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Bonus Spot Keno
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Introduction
I first encountered Bonus Spot Keno, a unique version of Keno, at the Rampart casino in Las Vegas on January 15, 2016. This variant operates similarly to conventional keno , with the key difference being that players can earn a higher payout if their initial number selection matches one of the drawn balls.
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Rules
- Players select between 2 to 10 numbers from 1 to 80.
- The initial number selected will be identified as the 'Bonus Spot', though players have the option to swap one of their other selections for the Bonus Spot simply by tapping the screen.
- The game will randomly select 20 numbers from the total pool of 1 to 80.
- The player's earnings will partially depend on how many of the selected numbers correspond with the 20 drawn by the game.
- Should the Bonus Spot correspond with one of the drawn numbers, payouts will be made according to the Bonus Spot pay table. If not, players will receive payouts based on the Standard pay table, which offers equal or lower payouts for winning combinations.
Analysis
Displayed here are the payout tables from the 5-cent game at Rampart casino, showcasing both the Standard and Bonus payout structures.
Standard Pay Table
Catch | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
---|---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 15 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 47 | 3 | 2 | 2 | 0 | 0 | 0 | 0 | |
4 | 100 | 10 | 2 | 1 | 1 | 0 | 0 | ||
5 | 820 | 50 | 18 | 10 | 5 | 3 | |||
6 | 1,500 | 240 | 70 | 25 | 14 | ||||
7 | 7,500 | 1,000 | 250 | 90 | |||||
8 | 10,000 | 4,000 | 800 | ||||||
9 | 10,000 | 4,000 | |||||||
10 | 10,000 |
Bonus Pay Table
Catch | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
---|---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 15 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 47 | 7 | 3 | 3 | 1 | 0 | 0 | 0 | |
4 | 100 | 12 | 6 | 3 | 2 | 2 | 0 | ||
5 | 820 | 80 | 30 | 14 | 7 | 8 | |||
6 | 1,500 | 415 | 90 | 47 | 24 | ||||
7 | 7,500 | 1,900 | 350 | 152 | |||||
8 | 10,000 | 5,000 | 1,000 | ||||||
9 | 10,000 | 5,000 | |||||||
10 | 10,000 |
This table indicates the average weighted winnings for each possible selection of numbers, factoring in the probability of hitting the Bonus Spot.
Weighted Average Pay Table
Catch | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
---|---|---|---|---|---|---|---|---|---|
0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 15.00 | 1.67 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
3 | 47.00 | 6.00 | 2.60 | 2.50 | 0.43 | 0.00 | 0.00 | 0.00 | |
4 | 100.00 | 11.60 | 4.67 | 2.14 | 1.50 | 0.89 | 0.00 | ||
5 | 820.00 | 75.00 | 26.57 | 12.50 | 6.11 | 5.50 | |||
6 | 1500.00 | 390.00 | 85.00 | 39.67 | 20.00 | ||||
7 | 7500.00 | 1787.50 | 327.78 | 133.40 | |||||
8 | 10000.00 | 4888.89 | 960.00 | ||||||
9 | 10000.00 | 4900.00 | |||||||
10 | 10000.00 |
Another table reveals the likelihood of achieving various combinations of selected numbers and matched ones.
Probability
Catch | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
---|---|---|---|---|---|---|---|---|---|
0 | 0.560127 | 0.416504 | 0.308321 | 0.227184 | 0.166602 | 0.121574 | 0.08826624 | 0.06374784 | 0.04579070 |
1 | 0.379747 | 0.430867 | 0.432732 | 0.405686 | 0.363495 | 0.315193 | 0.26646411 | 0.22066559 | 0.17957138 |
2 | 0.060127 | 0.138754 | 0.212635 | 0.270457 | 0.308321 | 0.326654 | 0.32814562 | 0.31642614 | 0.29525678 |
3 | 0.013875 | 0.043248 | 0.083935 | 0.129820 | 0.174993 | 0.21478623 | 0.24610922 | 0.26740237 | |
4 | 0.003063 | 0.012092 | 0.028538 | 0.052191 | 0.08150370 | 0.11410518 | 0.14731890 | ||
5 | 0.000645 | 0.003096 | 0.008639 | 0.01830259 | 0.03260148 | 0.05142769 | |||
6 | 0.000129 | 0.000732 | 0.00236671 | 0.00571956 | 0.01147939 | ||||
7 | 0.000024 | 0.00016046 | 0.00059168 | 0.00161114 | |||||
8 | 0.00000435 | 0.00003259 | 0.00013542 | ||||||
9 | 0.00000072 | 0.00000612 | |||||||
10 | 0.00000011 | ||||||||
Total | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.00000000 | 1.00000000 | 1.00000000 |
The concluding table illustrates how each combination of selected and matched numbers contributes to the overall return, calculated as the product of both the probability and the average winnings. The final row summarizes the total return.
Return
Catch | Pick 2 | Pick 3 | Pick 4 | Pick 5 | Pick 6 | Pick 7 | Pick 8 | Pick 9 | Pick 10 |
---|---|---|---|---|---|---|---|---|---|
0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
1 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
2 | 0.901899 | 0.231256 | 0.318953 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
3 | 0.652142 | 0.259487 | 0.218231 | 0.324549 | 0.074997 | 0.000000 | 0.000000 | 0.000000 | |
4 | 0.306339 | 0.140271 | 0.133177 | 0.111838 | 0.122256 | 0.101427 | 0.000000 | ||
5 | 0.528838 | 0.232173 | 0.229537 | 0.228782 | 0.199231 | 0.282852 | |||
6 | 0.193477 | 0.285510 | 0.201171 | 0.226876 | 0.229588 | ||||
7 | 0.183019 | 0.286814 | 0.193939 | 0.214926 | |||||
8 | 0.043457 | 0.159341 | 0.130003 | ||||||
9 | 0.007243 | 0.029991 | |||||||
10 | 0.001122 | ||||||||
Total | 0.901899 | 0.883398 | 0.884780 | 0.887341 | 0.883376 | 0.884901 | 0.882479 | 0.888057 | 0.888483 |
According to the Rampart 5-cent payout tables, the pick-2 variation offers the most favorable odds at 90.19%.