Bonus Keno

Introduction

Bonus Keno is the same thing as conventional four-card keno, except the wins are higher. To pay for the higher wins, the player must bet 25% more and the additional wager is a fee to pump up the pay table.

Rules

1. The player picks 3 to 10 spots on each of four cards.
2. The player bets 5 to 40 credits. For each five credits bet, one will go to each of the four cards and the fifth credit simply vanishes.
3. The five pay tables available are shown below, as provided by VideoPoker.com.

Analysis

The following table shows the probability of all combinations of picks and catches.

Probability Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266 0.063748 0.045791
1 0.430867 0.432732 0.405686 0.363495 0.315193 0.266464 0.220666 0.179571
2 0.138754 0.212635 0.270457 0.308321 0.326654 0.328146 0.316426 0.295257
3 0.013875 0.043248 0.083935 0.129820 0.174993 0.214786 0.246109 0.267402
4   0.003063 0.012092 0.028538 0.052191 0.081504 0.114105 0.147319
5     0.000645 0.003096 0.008639 0.018303 0.032601 0.051428
6       0.000129 0.000732 0.002367 0.005720 0.011479
7         0.000024 0.000160 0.000592 0.001611
8           0.000004 0.000033 0.000135
9             0.000001 0.000006
10               0.000000
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The following table shows the contribution to the return for of all combinations of picks and catches for pay table 95 below. The bottom line shows a maximum return of 95.54% for a pick 4. This is the product of the pay table, probability, and 4/5. The reason for deducting 20% is the wins are based on 80% of the bet only.

Return Table

Catch 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
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.333009 0.340217 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.621616 0.207590 0.268592 0.415423 0.139995 0.000000 0.000000 0.000000
4   0.399466 0.145108 0.114152 0.125258 0.195609 0.091284 0.000000
5     0.541737 0.205550 0.221146 0.204989 0.182568 0.246853
6       0.206376 0.304544 0.265072 0.247085 0.247955
7         0.156176 0.243892 0.284006 0.257783
8           0.034765 0.130370 0.162503
9             0.005794 0.029379
10               0.000898
Total 0.954625 0.947273 0.955437 0.941501 0.947119 0.944327 0.941107 0.945371

Pay Tables

The following table is what I call Pay Table 95. The bottom row shows the return for all number of picks. The greatest is 95.54% for the pick 5.

Pay Table 95

Catch 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
1 0 0 0 0 0 0 0 0
2 3 2 0 0 0 0 0 0
3 56 6 4 4 1 0 0 0
4   163 15 5 3 3 1 0
5     1,050 83 32 14 7 6
6       2,000 520 140 54 27
7         8,000 1,900 600 200
8           10,000 5,000 1,500
9             10,000 6,000
10               10,000
Return 95.46% 94.73% 95.54% 94.15% 94.71% 94.43% 94.11% 94.54%

The following table is what I call Pay Table 93. The bottom row shows the return for all number of picks. The greatest is 93.62% for the pick 10

Pay Table 93

Catch 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
1 0 0 0 0 0 0 0 0
2 3 2 0 0 0 0 0 0
3 54 6 4 4 1 0 0 0
4   155 15 5 3 3 1 0
5     1,000 80 30 14 7 6
6       2,000 515 140 52 26
7         8,000 1,800 600 200
8           10,000 5,000 1,500
9             10,000 6,000
10               10,000
Return 93.24% 92.77% 92.96% 93.41% 93.04% 93.15% 93.20% 93.62%

The following table is what I call Pay Table 91. The bottom row shows the return for all number of picks. The greatest is 91.78% for the pick 10

Pay Table 91

Catch 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
1 0 0 0 0 0 0 0 0
2 3 2 0 0 0 0 0 0
3 52 6 4 4 1 0 0 0
4   150 15 5 3 3 1 0
5     975 72 28 14 7 6
6       2,000 510 140 48 24
7         8,000 1,675 600 200
8           10,000 5,000 1,500
9             10,000 6,000
10               10,000
Return 91.02% 91.54% 91.67% 91.43% 91.36% 91.54% 91.37% 91.78%

The following table is what I call Pay Table 90. The bottom row shows the return for all number of picks. The greatest is 91.02% for the pick 3

Pay Table 90

Catch 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
1 0 0 0 0 0 0 0 0
2 3 2 0 0 0 0 0 0
3 52 6 4 4 1 0 0 0
4   145 15 5 3 3 1 0
5     960 70 27 14 7 6
6       2,000 510 140 47 23
7         8,000 1,600 600 200
8           10,000 5,000 1,500
9             10,000 6,000
10               10,000
Return 91.02% 90.32% 90.90% 90.93% 90.67% 90.58% 90.91% 90.86%

The following table is what I call Pay Table 88. The bottom row shows the return for all number of picks. The greatest is 88.84% for the pick 5

Pay Table 88

Catch 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
1 0 0 0 0 0 0 0 0
2 3 2 0 0 0 0 0 0
3 50 6 4 4 1 0 0 0
4   136 15 5 3 3 1 0
5     920 60 25 14 7 6
6       2,000 500 140 42 20
7         8,000 1,450 600 200
8           10,000 5,000 1,500
9             10,000 6,000
10               10,000
Return 88.80% 88.11% 88.84% 88.45% 88.70% 88.66% 88.62% 88.11%