# Hundred Play Wheel Poker

## Introduction

Hundred Play Wheel Poker plays like conventional 100-Play Video Poker for one to five coins bet per play. If the player bets a sixth coin, he will be awarded a wheel spin for a four of a kind on the draw. This sixth coin bet per play is a fee. If the player wins more than one four of a kind on the draw, then the possible wins on the wheel will be multiplied by the number of four of a kinds won.

In games with wild cards, all cards are treated as natural for purposes of triggering the Wheel Bonus. For example, in deuces wild, 2222Q or QQQQK would trigger the bonus, but 2QQQK would not.

The following table shows the possible wins on the wheel per four of a kind and the weighting of each. The column for "jacks or better" applies to all games where the minimum win is for a pair of jacks or better.

### Wheel Weights

Win Jacks
or
Better
Deuces
Wild
Deuces
Wild
Bonus
Super
Bonus
Deuces
Joker
Wild
175 10 5 6 8 5
4000 1 1 1 1 1
225 9 9 9 9 9
500 18 18 18 18 18
200 11 9 10 10 9
275 8 8 8 8 8
1000 3 3 3 3 3
250 10 10 10 10 10
600 12 15 14 14 15
375 26 26 26 26 26
750 8 12 11 9 12
Average 427.80 458.19 449.78 439.87 458.19

## Example

The following screenshots were taken from VideoPoker.com, with permission.

In the image above, I am playing Bonus Poker and get a three of a kind on the deal, which I held.

On the draw, I win five four-of-a-kinds.

The slices on the prize normally range from 200 to 4000. However, since I triggered the bonus five times, all slices are multiplied by 5, for a range of 1000 to 20,000. The wheel stops on 1,875.

In the the end, my win consisted of:

• 88 three of a kinds = 88×15 = 1320.
• 7 full houses = 7×35 = 245
• 5 four of a kinds = 5×125 = 625
• Bonus = 1875

The total win is thus 4065.

## Analysis

The following table shows my analysis of the "Jacks or Better" wheel. These reel weights apply to all games with a minimum win of a pair of jacks or better. The lower right cell shows an average win of 427.801724.

### Jacks or Better Wheel

Win Weight Probability Return
175 10 0.086207 15.086207
4000 1 0.008621 34.482759
225 9 0.077586 17.456897
500 18 0.155172 77.586207
200 11 0.094828 18.965517
275 8 0.068966 18.965517
1000 3 0.025862 25.862069
250 10 0.086207 21.551724
600 12 0.103448 62.068966
375 26 0.224138 84.051724
750 8 0.068966 51.724138
Totals 116 1.000000 427.801724

The following table shows my analysis of the Deuces Wild wheel. The lower right cell shows an average win of 458.189655.

### Deuces Wild Wheel

Win Weight Probability Return
175 5 0.043103 7.543103
4000 1 0.008621 34.482759
225 9 0.077586 17.456897
500 18 0.155172 77.586207
200 9 0.077586 15.517241
275 8 0.068966 18.965517
1000 3 0.025862 25.862069
250 10 0.086207 21.551724
600 15 0.129310 77.586207
375 26 0.224138 84.051724
750 12 0.103448 77.586207
Totals 116 1.000000 458.189655

The following table shows my analysis of the Deuces Wild Bonus wheel. The lower right cell shows an average win of 449.784483.

### Deuces Wild Bonus Wheel

Win Weight Probability Return
175 6 0.051724 9.051724
4000 1 0.008621 34.482759
225 9 0.077586 17.456897
500 18 0.155172 77.586207
200 10 0.086207 17.241379
275 8 0.068966 18.965517
1000 3 0.025862 25.862069
250 10 0.086207 21.551724
600 14 0.120690 72.413793
375 26 0.224138 84.051724
750 11 0.094828 71.120690
Totals 116 1.000000 449.784483

The following table shows my analysis of the Super Bonus Deuces Wild wheel. The lower right cell shows an average win of 439.870690.

