30-Ball Bingo

Introduction

30-Ball Bingo is a bingo-based game by Rival, which provides games for Internet casinos. It is a simple bingo game played on a 3 by 3 card and with 30 balls. The player plays against the game, not other players, and is paid on the highest paying pattern he covers on each card.

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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 (20, 22, or 24).
2. The total amount bet may not exceed \$50.
3. The game is played on 3 by 3 bingo cards, each with nine random numbers from 1 to 30.
4. The game shall randomly choose the number of bingo balls previously specified by the player.
5. The only win is for a coverall, which pays according to the number of balls in the draw, as follows:
• 20 balls pays 80.
• 22 balls pays 27.
• 24 balls pays 10.

Analysis

The following three tables show the probability and return for all possible events (winning and losing) for a 20-, 22-, and a 24-ball draw.

20 Ball Draw

Event Pays Combinations Probability Return
Coverall 80 352,716 0.011740 0.939167
Loser 0 29,692,299 0.988260 0.000000
Total   30,045,015 1.000000 0.939167

22 Ball Draw

Event Pays Combinations Probability Return
Coverall 27 203,490 0.034767 0.938715
Loser 0 5,649,435 0.965233 0.000000
Total   5,852,925 1.000000 0.938715

24 Ball Draw

Event Pays Combinations Probability Return
Coverall 10 54,264 0.091388 0.913882
Loser 0 539,511 0.908612 0.000000
Total   593,775 1.000000 0.913882

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 20-ball draw at 93.92%. So, if you must play, choose the 20-ball draw.

Ball Draw Return
20 93.92%
22 93.87%
24 91.39%