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Wolf Run Keno
Introduction
Wolf Run Keno is a keno variant by Action Gaming. The game features a free spin bonus with random multipliers, which can last over many spins.
Rules
- The game is based on conventional keno, which I assume the reader is familiar with.
- As in convention keno, the player will choose 3 to 10 spots. The game rules call these Marked Spots.
- Next, the player will pick five Bonus Spots.
- The player choose to let the game pick the Marked and/or Bonus spots randomly.
- As in conventional keno, the game will draw 20 random numbers and the player will be paid according to how many match his chosen non-bonus spots and a pay table.
- If the 20 ball draw by the game results in hitting at least four Bonus Spots, then the player shall play the bonus.
- In the first stage of the Bonus, the player will pick Free Game Multipliers. If four Bonus Spots are hit, the player will receive five multipliers. If five Bonus Spots are hit, he will received ten multipliers.
- The count of each possible multiplier is shown in the table below.
- After the selection of multipliers, the bonus will go into the second free spin stage.
- In free spins, the player will have the same number of spots as the initiating spin. The player may choose different spots, including Bonus Spots, if he wishes.
- The game will arrange the multipliers in order, from lowest to highest.
- Before the 20-ball draw, the game will pick a random unchosen spot to place a "Multiplier Shield." This shield will indicate the current multiplier.
- Any win from the ball draw will be multiplied by whatever the current multiplier is. The win does not depend on whether the Multiplier Shield is hit.
- If the Multiplier Shield is hit, then the game shall advance to the next available multiplier. In other words, it is a bad thing for the Multiplier Shield to be hit.
- Free games may trigger the bonus. If this happens, I assume the new multipliers are added to the ones prior to the bonus re-trigger.
- The bonus ends when the last Multiplier Shield is hit.
- There is a maximum limit in the bonus of 100 multipliers, 600 free spins, or a win of 20,000x the initiating bet.
The following pay table was taken from VideoPoker.com. I would expect most casinos to use stingier pay tables than this one.
VideoPoker.com Pay Table
| 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 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 16 | 2 | 1 | 1 | 1 | 0 | 0 | 0 |
| 4 | 23 | 18 | 6 | 2 | 2 | 1 | 1 | |
| 5 | 108 | 14 | 6 | 6 | 4 | 2 | ||
| 6 | 210 | 34 | 23 | 14 | 5 | |||
| 7 | 635 | 210 | 36 | 17 | ||||
| 8 | 2500 | 710 | 210 | |||||
| 9 | 3500 | 1250 | ||||||
| 10 | 5000 |
The following table shows the count of each possible multiplier according to whether four or five Bonus Spots were hit.
Multiplier Table
| Multiplier | Four Bonus Spots | Five Bonus Spots |
|---|---|---|
| 2 | 5 | 4 |
| 3 | 4 | 3 |
| 4 | 2 | 1 |
| 5 | 2 | 1 |
| 6 | 2 | 1 |
| 7 | 0 | 1 |
| 8 | 0 | 1 |
| 9 | 0 | 1 |
| 10 | 1 | 1 |
| 11 | 0 | 1 |
| 12 | 0 | 1 |
| 15 | 0 | 1 |
| 20 | 0 | 1 |
| 25 | 0 | 1 |
| Total | 16 | 19 |
Example
The following bonus example is based on a bet of one credit in the initiating spin.
In the image above, I chose the numbers 11 to 15 as my Bonus Spots. The game draw hit four of them, as evidenced by being marked with a wolf howling at the full moon.
In the image above I'm presented with 11 icons and directed to pick five of them.
The image above shows five I chose marked in green (3x, 3x, 3x, 4x, and 6x). The others show the unchosen multipliers. The average of all multipliers in this bonus was 39/11 =~ 3.5455.
The above image shows I choose to keep my picks the same. My ten Marked Spots are marked with X's. The five Bonus Spots are marked with wolves. You can also see my multipliers in the panel on left. One of the 3x multipliers is highlighted, which will apply to the next game.
