# American Bingo by Rival Software

## Introduction

American Bingo is a bingo-based game by Rival, which provides games for Internet casinos. It is played on a 5 by 5 card with a free square. 75 balls are used. The player plays against the game, not other players, and is paid on the highest paying pattern he covers on each card.

## Top 4 Rival casinos

Wizard Of Odds - Approved

## 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 5 by 5 bingo cards. The center square is the "free square" and is pre-marked. The other spots are covered with 24 random numbers from 1 to 75.
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 4,000 25
Frame 5,000 1,500 4
Double Hard Way 20 2 1
X 20 2 1
Single Hard Way 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 47,626,016,970 0.000000 0.000000
Frame 5000 1,397,233,875,918,200 0.000000 0.002374
Double Hard Way 20 57,283,562,595,048,800,000 0.019467 0.389337
X 20 3,743,691,587,820,400,000 0.001272 0.025445
Single Hard Way 2 559,569,139,584,055,000,000 0.190160 0.380321
Single Diagonal 2 179,582,166,099,521,000,000 0.061028 0.122056
Four corners 1 53,705,011,835,501,400,000 0.018251 0.018251
Loser 0 2,088,733,846,420,210,000,000 0.709821 0.000000
Total   2,942,618,815,403,660,000,000 1.000000 0.937783

### 45 Ball Draw

Event Pays Combinations Probability Return
Coverall 4000 430,759,913,983,245 0.000000 0.000586
Frame 1500 222,114,794,603,291,000 0.000075 0.113223
Double Hard Way 2 467,159,125,105,607,000,000 0.158756 0.317512
X 2 23,492,215,956,294,200,000 0.007983 0.015967
Single Hard Way 1 1,150,516,991,243,150,000,000 0.390984 0.390984
Single Diagonal 1 242,124,192,220,706,000,000 0.082282 0.082282
Four corners 1 48,603,269,059,272,700,000 0.016517 0.016517
Loser 0 1,010,500,476,264,110,000,000 0.343402 0.000000
Total   2,942,618,815,403,660,000,000 1.000000 0.937071

### 55 Ball Draw

Event Pays Combinations Probability Return
Coverall 25 77,535,155,627,160 0.000097 0.002413
Frame 4 2,717,027,848,243,170 0.003383 0.013532
Double Hard Way 1 460,543,806,230,750,000 0.573409 0.573409
X 1 12,224,490,989,088,800 0.015220 0.015220
Single Hard Way 1 245,050,644,309,805,000 0.305105 0.305105
Single Diagonal 1 28,111,973,699,498,400 0.035001 0.035001
Four corners 1 3,225,302,070,430,430 0.004016 0.004016
Loser 0 51,217,218,190,630,500 0.063769 0.000000
Total   803,167,998,494,073,000 1.000000 0.948697

## 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 55-ball draw at 94.87%. So, if you must play, choose the 55-ball draw.

Ball Draw Return
35 93.78%
45 93.71%
55 94.87%