Last Updated: January 7, 2015

European Bingo

Introduction

European Bingo is a bingo-based game by Rival, which provides games for Internet casinos. It is played on 3 by 9 bingo cards with five numbers on each of the three rows. 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 bingo cards with three rows and nine columns. Each row has five numbers and four blank spots. All numbers are drawn from 1 to 90 without replacement.
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

Rows Covered 45 Ball Draw 55 Ball Draw 65 Ball Draw
3 10,000 1,000 50
2 275 20 4
1 5 2 1

Analysis

The following three tables show the probability and return for all possible events for a 45-, 55-, and a 65-ball draw. Please forgive the only 15 significant digits in the number of combinations. That is the maximum that Excel can handle.

45 Ball Draw

Event Pays Combinations Probability Return
3 10000 781,879,430,625,944,000,000 0.000008 0.075306
2 275 171,356,221,250,483,000,000,000 0.001650 0.453859
1 5 8,313,931,625,579,070,000,000,000 0.080075 0.400373
0 0 95,341,351,561,293,400,000,000,000 0.918268 0.000000
Total 103,827,421,287,554,000,000,000,000 1.000000 0.929537

55 Ball Draw

Event Pays Combinations Probability Return
3 1000 2,942,618,815,403,660,000,000 0.000260 0.259843
2 20 164,874,003,096,150,000,000,000 0.014559 0.291179
1 2 2,350,584,069,921,270,000,000,000 0.207565 0.415129
0 0 8,806,187,820,277,460,000,000,000 0.777617 0.000000
Total 11,324,588,512,110,300,000,000,000 1.000000 0.966151

65 Ball Draw

Event Pays Combinations Probability Return
3 50 52,588,547,141,148,900,000 0.004528 0.226413
2 4 932,475,551,941,065,000,000 0.080293 0.321172
1 1 4,525,207,169,948,350,000,000 0.389654 0.389654
0 0 6,103,141,366,229,710,000,000 0.525525 0.000000
Total 11,613,412,635,260,300,000,000 1.000000 0.937238

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 96.62%. So, if you must play, choose the 55-ball draw.

Ball Draw Return
45 92.95%
55 96.62%
65 93.72%

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