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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.

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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.

80 Ball Bingo Summary

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

 

Written by: Michael Shackleford