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.
Rules
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).
The total amount bet may not exceed $50.
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.
The game shall randomly choose the number of bingo balls previously specified by the player.
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
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.
