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
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 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.
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
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.
