Last Updated: June 10, 2013

Circus Keno

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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.

  1. The player chooses 2 to 10 numbers from a range of 1 to 80.
  2. 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.
  3. 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

  4. 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.

  5. 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.

  6. 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.

  1. Free spins shall have the same number of marks and wager as the initiating spin.
  2. Every free spins shall have two bonuses of the following three types:
    • Multiplier.
    • Extra balls.
    • Extra free spins.
  3. The game shall represent the two bonuses with two spinners, a left one and a right one.
  4. The game shall choose from two tables of possible wins for both bonuses.
  5. The game shall then choose the win randomly for each spinner according the following tables. The two wins for each spinner are drawn independently.
  6. The following tables show the possible wins for both spinners according to the table chosen.

  7. Pick 2 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 6% 2x multiplier 6% 2 extra balls 6% 2x multiplier 6%
    3 extra balls 10% 3x multiplier 14% 3 extra balls 12% 3x multiplier 10%
    4 extra balls 12% 4x multiplier 16% 4 extra balls 16% 4x multiplier 12%
    5 extra balls 12% 5x multiplier 16% 5 extra balls 16% 5x multiplier 12%
    7 extra balls 12% 6x multiplier 16% 7 extra balls 18% 6x multiplier 14%
    10 extra balls 16% 8x multiplier 16% 10 extra balls 16% 8x multiplier 14%
    12 extra balls 14% 10x multiplier 16% 12 extra balls 16% 10x multiplier 14%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 3 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 8% 2x multiplier 10% 2 extra balls 10% 2x multiplier 8%
    3 extra balls 10% 3x multiplier 12% 3 extra balls 12% 3x multiplier 12%
    4 extra balls 12% 4x multiplier 18% 4 extra balls 16% 4x multiplier 12%
    5 extra balls 16% 5x multiplier 16% 5 extra balls 18% 5x multiplier 14%
    7 extra balls 14% 6x multiplier 18% 7 extra balls 18% 6x multiplier 14%
    10 extra balls 12% 8x multiplier 14% 10 extra balls 14% 8x multiplier 12%
    12 extra balls 10% 10x multiplier 12% 12 extra balls 12% 10x multiplier 10%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 4 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 12% 2x multiplier 12% 2 extra balls 12% 2x multiplier 12%
    3 extra balls 14% 3x multiplier 18% 3 extra balls 18% 3x multiplier 14%
    4 extra balls 14% 4x multiplier 18% 4 extra balls 18% 4x multiplier 12%
    5 extra balls 12% 5x multiplier 18% 5 extra balls 18% 5x multiplier 14%
    7 extra balls 14% 6x multiplier 14% 7 extra balls 14% 6x multiplier 14%
    10 extra balls 10% 8x multiplier 12% 10 extra balls 12% 8x multiplier 10%
    12 extra balls 6% 10x multiplier 8% 12 extra balls 8% 10x multiplier 6%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 5 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 14% 2 extra balls 14% 2x multiplier 14%
    3 extra balls 14% 3x multiplier 16% 3 extra balls 18% 3x multiplier 14%
    4 extra balls 14% 4x multiplier 18% 4 extra balls 18% 4x multiplier 14%
    5 extra balls 14% 5x multiplier 18% 5 extra balls 16% 5x multiplier 14%
    7 extra balls 12% 6x multiplier 18% 7 extra balls 18% 6x multiplier 12%
    10 extra balls 8% 8x multiplier 10% 10 extra balls 10% 8x multiplier 8%
    12 extra balls 6% 10x multiplier 6% 12 extra balls 6% 10x multiplier 6%
    1 free game 4% 1 free game 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 6 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 18% 2 extra balls 18% 2x multiplier 14%
    3 extra balls 16% 3x multiplier 18% 3 extra balls 18% 3x multiplier 16%
    4 extra balls 16% 4x multiplier 20% 4 extra balls 20% 4x multiplier 14%
    5 extra balls 14% 5x multiplier 20% 5 extra balls 20% 5x multiplier 16%
    7 extra balls 12% 6x multiplier 14% 7 extra balls 14% 6x multiplier 12%
    10 extra balls 6% 8x multiplier 6% 10 extra balls 6% 8x multiplier 6%
    12 extra balls 4% 10x multiplier 4% 12 extra balls 4% 10x multiplier 4%
    1 free game 4% 1 free game 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 7 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 18% 2 extra balls 18% 2x multiplier 14%
    3 extra balls 16% 3x multiplier 18% 3 extra balls 18% 3x multiplier 14%
    4 extra balls 14% 4x multiplier 18% 4 extra balls 18% 4x multiplier 16%
    5 extra balls 14% 5x multiplier 18% 5 extra balls 18% 5x multiplier 14%
    7 extra balls 14% 6x multiplier 16% 7 extra balls 16% 6x multiplier 14%
    10 extra balls 6% 8x multiplier 8% 10 extra balls 8% 8x multiplier 6%
    12 extra balls 4% 10x multiplier 4% 12 extra balls 4% 10x multiplier 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 8 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 18% 2 extra balls 18% 2x multiplier 14%
    3 extra balls 16% 3x multiplier 20% 3 extra balls 20% 3x multiplier 16%
    4 extra balls 16% 4x multiplier 20% 4 extra balls 20% 4x multiplier 16%
    5 extra balls 16% 5x multiplier 20% 5 extra balls 20% 5x multiplier 14%
    7 extra balls 12% 6x multiplier 12% 7 extra balls 14% 6x multiplier 12%
    10 extra balls 4% 8x multiplier 6% 10 extra balls 4% 8x multiplier 6%
    12 extra balls 4% 10x multiplier 4% 12 extra balls 4% 10x multiplier 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 9 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 18% 2 extra balls 18% 2x multiplier 14%
    3 extra balls 16% 3x multiplier 20% 3 extra balls 20% 3x multiplier 16%
    4 extra balls 16% 4x multiplier 20% 4 extra balls 20% 4x multiplier 18%
    5 extra balls 16% 5x multiplier 18% 5 extra balls 20% 5x multiplier 14%
    7 extra balls 12% 6x multiplier 14% 7 extra balls 14% 6x multiplier 10%
    10 extra balls 4% 8x multiplier 6% 10 extra balls 4% 8x multiplier 6%
    12 extra balls 4% 10x multiplier 4% 12 extra balls 4% 10x multiplier 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

    Pick 10 BonusesExpand

    Table 1 Table 2
    Left Spinner Right Spinner Left Spinner Right Spinner
    Win Probability Win Probability Win Probability Win Probability
    2 extra balls 14% 2x multiplier 18% 2 extra balls 18% 2x multiplier 14%
    3 extra balls 16% 3x multiplier 20% 3 extra balls 20% 3x multiplier 16%
    4 extra balls 16% 4x multiplier 20% 4 extra balls 20% 4x multiplier 14%
    5 extra balls 16% 5x multiplier 18% 5 extra balls 20% 5x multiplier 16%
    7 extra balls 10% 6x multiplier 14% 7 extra balls 14% 6x multiplier 12%
    10 extra balls 6% 8x multiplier 6% 10 extra balls 4% 8x multiplier 6%
    12 extra balls 4% 10x multiplier 4% 12 extra balls 4% 10x multiplier 4%
    1 free game 4% 1 free game 4%
    2 free games 8% 2 free games 8%
    3 free games 4% 3 free games 4%
    4 free games 2% 4 free games 2%

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.

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