# Cleopatra Max Keno

## Introduction

Cleopatra Max is a keno variant in which if the last ball drawn contributes to a win, then the player will play a free game bonus round. In the bonus round, the player gets 12 free games with a random multiplier of 3x to 5x.

The game is the same as Cleopatra Keno, except in that game the bonus multiplier is always 2x, and in the "Max" version it is 3x to 5x. To pay for that increase, the base pay table is less.

## Rules

1. The player picks 3 to 10 numbers from 1 range of 1 to 80 on four separate cards.
2. The player shall bet 8 to 40 credits, in increments of 8. The total bet shall be divided equally on the four cards played.
3. The game shall draw 20 numbers from a range of 1 to 80. This ball draw shall apply to all four cards.
4. The player shall win according to the number balls drawn by the game that match his numbers chosen. The more that match, the more the player wins. Various pay table are available, as shown below.
5. If the last ball drawn by the game, as marked by a scarab on the cards, contributes to a win, then the player shall play a bonus round on the card(s) that trigger the bonus.
6. In the bonus round the player shall play 12 free games.
7. A multiplier of 3x to 5x shall be applied to free games. The probability of each multiplier is as follows:
• 3x: 1/6
• 4x: 4/6
• 5x: 1/6
8. Bonus games shall have the same player picks and bet per card as the initiating game.
9. Bonus games may not trigger the bonus.

## Example

In the screen above, on card C, I caught 4 out of 6 numbers. The last ball drawn was the 3, as evidenced by a scarab on the card, which was one of the four numbers caught (23,56,3,75) on card C, thus triggering the bonus. The bonus multiplier is randomly chosen as 4x.

In the screen above, I am informed of the 12 free games I won and reminded of the 4x multiplier.

The screen above is the 3rd of my 12 free games. Note I caught 3 out of my 6 picks. In a regular game, this would pay 2 for a bet of 2 per card, or total bet of 8. However, I bet a total of 40, or 10 per card, so the win should be five times as much as for a total bet of 8. There is also my multiplier of 4x. Thus, my total win for that game is 2×5×4 = 40.

The screen above shows my total bonus win of 200 by the end of the bonus. This happened by catching 3 out of 6 five different times. The total win was thus 40×5=200.

The screen above summarizes my win for that game. For catching 4 out of 6 on card C, I won 5×7 = 35. The base win plus the bonus win is 35+200=235.

## Analysis

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

### 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 0.000000 0.003063 0.012092 0.028538 0.052191 0.081504 0.114105 0.147319
5 0.000000 0.000000 0.000645 0.003096 0.008639 0.018303 0.032601 0.051428
6 0.000000 0.000000 0.000000 0.000129 0.000732 0.002367 0.005720 0.011479
7 0.000000 0.000000 0.000000 0.000000 0.000024 0.000160 0.000592 0.001611
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.000004 0.000033 0.000135
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000001 0.000006
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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 in the base game for pay table 95 below.

### Base Game Return -- Pay Table 95

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 0.277507 0.106318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.263632 0.129744 0.167870 0.129820 0.087497 0.000000 0.000000 0.000000
4 0.000000 0.166955 0.229754 0.099883 0.104382 0.163007 0.171158 0.073659
5 0.000000 0.000000 0.154782 0.136208 0.043193 0.091513 0.097804 0.077142
6 0.000000 0.000000 0.000000 0.058043 0.078698 0.145553 0.028598 0.045918
7 0.000000 0.000000 0.000000 0.000000 0.018302 0.064182 0.045855 0.059612
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.004346 0.024444 0.033855
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000724 0.004590
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000112
Total 0.541139 0.403016 0.552406 0.423954 0.332071 0.468601 0.368584 0.294888

The following table shows the contribution to the return from the bonus for pay table 95 below.

