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Last Updated: August 9, 2019

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Rival Powered Bingo

Introduction

This game presented a problem in how to title it. The game itself is titled just bingo. However, I already write about live bingo and didn't want to confuse my readers between that and this game created by Rival Powered. For lack of a better idea, I shall call this game Rival Powered Bingo.

Rival Powered bingo is not played against other players but only against the ball draw of the game, much like in keno. The player may choose a 30, 75, 80, or 90 number game. Within each game, there are three choices for the number of balls. The fewer the balls, the greater the wins.

In all games only the highest win per card is paid. For purposes of this game a "line" is vertical or diagonal. Diagonal lines are treated separately. Also, contrary to what the rules may imply, a double bingo must consist of one vertical and one horizontal line.

The player may play 1 to 100 cards and may bet 1¢, 5¢, 10¢, 25¢, 50¢, or $1 per card. However, the total amount bet may not exceed $20.

30 Numbers



The 30-number game is played on a 3 by 3 card. The only win is for a coverall. The player may choose to have 20, 22, or 24 numbers drawn. The fewer the balls, the more the player stands to win.

The following three tables shows the probability and return of all possible wins for 20, 22, and 24 balls respectively. The greatest return is for 20 balls at 93.92%.

30 Number Bingo — 20 Balls

Event Pays Probability Return
Coverall 80 0.011740 0.939167
Loser 0 0.988260 0.000000
Total 1.000000 0.939167


30 Number Bingo — 22 Balls

Event Pays Probability Return
Coverall 27 0.034767 0.938715
Loser 0 0.965233 0.000000
Total 1.000000 0.938715


30 Number Bingo — 24 Balls

Event Pays Probability Return
Coverall 10 0.091388 0.913882
Loser 0 0.908612 0.000000
Total 1.000000 0.913882


75 Numbers



The 75-number game is played on a 5 by 5 card with a free square in the middle. There are seven different ways to win. On each card, only the highest win is paid. The player may choose to have 35, 45, or 55 numbers drawn. The fewer the balls, the more the player stands to win.

The online rules don't make this clear, but a double bingo must be one horizontal and one vertical bingo.

The following three tables shows the probability and return of all possible wins for 35, 45, and 55 balls respectively. The greatest return is for 55 balls at 94.87%.

75 Number Bingo — 35 Balls

Event Pays Probability Return
Coverall 10000 0.000000 0.000000
Frame 5000 0.000000 0.002374
Double bingo 20 0.019344 0.386881
X 20 0.001395 0.027901
Single line 2 0.190160 0.380321
Diagonal line 2 0.061028 0.122056
Four corners 1 0.018251 0.018251
Loser 0 0.709821 0.000000
Total 1.000000 0.937783


75 Number Bingo — 45 Balls

Event Pays Probability Return
Coverall 4000 0.000000 0.000586
Frame 1500 0.000075 0.113223
X 2 0.153967 0.307934
Double bingo 2 0.012773 0.025545
Single line 1 0.390984 0.390984
Diagonal line 1 0.082282 0.082282
Four corners 1 0.016517 0.016517
Loser 0 0.343402 0.000000
Total 1.000000 0.937071


75 Number Bingo — 55 Balls

Event Pays Probability Return
Coverall 25 0.000097 0.002413
Frame 4 0.003383 0.013532
X 1 0.517089 0.517089
Double bingo 1 0.071540 0.071540
Single line 1 0.305105 0.305105
Diagonal line 1 0.035001 0.035001
Four corners 1 0.004016 0.004016
Loser 0 0.063769 0.000000
Total 1.000000 0.948697


80 Numbers



The 80-number game is played on a 4 by 4 card with no free square. There are seven different ways to win. On each card, only the highest win is paid. The player may choose to have 35, 45, or 55 numbers drawn. The fewer the balls, the more the player stands to win.

The online rules don't make this clear, but a double bingo must be one horizontal and one vertical bingo.

The following three tables shows the probability and return of all possible wins for 35, 45, and 55 balls respectively. The greatest return is for 45 balls at 95.06%.

80 Number Bingo — 35 Balls

Event Pays Probability Return
Coverall 10000 0.000000 0.001506
Frame 1000 0.000014 0.013700
X 15 0.000812 0.012177
Double bingo 15 0.028844 0.432660
Single line 2 0.196763 0.393526
Diagonal line 2 0.040410 0.080819
Four corners 1 0.010509 0.010509
Loser 0 0.722648 0.000000
Total 1.000000 0.944898


80 Number Bingo — 45 Balls

Event Pays Probability Return
Coverall 1200 0.000024 0.028783
Frame 400 0.000453 0.181354
X 2 0.007412 0.014824
Double bingo 2 0.150759 0.301518
Single line 1 0.355155 0.355155
Diagonal line 1 0.058784 0.058784
Four corners 1 0.010135 0.010135
Loser 0 0.417277 0.000000
Total 1.000000 0.950554


80 Number Bingo — 55 Balls

Event Pays Probability Return
Coverall 55 0.001104 0.060694
Frame 5 0.006179 0.030893
X 1 0.040900 0.040900
Double bingo 1 0.424063 0.424063
Single line 1 0.341052 0.341052
Diagonal line 1 0.040901 0.040901
Four corners 1 0.004035 0.004035
Loser 0 0.141767 0.000000
Total 1.000000 0.942538


90 Numbers



The 90-number game is played on card with nine columns and three rows. Each row is populated with five numbers . There are three different ways to win, for covering 1, 2, or 3 rows. On each card, only the highest win is paid. The player may choose to have 45, 55, or 65 numbers drawn. The fewer the balls, the more the player stands to win.

The following three tables shows the probability and return of all possible wins for 45, 55, and 65 balls respectively. The greatest return is for 55 balls at 96.62%.

90 Number Bingo — 45 Balls

Event Pays Probability Return
Three lines 10000 0.000008 0.075306
Two lines 275 0.001650 0.453859
One line 5 0.080075 0.400373
Loser 0 0.918268 0.000000
Total 1.000000 0.929537


90 Number Bingo — 55 Balls

Event Pays Probability Return
Three lines 1000 0.000260 0.259843
Two lines 20 0.014559 0.291179
One line 2 0.207565 0.415129
Loser 0 0.777617 0.000000
Total 1.000000 0.966151


90 Number Bingo — 65 Balls

Event Pays Probability Return
Three lines 50 0.004528 0.226413
Two lines 4 0.080293 0.321172
One line 1 0.389654 0.389654
Loser 0 0.525525 0.000000
Total 1.000000 0.937238


Summary

The following table shows the return of all 12 games in order of balls first and picks second.

Summary

Balls Picks Return
30 20 93.92%
30 22 93.87%
30 24 91.39%
75 35 93.78%
75 45 93.71%
75 55 94.87%
80 35 94.49%
80 45 95.06%
80 55 94.25%
90 45 92.95%
90 55 96.62%
90 65 93.72%


The final table shows the same information in order of return, from highest to lowest.

Summary

Balls Picks Return
90 55 96.62%
80 45 95.06%
75 55 94.87%
80 35 94.49%
80 55 94.25%
30 20 93.92%
30 22 93.87%
75 35 93.78%
90 65 93.72%
75 45 93.71%
90 45 92.95%
30 24 91.39%



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