Last Updated: March 15, 2013

Caveman Keno Plus

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Introduction

Caveman Keno Plus is a keno variant I noticed on a Game King machine at the Red Rock casino in Las Vegas on March 21, 2012. It plays like regular keno, except it adds the possibility of multipliers and extra balls. Of course, the cost for that is a lower base pay table.

Rules

  1. The player chooses 2 to 10 numbers from 1 to 80.
  2. When the player is done, the game randomly picks three of the remaining numbers and marks them with eggs.
  3. The game will then randomly pick 20 numbers from 1 to 80.
  4. The player's base prize will pay according to how many of the balls drawn by the game match those chosen by the player.
  5. If the game chooses a number with an egg, then that egg will hatch.
  6. If exactly two eggs hatch, then any win will be multiplied by 4. If all three eggs hatch, then any win will be multiplied by 8. There is no multiplier for zero or one hatched eggs.
  7. If at least two eggs hatch, AND the player already has a winning card based on the pay table, then the game will draw three extra balls, possibly resulting in a larger base prize if these three balls match any of the player's chosen numbers.
  8. In the event the player wins the extra three balls with two eggs, and one of the extra balls matches the third egg, then the multiplier will go from 4 to 8.
  9. The final award will be the product of the base prize and multiplier.

The following pay table was observed at the Red Rock casino in Las Vegas on March 21, 2012.

Caveman Keno Plus Base Pay Table

Catch Pick
2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0
2 3 2 1 1 0 0 0 0 0
3 20 4 2 1 1 1 0 0
4 50 5 5 3 2 2 1
5 88 55 10 4 4 2
6 500 110 20 15 10
7 1,000 200 120 60
8 2,000 500 250
9 2,000 1,000
10 2,000

Analysis

This was a complicated game to analyze, so forgive me if I don't break down the details of the calculations. Instead, I would like to boil down the effect of the multipliers and extra balls with the following effective multipliers. The actual value of initially catching any number of balls is the product of the base win in the pay table and the effective multiplier.

For example, normally catching 5 out of 7 pays 10. The multiplication factor for catching 5 out of 7 is 1.889191. Thus the average value of catching 5 out of 7 after the initial ball draw is 10×1.889191 = 18.891914.

Caveman Keno Plus Effective Multipliers

Catch Pick
2 3 4 5 6 7 8 9 10
0 1.568432 1.582857 1.597838 1.600894 1.629582 1.646408 1.663917 1.682145 1.701133
1 1.578571 1.526597 1.540162 1.421096 1.568910 1.584150 1.600010 1.616523 1.633727
2 1.461223 1.742794 1.713860 1.600362 1.511070 1.524793 1.539074 1.553946 1.569441
3 1.422037 1.748871 1.566541 1.942363 1.741648 1.646076 1.494459 1.508323
4 1.383499 1.808542 1.984938 1.684706 1.577105 1.625618 1.733488
5 1.345724 1.537548 1.889191 1.762929 1.771741 2.082030
6 1.308836 1.480567 1.755390 1.822426 1.846242
7 1.272976 1.441355 1.410382 1.493494
8 1.238296 1.291845 1.348855
9 1.204969 1.224260
10 1.173182

The next nine tables show the return for pick 2 to 10 games according to the Red Rock pay table.

Caveman Keno Plus Pick 2

Catch Pays Multiplier Probability Return
0 0 1.568432 0.560127 0.000000
1 1 1.578571 0.379747 0.599458
2 3 1.461223 0.060127 0.263575
Total 1.000000 0.863033

Caveman Keno Plus Pick 3

Catch Pays Multiplier Probability Return
0 0 1.582857 0.416504 0.000000
1 0 1.526597 0.430867 0.000000
2 2 1.742794 0.138754 0.483638
3 20 1.422037 0.013875 0.394626
Total 1.000000 0.878264

Caveman Keno Plus Pick 4

Catch Pays Multiplier Probability Return
0 0 1.597838 0.308321 0.000000
1 0 1.540162 0.432732 0.000000
2 1 1.713860 0.212635 0.364427
3 4 1.748871 0.043248 0.302540
4 50 1.383499 0.003063 0.211910
Total 1.000000 0.878877

