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# Circus Keno

## Introduction

Circus Keno is a game found on multi-game machines made by U1 Gaming. I have seen such machines at the Las Vegas Club, Rampart and Dotty's casinos in Las Vegas. The thrust of Circus Keno is after the player picks his numbers, the game will randomly pick six circus tents from among the remaining numbers. By hitting the circus tents with the 20 drawn numbers, the player can earn multipliers or a free spin bonus.

## Rules

The following are the rules of the base game.

- The player chooses 2 to 10 numbers from a range of 1 to 80.
- The game will randomly choose six numbers from among the numbers the player didn't choose. Two will be marked with green tents, two with purple tents, and two with blue tents.
- The player will win in part according to the number of balls that match his chosen numbers. The pay table will depend on the amount bet. Below is an example for a $2 bet.

### Pay Table — $2 bet

Catch Pick 2 3 4 5 6 7 8 9 10 10 10000 9 5000 2000 8 2500 1150 178.5 7 1030 344 100 35.5 6 535 97 40 12 7 5 212.5 40 10 6 4 2 4 49.625 12 5 2 2 1 1 3 15.075 3 2 1 1 0 0 0 2 8 2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - The player can win multipliers according to the following patterns of tents that match the 20-ball draw, as follows.
- One pair of tents of one color = 2x multiplier.
- One pair of tents of one color plus one tent of another color = 3x multiplier.
- One pair of tents of one color plus one tent each of the other two colors = 4x multiplier.

- The player can win a free spin bonus round according to the following patterns of tents that match the 20-ball draw, as follows.
- Two pairs of tents = Four free spins.
- Five total tents = Seven free spins.
- Six total tents = 20 free spins.

- Finally, there is a random bonus game that adds 0.5025% to the return. This random bonus is not otherwise addressed in this page, because I consider it outside the scope of the Circus game.

Following are the rules for free spins.

- Free spins shall have the same number of marks and wager as the initiating spin.
- Every free spins shall have two bonuses of the following three types:
- Multiplier.
- Extra balls.
- Extra free spins.

- The game shall represent the two bonuses with two spinners, a left one and a right one.
- The game shall choose from two tables of possible wins for both bonuses.
- The game shall then choose the win randomly for each spinner according the following tables. The two wins for each spinner are drawn independently.
- The following tables show the possible wins for both spinners according to the table chosen.

## Examples

The image above and to the left was an initial spin. I bet $0.05 and picked ten numbers. I caught four of them, for a base win of $0.05. In addition, I caught both blue tents, one purple tent, and one green tent for a 4x multiplier. Thus, my final win was $0.05 × 4 = $0.20.

The image above and to the right was a bonus spin. On the initial spin I bet $0.05 and picked ten numbers, which carried over to the bonus spins. My two bonuses were three extra balls and a 6x multiplier. Normally, I would have caught five numbers, but one of the three extra balls hit number 25, for a total of six catches andr a base win of $0.35. Then, the 6x multiplier increased my final win for that spin to $0.35 * 6 = $2.10.

## Pick 10

The following table shows the return table for the base game given ten numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 10 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

10 | 10000 | 184,756 | 0.00000011 | 0.00112212 |

9 | 2000 | 10,077,600 | 0.00000612 | 0.01224130 |

8 | 178.5 | 222,966,900 | 0.00013542 | 0.02417235 |

7 | 35.5 | 2,652,734,400 | 0.00161114 | 0.05719558 |

6 | 7 | 18,900,732,600 | 0.01147939 | 0.08035576 |

5 | 2 | 84,675,282,048 | 0.05142769 | 0.10285538 |

4 | 1 | 242,559,401,700 | 0.14731890 | 0.14731890 |

3 | 0 | 440,275,888,800 | 0.26740237 | 0.00000000 |

2 | 0 | 486,137,960,550 | 0.29525678 | 0.00000000 |

1 | 0 | 295,662,853,200 | 0.17957138 | 0.00000000 |

0 | 0 | 75,394,027,566 | 0.04579070 | 0.00000000 |

Total | 1,646,492,110,120 | 1.00000000 | 0.42526139 |

The next table summarizes the return of the pick-10 game with a $2 bet.

### Pick 10 Summary — $2 bet

Win Source | Return |
---|---|

Base win | 0.425261 |

Multipliers | 0.081177 |

Bonus | 0.453668 |

Total | 0.960106 |

## Pick 9

The following table shows the return table for the base game given nine numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 9 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

9 | 5000 | 167,960 | 0.00000072 | 0.00362138 |

8 | 1150 | 7,558,200 | 0.00003259 | 0.03748132 |

7 | 100 | 137,210,400 | 0.00059168 | 0.05916784 |

6 | 12 | 1,326,367,200 | 0.00571956 | 0.06863470 |

5 | 4 | 7,560,293,040 | 0.03260148 | 0.13040592 |

4 | 1 | 26,461,025,640 | 0.11410518 | 0.11410518 |

3 | 0 | 57,072,800,400 | 0.24610922 | 0.00000000 |

2 | 0 | 73,379,314,800 | 0.31642614 | 0.00000000 |

1 | 0 | 51,172,416,900 | 0.22066559 | 0.00000000 |

0 | 0 | 14,783,142,660 | 0.06374784 | 0.00000000 |

Total | 231,900,297,200 | 1.00000000 | 0.41341635 |

The next table summarizes the return of the pick-9 game with a $2 bet.

