500,000 0.040900 0.040900
Two lines 1 154,110,480,268,896,000,000 0.424063 0.424063
One line 1 123,942,806,088,621,000,000 0.341052 0.341052
Single Diagonal 1 14,863,979,567,634,600,000 0.040901 0.040901
Four corners 1 1,466,305,593,798,800,000 0.004035 0.004035
Loser 0 51,520,234,433,261,200,000 0.141767 0.000000
Total   363,413,731,121,504,000,000 1.000000 0.942538

## Strategy

The following table shows the return according to the number of balls in the draw. As you can see, the greatest return is for a 45-ball draw at 95.06%. So, if you must play, choose the 45-ball draw.

Ball Draw Return
35 94.49%
45 95.06%
55 94.25%

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