Caveman Keno Plus Pick 5

Catch Pays Multiplier Probability Return
0 0 1.603437 0.227184 0.000000
1 0 1.449046 0.405686 0.000000
2 1 1.600362 0.270457 0.432830
3 2 1.566541 0.083935 0.262975
4 5 1.808542 0.012092 0.109348
5 88 1.345724 0.000645 0.076374
Total 1.000000 0.881527

Caveman Keno Plus Pick 6

Catch Pays Multiplier Probability Return
0 0 1.629582 0.166602 0.000000
1 0 1.568910 0.363495 0.000000
2 0 1.511070 0.308321 0.000000
3 1 1.942363 0.129820 0.252157
4 5 1.984938 0.028538 0.283230
5 55 1.537548 0.003096 0.261783
6 500 1.308836 0.000129 0.084410
Total 1.000000 0.881580

Caveman Keno Plus Pick 7

Catch Pays Multiplier Probability Return
0 0 1.646408 0.121574 0.000000
1 0 1.584150 0.315193 0.000000
2 0 1.524793 0.326654 0.000000
3 1 1.741648 0.174993 0.304777
4 3 1.684706 0.052191 0.263779
5 10 1.889191 0.008639 0.163198
6 110 1.480567 0.000732 0.119228
7 1000 1.272976 0.000024 0.031064
Total 1.000000 0.882045

Caveman Keno Plus Pick 8

Catch Pays Multiplier Probability Return
0 0 1.663917 0.088266 0.000000
1 0 1.600010 0.266464 0.000000
2 0 1.539074 0.328146 0.000000
3 1 1.646076 0.214786 0.353554
4 2 1.577105 0.081504 0.257080
5 4 1.762929 0.018303 0.129065
6 20 1.755390 0.002367 0.083090
7 200 1.441355 0.000160 0.046255
8 2000 1.238296 0.000004 0.010762
Total 1.000000 0.879806

Caveman Keno Plus Pick 9

Catch Pays Multiplier Probability Return
0 0 1.682145 0.063748 0.000000
1 0 1.616523 0.220666 0.000000
2 0 1.553946 0.316426 0.000000
3 0 1.494459 0.246109 0.000000
4 2 1.625618 0.114105 0.370983
5 4 1.771741 0.032601 0.231046
6 15 1.822426 0.005720 0.156352
7 120 1.410382 0.000592 0.100139
8 500 1.291845 0.000033 0.021052
9 2000 1.204969 0.000001 0.001745
Total 1.000000 0.881317

Caveman Keno Plus Pick 10

Catch Pays Multiplier Probability Return
0 0 1.701133 0.045791 0.000000
1 0 1.633727 0.179571 0.000000
2 0 1.569441 0.295257 0.000000
3 0 1.508323 0.267402 0.000000
4 1 1.733488 0.147319 0.255376
5 2 2.082030 0.051428 0.214148
6 10 1.846242 0.011479 0.211937
7 60 1.493494 0.001611 0.144374
8 250 1.348855 0.000135 0.045665
9 1000 1.224260 0.000006 0.007493
10 2000 1.173182 0.000000 0.000263
Total 1.000000 0.879257

The final table shows the overall return according to the number of balls picked. The highest return is the pick-7 at 88.20%.

Caveman Keno Plus Summary

Pick Return
2 86.30%
3 87.83%
4 87.89%
5 88.15%
6 88.16%
7 88.20%
8 87.98%
9 88.13%
10 87.93%

Finally, here is another more liberal pay table. The return is in the bottom row.

Caveman Keno Plus Base Pay Table 2

Catch Pick
2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0
2 3 2 1 1 0 0 0 0 0
3 21 4 2 1 1 1 0 0
4 54 5 5 3 2 2 1
5 105 58 11 4 4 2
6 500 112 21 16 11
7 1,000 250 125 60
8 2,000 500 250
9 2,000 1,000
10 2,000
Return 86.30% 90.22% 90.15% 90.29% 89.93% 90.13% 90.18% 89.88% 90.13%

Acknowledgements

The Wizard would like to thank Wizard of Vegas forum member CrystalMath for confirming my results on this game.

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