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  • Dream Ball Keno

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Dream Ball Keno

Introduction

Dream Ball Keno operates similarly to traditional Keno, but it occasionally grants players an additional pick marked on their card.

Rules

  1. This game is styled after the typical 4-card spot keno, which I trust you are already acquainted with.
  2. Players can wager between 2 and 10 coins on each card, meaning the total stake can range from 8 to 40.
  3. At random points during the game, players may be rewarded with an extra pick marked on their cards, except when all picks have already been marked. Below is the probability according to the specified pay tables:
    • Pay Table 95 -- 10.6%
    • Pay Table 93 -- 10.6%
    • Pay Table 91 -- 10.5%
    • Pay Table 90 -- 10.2%
    • Pay Table 88 -- 10.0%

Example

dream ball keno

In the previous image, I placed a wager of 10 credits per card. The extra feature was active. Here are the numbers of successful picks I had on each card prior to this feature:

  • Card A (Purple): 1 out of 4, win = 0
  • Card B (Green): 2 out of 6, win = 0
  • Card C (Yellow): 1 out of 8, win = 0
  • Card D (Pink): 1 out of 10, win = 0

After receiving the additional mark on each card, here’s the updated count of successful picks per card:

  • Card A (Purple): 2 out of 4, win = 10
  • Card B (Green): 4 out of 6, win = 15
  • Card C (Yellow): 2 out of 8, win = 0
  • Card D (Pink): 2 out of 10, win = 0

Thus, the additional mark transformed a zero 'win' into a 'win' of 25.

Analysis

The table below outlines the likelihood of achieving different numbers of successful picks based on the number of selections, assuming the extra feature is deactivated.

Probabilities

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 subsequent table illustrates how contributions to returns are calculated according to Pay Table 95, considering each possible combination of picks and successful outcomes when the extra feature isn't active.

Return Table without Feature

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 0.138754 0.212635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.381573 0.172992 0.125903 0.194729 0.087497 0.000000 0.000000 0.000000
4   0.188399 0.078600 0.128421 0.078286 0.081504 0.057053 0.073659
5     0.224111 0.126921 0.185728 0.183026 0.179308 0.154283
6       0.090289 0.161789 0.130169 0.165867 0.200889
7         0.030503 0.144410 0.128690 0.138558
8           0.005432 0.054755 0.067710
9             0.002173 0.010711
10               0.000337
Total 0.520326 0.574026 0.428614 0.540361 0.543803 0.544541 0.587846 0.646148

The next table represents the expected outcomes under Pay Table 95 with the extra marking feature in play, based on the number of picks and successful outcomes recorded prior to the extra mark.

Pay Table with Feature

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 0.430867 0.432732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 3.815725 0.850542 0.405686 0.462482 0.163327 0.000000 0.000000 0.000000
3 0.381573 2.659745 0.545578 0.584188 0.262490 0.214786 0.123055 0.133701
4   0.188399 4.202087 1.170055 1.122106 0.815037 0.627579 0.441957
5     0.224111 2.166947 1.909110 1.006642 0.945443 0.899985
6       0.090289 0.915096 2.130042 1.244004 0.987228
7         0.030503 0.200569 0.994020 0.805572
8           0.005432 0.097777 0.236984
9             0.002173 0.018362
10               0.000337
Total 4.628165 4.131418 5.377463 4.473961 4.402631 4.372509 4.034050 3.524124

The final table shows the expected return both with and without the feature enabled, under Pay Table 95. Recall that the probability of the feature is 1 in 9.43 = 10.6%. The combined column is a weighted average between 89.4% of the time when the feature is not enabled and 10.6% when it is. You can see the overall return, under this pay table, is 95.05% to 95.59%.

Pay Table with Feature

Pick Without
Feature		 With
Feature		 Weighted
Average
3 0.520326 4.628165 0.955940
4 0.574026 4.131418 0.951268
5 0.428614 5.377463 0.953412
6 0.540361 4.473961 0.957497
7 0.543803 4.402631 0.953011
8 0.544541 4.372509 0.950476
9 0.587846 4.034050 0.953297
10 0.646148 3.524124 0.951341

Return Tables

The pay tables presented below are calculated based on a wager of eight credits.

The following table corresponds to what I refer to as Pay Table 95, where the probability of utilizing the feature stands at 10.6%. The last row reveals the return percentages for varying pick counts, peaking at 95.73% for selecting 6 picks.

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 2 2 0 0 0 0 0 0
3 55 8 3 3 1 0 0 0
4 123 13 9 3 2 1 1
5 695 82 43 20 11 6
6 1400 442 110 58 35
7 2500 1800 435 172
8 2500 3360 1000
9 6000 3500
10 6000
Return 0.955757 0.951109 0.953192 0.957322 0.952839 0.950305 0.953144 0.951213

Next is the table I label as Pay Table 93. The feature has a probability of 10.6%, and the last row shows the returns for all pick numbers, with the highest return being 93.96% for selecting 4 picks.

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 2 2 0 0 0 0 0 0
3 53 8 3 3 1 0 0 0
4 120 12 8 3 2 1 1
5 690 82 40 19 10 6
6 1400 442 110 58 34
7 2500 1800 435 166
8 2500 3360 1000
9 6000 3500
10 6000
Return 0.927174 0.939638 0.938521 0.937685 0.932956 0.937804 0.932523 0.935385

Another table is what I call Pay Table 91. With a feature probability of 10.5%, the final row demonstrates the return percentages, where the maximum return is 91.64% for 10 picks.

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 2 2 0 0 0 0 0 0
3 52 8 3 3 1 0 0 0
4 114 12 7 3 2 1 1
5 670 82 38 18 10 6
6 1405 442 107 56 33
7 2500 1800 430 160
8 2500 3360 1000
9 5000 3500
10 5000
Return 0.908982 0.913332 0.914493 0.915351 0.915951 0.915479 0.915677 0.916400

The subsequent table represents what I term Pay Table 90, which has a feature probability of 10.2%. The final row corresponds to the returns for every pick number, with the highest yield being 90.94% for a selection of 9.

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 2 2 0 0 0 0 0 0
3 52 8 3 3 1 0 0 0
4 114 12 7 3 2 1 1
5 674 83 39 19 10 6
6 1400 436 102 56 33
7 2500 1800 430 159
8 2500 3400 1000
9 6000 3500
10 6000
Return 0.897283 0.903244 0.903964 0.905565 0.906626 0.906650 0.909446 0.907132

Lastly, the table referred to as Pay Table 88 shows a feature probability of 10.0%, with the concluding row indicating the returns for all selections, the highest being 88.63% for choosing 9.

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 2 2 0 0 0 0 0 0
3 51 8 3 3 1 0 0 0
4 110 12 7 3 2 1 1
5 664 78 37 18 10 6
6 1400 435 101 55 32
7 2500 1800 420 153
8 2500 3250 1000
9 6000 3500
10 6000
Return 0.875609 0.881742 0.885121 0.883775 0.885375 0.884893 0.886328 0.886053

External Links

VideoPoker.com — Experience Dream Ball Keno and many other games without any cost.

Written by: Michael Shackleford