### Pick 9 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.413416 |

Multipliers | 0.075515 |

Bonus | 0.471319 |

Total | 0.960250 |

## Pick 8

The following table shows the return table for the base game given eight numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 8 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

8 | 2500 | 125,970 | 0.00000435 | 0.01086415 |

7 | 344 | 4,651,200 | 0.00016046 | 0.05519658 |

6 | 40 | 68,605,200 | 0.00236671 | 0.09466855 |

5 | 6 | 530,546,880 | 0.01830259 | 0.10981551 |

4 | 2 | 2,362,591,575 | 0.08150370 | 0.16300740 |

3 | 0 | 6,226,123,680 | 0.21478623 | 0.00000000 |

2 | 0 | 9,512,133,400 | 0.32814562 | 0.00000000 |

1 | 0 | 7,724,138,400 | 0.26646411 | 0.00000000 |

0 | 0 | 2,558,620,845 | 0.08826624 | 0.00000000 |

Total | 28,987,537,150 | 1.00000000 | 0.43355219 |

The next table summarizes the return of the pick-8 game with a $2 bet.

### Pick 8 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.433552 |

Multipliers | 0.080345 |

Bonus | 0.446053 |

Total | 0.959950 |

## Pick 7

The following table shows the return table for the base game given seven numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 7 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

7 | 1030 | 77,520 | 0.00002440 | 0.02513463 |

6 | 97 | 2,325,600 | 0.00073208 | 0.07101144 |

5 | 10 | 27,442,080 | 0.00863850 | 0.08638505 |

4 | 2 | 165,795,900 | 0.05219097 | 0.10438193 |

3 | 1 | 555,903,900 | 0.17499324 | 0.17499324 |

2 | 0 | 1,037,687,280 | 0.32665405 | 0.00000000 |

1 | 0 | 1,001,277,200 | 0.31519251 | 0.00000000 |

0 | 0 | 386,206,920 | 0.12157425 | 0.00000000 |

Total | 3,176,716,400 | 1.00000000 | 0.46190629 |

The next table summarizes the return of the pick-7 game with a $2 bet.

### Pick 7 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.461906 |

Multipliers | 0.094927 |

Bonus | 0.403064 |

Total | 0.959898 |

## Pick 6

The following table shows the return table for the base game given six numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 6 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

6 | 535 | 38,760 | 0.00012898 | 0.06900694 |

5 | 40 | 930,240 | 0.00309564 | 0.12382554 |

4 | 5 | 8,575,650 | 0.02853792 | 0.14268959 |

3 | 1 | 39,010,800 | 0.12981955 | 0.12981955 |

2 | 0 | 92,650,650 | 0.30832143 | 0.00000000 |

1 | 0 | 109,230,240 | 0.36349473 | 0.00000000 |

0 | 0 | 50,063,860 | 0.16660175 | 0.00000000 |

Total | 300,500,200 | 1.00000000 | 0.46534162 |

The next table summarizes the return of the pick-6 game with a $2 bet.

### Pick 6 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.465342 |

Multipliers | 0.092483 |

Bonus | 0.401962 |

Total | 0.959787 |

## Pick 5

The following table shows the return table for the base game given five numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 5 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

5 | 212.5 | 15,504 | 0.00064492 | 0.13704650 |

4 | 12 | 290,700 | 0.01209234 | 0.14510806 |

3 | 2 | 2,017,800 | 0.08393505 | 0.16787010 |

2 | 0 | 6,501,800 | 0.27045739 | 0.00000000 |

1 | 0 | 9,752,700 | 0.40568609 | 0.00000000 |

0 | 0 | 5,461,512 | 0.22718421 | 0.00000000 |

Total | 24,040,016 | 1.00000000 | 0.45002466 |

The next table summarizes the return of the pick-5 game with a $2 bet.

### Pick 5 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.450025 |

Multipliers | 0.091117 |

Bonus | 0.418854 |

Total | 0.959995 |

## Pick 4

The following table shows the return table for the base game given four numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 4 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

4 | 49.625 | 4,845 | 0.00306339 | 0.15202084 |

3 | 3 | 68,400 | 0.04324789 | 0.12974367 |

2 | 1 | 336,300 | 0.21263547 | 0.21263547 |

1 | 0 | 684,400 | 0.43273183 | 0.00000000 |

0 | 0 | 487,635 | 0.30832143 | 0.00000000 |

Total | 1,581,580 | 1.00000000 | 0.49439998 |

The next table summarizes the return of the pick-4 game with a $2 bet.