### Bonus Return -- Pay Table 95

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 0.360408 0.411339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.054061 0.125493 0.333837 0.396270 0.418394 0.000000 0.000000 0.000000
4 0.000000 0.011852 0.064127 0.116148 0.166379 0.366650 0.403750 0.417049
5 0.000000 0.000000 0.004275 0.015749 0.034423 0.102919 0.144196 0.181985
6 0.000000 0.000000 0.000000 0.000787 0.003501 0.015970 0.030357 0.048746
7 0.000000 0.000000 0.000000 0.000000 0.000136 0.001263 0.003664 0.007982
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.000039 0.000231 0.000767
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000006 0.000039
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000001
Total 0.414469 0.548684 0.402239 0.528954 0.622832 0.486842 0.582204 0.656569

The following table shows the combined contribution from the base game and return for pay table 95 below.

### Combined Return -- Pay Table 95

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 0.637916 0.517656 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.317693 0.255237 0.501707 0.526089 0.505890 0.000000 0.000000 0.000000
4 0.000000 0.178807 0.293881 0.216031 0.270761 0.529657 0.574908 0.490709
5 0.000000 0.000000 0.159057 0.151957 0.077616 0.194432 0.242001 0.259127
6 0.000000 0.000000 0.000000 0.058831 0.082199 0.161523 0.058955 0.094664
7 0.000000 0.000000 0.000000 0.000000 0.018438 0.065445 0.049519 0.067594
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.004385 0.024675 0.034622
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000730 0.004629
10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000113
Return 95.56% 95.17% 95.46% 95.29% 95.49% 95.54% 95.08% 95.15%

## Return Tables

The following pay table 95 is based on a total bet of 8 credits. The highest return is for a pick-3 at 95.56%.

### 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 4 1 0 0 0 0 0 0
3 38 6 4 2 1 0 0 0
4   109 38 7 4 4 3 1
5     480 88 10 10 6 3
6       900 215 123 10 8
7         1500 800 155 74
8           2000 1500 500
9             2000 1500
10               2000
Return 95.56% 95.17% 95.46% 95.29% 95.49% 95.54% 95.08% 95.15%

The following pay table 93 is based on a total bet of 8 credits. The highest return is for a pick-4 at 93.72%.

### 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 4 1 0 0 0 0 0 0
3 36 6 4 2 1 0 0 0
4 105 36 7 4 4 3 1
5 480 82 9 10 6 3
6 900 205 115 10 8
7 1500 800 130 68
8 2000 1500 500
9 2000 1500
10 2000
Total 93.11% 93.72% 93.37% 93.2% 93.2% 93.61% 93.17% 93.59%

The following pay table 91 is based on a total bet of 8 credits. The highest return is for a pick-3 at 91.89%.

### 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 4 1 0 0 0 0 0 0
3 35 6 4 2 1 0 0 0
4 99 34 7 4 4 3 1
5 480 77 8 10 6 3
6 900 200 105 10 7
7 1500 800 110 68
8 2000 1500 500
9 2000 1500
10 2000
Total 91.89% 91.55% 91.29% 91.46% 91.43% 91.2% 91.64% 91.73%

The following pay table 90 is based on a total bet of 8 credits. The highest return is for a pick-6 at 90.77%.

### 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 4 1 0 0 0 0 0 0
3 34 6 4 2 1 0 0 0
4 95 33 7 4 4 3 1
5 480 75 8 10 6 3
6 900 190 102 10 7
7 1500 800 110 62
8 2000 1200 500
9 2000 1500
10 2000
Total 90.66% 90.11% 90.24% 90.77% 90.37% 90.48% 90.38% 90.17%

The following pay table 88 is based on a total bet of 8 credits. The highest return is for a pick-9 at 88.86%.

### 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 4 1 0 0 0 0 0 0
3 32 6 4 2 1 0 0 0
4 90 31 6 4 4 3 1
5 480 77 8 10 6 3
6 900 170 100 10 7
7 1500 700 90 55
8 2000 1200 500
9 2000 1500
10 2000
Return 0.882100 0.882977 0.881504 0.882567 0.882697 0.883591 0.888573 0.883554