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# caveman keno plus

## Caveman Keno Plus

### 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 makes a bet and chooses 2 to 10 numbers from 1 to 80.
2. When the player is done, the game randomly picks three of the unpicked 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.
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.

### Pay Tables

Let me get right to what you want to know. The following tables show pay tables for Caveman Keno Plus. The bottom row shows the expected return for each number of picks for that pay table. The tables are organzied from lowest to highest returns.

Pay Table 1 has a maximum return of 88.20% for a pick 7.

#### Pay Table 1 Expand

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 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 1000 200 120 60
8 2000 500 250
9 2000 1000
10 2000
Return 86.30% 87.83% 87.89% 88.15% 88.16% 88.20% 87.98% 88.13% 87.93%

Pay Table 2 has a maximum return of 90.29% for a pick 5.

#### Pay Table 2 Expand

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 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 1000 250 125 60
8 2000 500 250
9 2000 1000
10 2000
Return 86.30% 90.22% 90.15% 90.29% 89.93% 90.13% 90.18% 89.88% 90.13%

Pay Table 3 has a maximum return of 91.16% for a pick 7.

#### Pay Table 3 Expand

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 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 55 5 5 3 2 2 1
5 110 60 12 4 4 2
6 500 108 22 17 11
7 1000 108 125 63
8 1000 500 250
9 2000 1000
10 2000
Return 86.30% 90.22% 90.71% 90.91% 91.11% 91.16% 84.73% 90.99% 91.14%

Pay Table 4 has a maximum return of 92.19% for a pick 7.

#### Pay Table 4 Expand

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 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 57 6 6 3 2 2 1
5 100 53 13 4 4 2
6 500 104 25 18 12
7 1000 250 125 59
8 2000 500 250
9 2000 1000
10 2000
Return 86.30% 90.22% 91.84% 91.85% 91.89% 92.19% 92.07% 92.11% 92.00%

Pay Table 5 has a maximum return of 94.25% for a pick 5.

#### Pay Table 5 Expand

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 1 0 0 0 0 0 0 0 0
2 3 2 1 1 0 0 0 0 0
3 22 4 2 1 1 1 0 0
4 61 6 6 3 2 2 1
5 118 57 14 5 4 2
6 500 106 22 19 12
7 1000 250 132 65
8 2000 500 250
9 2000 1000
10 2000
Return 86.30% 92.60% 94.10% 94.11% 94.25% 94.11% 94.05% 94.10% 94.02%

### Analysis

This game was a bit complicated to analyze. In the interests of brevity, I will show my analysis for a pick-5 game only. For the purposes of example, I will use the following pay table.

#### Pick 5 Pay Table

Catch Pays
5 110
4 5
3 2
2 1
1 0
0 0

The next table shows the number of combinations for all possible outcomes. An “n/a” denotes a situation where the player did not early the three extra balls. The bottom right cell shows a return of 90.81%.

#### Pick 5 Detailed Return Table Expand

Orig.
Catch
Orig.
Eggs
Extra
Catch
Extra
Eggs
Win Combinations Probability Return
0 0 n/a n/a 0 143,282,767,320 0.088266 0.000000
0 1 n/a n/a 0 162,206,906,400 0.099924 0.000000
0 2 n/a n/a 0 57,072,800,400 0.035158 0.000000
0 3 n/a n/a 0 6,226,123,680 0.003835 0.000000
1 0 n/a n/a 0 270,344,844,000 0.166540 0.000000
1 1 n/a n/a 0 285,364,002,000 0.175792 0.000000
1 2 n/a n/a 0 93,391,855,200 0.057532 0.000000
1 3 n/a n/a 0 9,450,366,300 0.005822 0.000000
2 0 n/a n/a 1 190,242,668,000 0.117195 0.117195
2 1 n/a n/a 1 186,783,710,400 0.115064 0.115064
3 0 n/a n/a 2 62,261,236,800 0.038355 0.076709
3 1 n/a n/a 2 56,702,197,800 0.034930 0.069860
4 0 n/a n/a 5 9,450,366,300 0.005822 0.029108
4 1 n/a n/a 5 7,958,203,200 0.004902 0.024512
5 0 n/a n/a 110 530,546,880 0.000327 0.035952
5 1 n/a n/a 110 411,631,200 0.000254 0.027893
2 2 0 0 4 45,931,762,800 0.028295 0.113181
2 2 0 1 8 2,551,764,600 0.001572 0.012576
2 3 0 0 8 4,536,470,400 0.002795 0.022357
2 2 1 0 8 7,655,293,800 0.004716 0.037727
2 2 1 1 16 278,374,320 0.000171 0.002744
2 3 1 0 16 742,331,520 0.000457 0.007317
2 2 2 0 20 278,374,320 0.000171 0.003430
2 2 2 1 40 4,970,970 0.000003 0.000122
2 3 2 0 40 26,511,840 0.000016 0.000653
2 2 3 0 440 1,656,990 0.000001 0.000449
2 3 3 0 880 155,040 0.000000 0.000084
3 2 0 0 8 13,609,411,200 0.008384 0.067070
3 2 0 1 16 742,331,520 0.000457 0.007317
3 3 0 0 16 1,237,219,200 0.000762 0.012195
3 2 1 0 20 1,484,663,040 0.000915 0.018292
3 2 1 1 40 53,023,680 0.000033 0.001307
3 3 1 0 40 132,559,200 0.000082 0.003266
3 2 2 0 440 26,511,840 0.000016 0.007186
3 2 2 1 880 465,120 0.000000 0.000252
3 3 2 0 880 2,325,600 0.000001 0.001261
4 2 0 0 20 1,855,828,800 0.001143 0.022865
4 2 0 1 40 99,419,400 0.000061 0.002450
4 3 0 0 40 154,652,400 0.000095 0.003811
4 2 1 0 440 99,419,400 0.000061 0.026948
4 2 1 1 880 3,488,400 0.000002 0.001891
4 3 1 0 880 8,139,600 0.000005 0.004413
5 2 0 0 440 92,791,440 0.000057 0.025151
5 2 0 1 880 4,883,760 0.000003 0.002648
5 3 0 0 880 7,054,320 0.000004 0.003824
Total 1,623,302,080,400 1.000000 0.909080

