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Last Updated: Jan. 8, 2015

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.

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.

American Bingo Summary

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