The image above shows the second free game. Only two Marked Spots were hit, which didn't win anything. Unfortunately, the Multiplier Shield was hit on number 72. It is hard to tell, but the background behind the shield is dark purple, indicating it was hit. That caused the game to advance to the second of my five multipliers, another 3x, in the next free game.
In the game above, I caught six of my ten Marked Spots, for a base win of 5. At the time, I was using my second 3x multiplier, so my win for that spin was 5×3 = 15. The lower right corner shows a win of 18, because I won 3 credits on a previous spin.
The image above is from later in the bonus, when I hit five Marked Spots with my final multiplier of 6x, for a win of 2×6 = 12 for that game.
The image above is my final game of the bonus. You can see the Multiplier Shield is on 39 and it was hit, as evidenced by the dark purple background. Only two Marked Spots were hit for a win of zero on that spin.
The image above summarizes my bonus results -- 23 games played and a win of 43 credits.
Analysis
Let me start with the easy part, the base game. I already stated the VideoPoker.com pay table in the rules section. The following table shows the return for any combination of number of picks and catches.
Base Game Return Table
| 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 | 0.138754 | 0.212635 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 3 | 0.222006 | 0.086496 | 0.083935 | 0.129820 | 0.174993 | 0.000000 | 0.000000 | 0.000000 |
| 4 | 0.070458 | 0.217662 | 0.171228 | 0.104382 | 0.163007 | 0.114105 | 0.147319 | |
| 5 | 0.069652 | 0.043339 | 0.051831 | 0.109816 | 0.130406 | 0.102855 | ||
| 6 | 0.027087 | 0.024891 | 0.054434 | 0.080074 | 0.057397 | |||
| 7 | 0.015496 | 0.033696 | 0.021300 | 0.027389 | ||||
| 8 | 0.010864 | 0.023141 | 0.028438 | |||||
| 9 | 0.002535 | 0.007651 | ||||||
| 10 | 0.000561 | |||||||
| Total | 0.360759 | 0.369589 | 0.371249 | 0.371473 | 0.371592 | 0.371817 | 0.371561 | 0.371611 |
As you can see, the base game return ranges from 37.0% to 37.2% for all number of picks, except three. I would like to emphasize this is based on the VideoPoker.com pay table, which is probably the most liberal one available. Most casino slot managers will choose a stingier one.
The probability of catching at least four Bonus Spots is 0.012737. Of those bonuses, 94.9% will be for catching four Bonus Spots and 5.1% for catching all five. The probability of at least four Bonus Spots is 0.012737.
The average multiplier for catching four Bonus Spots is 3.875. For catching five, it is 7.842105. A weighted average is 4.075866.
The weighted average of the number of spins per bonus is 21.012658. When considering infinite possible bonus re-triggers, the average final number of final spins per bonus is 28.691853.
Overall, the average value of the bonus feature is 28.691853 × 7.842105 = 116.944152 times the value of the base pay table. Taking the product of that with the bonus probability, we get a bonus value of 0.012737 × 116.94415 = 1.489548 times the value of the base pay table.
The following table shows the total return to player from both the base table and the bonus feature.
Return to Player Summary
| Pick | Base Game | Bonus | Total |
|---|---|---|---|
| 3 | 36.08% | 53.74% | 89.81% |
| 4 | 36.96% | 55.05% | 92.01% |
| 5 | 37.12% | 55.30% | 92.42% |
| 6 | 37.15% | 55.33% | 92.48% |
| 7 | 37.16% | 55.35% | 92.51% |
| 8 | 37.18% | 55.38% | 92.57% |
| 9 | 37.16% | 55.35% | 92.50% |
| 10 | 37.16% | 55.35% | 92.51% |
Acknowledgements
I would like to thank VideoPoker.com for sharing with me the multiplier table, which is not indicated in the game rules.
External Links
Discussion about Wolf Run Keno in my forum at WizardOfVegas.com.