### Pick 4 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.494400 |

Multipliers | 0.112217 |

Bonus | 0.353243 |

Total | 0.959860 |

## Pick 3

The following table shows the return table for the base game given three numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 3 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

3 | 15.075 | 1,140 | 0.01387537 | 0.20917113 |

2 | 2 | 11,400 | 0.13875365 | 0.27750730 |

1 | 0 | 35,400 | 0.43086660 | 0.00000000 |

0 | 0 | 34,220 | 0.41650438 | 0.00000000 |

Total | 82,160 | 1.00000000 | 0.48667843 |

The next table summarizes the return of the pick-3 game with a $2 bet.

### Pick 3 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.486678 |

Multipliers | 0.113523 |

Bonus | 0.359689 |

Total | 0.959891 |

## Pick 2

The following table shows the return table for the base game given two numbers picked and a $2 bet, before considering multipliers and the bonus.

### Pick 2 Return Table — $2 bet

Catch | Pays | Combinations | Probability | Return |
---|---|---|---|---|

2 | 8 | 190 | 0.06012658 | 0.48101266 |

1 | 0 | 1,200 | 0.37974684 | 0.00000000 |

0 | 0 | 1,770 | 0.56012658 | 0.00000000 |

Total | 3,160 | 1.00000000 | 0.48101266 |

The next table summarizes the return of the pick-2 game with a $2 bet.

### Pick 2 Summary — $2 bet

Win Source | Return |
---|---|

Initial spin | 0.481013 |

Multipliers | 0.115039 |

Bonus | 0.361551 |

Total | 0.957603 |

## Bonus

The following table shows the probability of each tent pattern. It should be noted that actual probabilities will be correlated to the number of catches. These are just overall averages.

### Tent Pattern Probabilities

Pattern | Win | Combinations | Probability |
---|---|---|---|

None | Nothing | 588,989,865,562,321,000 | 0.166602 |

One | Nothing | 1,285,068,797,590,520,000 | 0.363495 |

Two — different colors | Nothing | 872,010,969,793,565,000 | 0.246657 |

Three — different colors | Nothing | 183,581,256,798,645,000 | 0.051928 |

One pair | 2x multiplier | 218,002,742,448,391,000 | 0.061664 |

One pair + one singleton | 3x multiplier | 275,371,885,197,968,000 | 0.077892 |

One pair + two singletons | 4x multiplier | 80,712,449,109,749,200 | 0.022830 |

Two pair | 4 free games | 20,178,112,277,437,300 | 0.005708 |

Five total | 7 free games | 10,944,060,896,237,200 | 0.003096 |

Six total | 20 free games | 456,002,537,343,216 | 0.000129 |

Total | 3,535,316,142,212,170,000 | 1.000000 |

The following table shows the average bonus win per spin according to both table 1 and table 2 (refer to the rules above), as well as the average. The final three columns show the average win per bonus, according to whether it starts with 4, 7 or 20 free spins. The average win per bonus is the product of the average win per spin, initial spins, and 5/3. The reason for the 5/3 is that on average the player will earn 0.666667 extra spins for every initial spin, due to earning more free spins within the bonus.

### Average Win per Bonus Spin and Round

Pick | Table 1 | Table 2 | Average | 4 F.G. | 7 F.G. | 20 F.G. |
---|---|---|---|---|---|---|

2 | 4.768569 | 4.446939 | 4.607754 | 30.718359 | 53.757129 | 153.591797 |

3 | 4.744718 | 4.423332 | 4.584025 | 30.560166 | 53.480291 | 152.800832 |

4 | 4.635971 | 4.367764 | 4.501867 | 30.012449 | 52.521786 | 150.062246 |

5 | 5.462527 | 5.213562 | 5.338045 | 35.586964 | 62.277186 | 177.934818 |

6 | 5.216845 | 5.028689 | 5.122767 | 34.151779 | 59.765614 | 170.758897 |

7 | 5.209431 | 5.064194 | 5.136813 | 34.245417 | 59.92948 | 171.227085 |

8 | 5.761232 | 5.608121 | 5.684676 | 37.897843 | 66.321225 | 189.489214 |

9 | 6.133279 | 5.880078 | 6.006679 | 40.044524 | 70.077918 | 200.222622 |

10 | 5.949647 | 5.613796 | 5.781721 | 38.544809 | 67.453416 | 192.724045 |

## Summary

The final table shows the total return according to the number of picks for a $2 bet.

### Average Win per Bonus Spin and Round

Pick | Return |
---|---|

2 | 95.76% |

3 | 95.99% |

4 | 95.99% |

5 | 96.00% |

6 | 95.98% |

7 | 95.99% |

8 | 95.99% |

9 | 96.03% |

10 | 96.01% |

These returns do not include the random bonus, which adds another 0.5025%.

The final pictures above show a U1 Gaming machine on the left and the pay table and return percentages for a $0.05 bet on the right.

For more information about returns for bet amounts other than exactly $2, please visit my page on U1 Gaming theoretical returns.

Written by:Michael Shackleford