If the table above was too much information, here is the same kind of thing but summarizing each possible total win.

#### Summarized Return

Win Combinations Probability Return
880 26,511,840 0.000016 0.014372
440 220,379,670 0.000136 0.059734
110 942,178,080 0.000580 0.063845
40 471,137,490 0.000290 0.011609
20 3,618,866,160 0.002229 0.044586
16 3,000,256,560 0.001848 0.029572
8 28,352,940,000 0.017466 0.139730
5 17,408,569,500 0.010724 0.053621
4 45,931,762,800 0.028295 0.113181
2 118,963,434,600 0.073285 0.146570
1 377,026,378,400 0.232259 0.232259
0 1,027,339,665,300 0.632870 0.000000
Total 1,623,302,080,400 1.000000 0.909080

It can be easily see from the table above that the player wins nothing 63.3% of the time, meaning the hit frequency is 36.7%. The variance can be easily calculated as 49.32, so the standard deviation is 7.02.

### Calculator

To analyze any Caveman Keno Plus pay table, please make use of my Caveman Keno Plus Calculator.

### Acknowledgements

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

Mathematical Analysis of Caveman Keno Plus

## Caveman Keno Plus

### Recommended online casinos

This is a keno variant I noticed yesterday on a Game King machine. Here are the rules.

1. Player picks 2 to 10 numbers out of 80.
2. Game picks three numbers from the 70 to 78 unchosen numbers and marks them with eggs.
3. Game picks 20 numbers out of 80.
3. If 2 eggs are hit, player win is multiplied by 4.
4. If 3 eggs are hit, player win is multiplied by 8.
5. In addition, if 2 or 3 eggs are hit, the game draws 3 extra balls.
6. Player is paid according to the base pay table below.

 Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10 Catch 0 0 0 0 0 0 0 0 0 0 Catch 1 1 0 0 0 0 0 0 0 0 Catch 2 3 2 1 1 0 0 0 0 0 Catch 3 0 20 4 2 1 1 1 0 0 Catch 4 0 0 50 5 5 3 2 2 1 Catch 5 0 0 0 88 55 10 4 4 2 Catch 6 0 0 0 0 500 110 20 15 10 Catch 7 0 0 0 0 0 1000 200 120 60 Catch 8 0 0 0 0 0 0 2000 500 250 Catch 9 0 0 0 0 0 0 0 2000 1000 Catch 10 0 0 0 0 0 0 0 0 2000

What is unclear to me is what happens if the get hits two eggs on the initial 20 ball draw, and then hits the third egg with the three extra balls. Does the player with 4X or 8X. Here is what the rules say:

If two eggs are hit, all wins pay 4X. If three eggs are hit, all wins pay 8X! Two or more hit eggs on a winning card awards three extra balls!

I tend to think that the game would still pay 4X. Based on that assumption for the pick-10 game I get a return of 93.4114% for the pick-10.

Would anyone up for a math challenge care to confirm or refute that?

This is a keno variant I noticed yesterday on a Game King machine. Here are the rules.1. Player picks 2 to 10 numbers out of 80.2. Game picks three…