### Super Bonus Deuces Wild Wheel

Win Weight Probability Return
175 8 0.068966 12.068966
4000 1 0.008621 34.482759
225 9 0.077586 17.456897
500 18 0.155172 77.586207
200 10 0.086207 17.241379
275 8 0.068966 18.965517
1000 3 0.025862 25.862069
250 10 0.086207 21.551724
600 14 0.120690 72.413793
375 26 0.224138 84.051724
750 9 0.077586 58.189655
Totals 116 1.000000 439.870690

The following table shows my analysis of the Joker Poker wheel. The lower right cell shows an average win of 458.189655.

### Joker Poker Wheel

Win Weight Probability Return
175 5 0.043103 7.543103
4000 1 0.008621 34.482759
225 9 0.077586 17.456897
500 18 0.155172 77.586207
200 9 0.077586 15.517241
275 8 0.068966 18.965517
1000 3 0.025862 25.862069
250 10 0.086207 21.551724
600 15 0.129310 77.586207
375 26 0.224138 84.051724
750 12 0.103448 77.586207
Totals 116 1.000000 458.189655

To calculate the return of the game, simply add the average wheel spin value to the pay for a four of a kind. For example, in jacks or better a four of a kind pays 125. To this value, add the average wheel win of 427.80172, for a total win per four of a kind of 552.80172. Then put that win and the standard win for all others in my video poker calculator.

In general, the probability of four of a kind on the draw is about 0.0024 in games with no wild cards. Assuming that probability exactly, the expected return per play is 0.0024 × 427.801724 = 1.026724. Thus, paying an extra coin to enable the wheel is a good value. The value gets even marginally better with strategy changes to more aggressively go after four of a kinds. The overall increase to the return for betting six coins per play compared to five ranges from 0.004% to 2.034%. The more generous the base pay table, the lesser the benefit of betting the sixth coin. Also, the more four of a kinds pay to begin with, the greater the benefit of betting the sixth coin.

Our friends at VideoPoker.com were kind enough to provide me all the available games and pay tables as well as the return for each one for 1 to 6 coins bet. Follows is that list.

### Full Return Table

Game Pay Table 1-4 Coins 5 Coins 6 Coins
Triple Triple Bonus 9-5 0.973696 0.986087 0.988656
Triple Triple Bonus 8-5 0.963119 0.975516 0.979842
Triple Triple Bonus 7-5 0.952547 0.964948 0.972365
Triple Triple Bonus 6-5 0.941982 0.954392 0.965425
Double Double Bonus 9-5 0.966409 0.978729 0.987532
Double Double Bonus 8-5 0.955539 0.967861 0.980585
Double Double Bonus 7-5 0.944795 0.957120 0.973654
Double Double Bonus 6-5 0.934238 0.946569 0.966735
Triple Double Bonus 9-6 0.970264 0.981540 0.984713
Triple Double Bonus 9-5 0.957820 0.970204 0.975930
Triple Double Bonus 8-5 0.947295 0.959687 0.967136
Triple Double Bonus 7-5 0.936773 0.949178 0.959679
Super Double Bonus 6-5 0.956584 0.968710 0.985054
Double Bonus 9-6-5 0.966635 0.978062 0.985340
Double Bonus 9-6-4 0.952365 0.963754 0.974321
Double Bonus 8-5-4 0.929740 0.941897 0.958310
Double Bonus 7-5-4 0.918905 0.931060 0.951396
Bonus Poker 7-5 0.967795 0.980147 0.987232
Bonus Poker 6-5 0.956329 0.968687 0.978676
Bonus Poker 10-8-5-3-1 0.931122 0.941829 0.950055
Bonus Poker Deluxe 8-5 0.961937 0.974009 0.986512
Bonus Poker Deluxe 7-5 0.950447 0.962526 0.979569
Bonus Poker Deluxe 6-5 0.941523 0.953611 0.972631
Jacks or Better 9-5 0.972156 0.984498 0.989393
Jacks or Better 8-6 0.972233 0.983927 0.988585
Jacks or Better 8-5 0.960635 0.972984 0.979722
Jacks or Better 7-5 0.949117 0.961472 0.971043
Jacks or Better 6-5 0.937600 0.949961 0.962501
White Hot Aces 7-5 0.961970 0.974405 0.988131
White Hot Aces 6-5 0.951416 0.963861 0.981207
Double Double Bonus Plus 8-5 0.960144 0.972462 0.984647
Double Double Bonus Plus 7-5 0.949399 0.961719 0.977704
Double Double Bonus Plus 6-5 0.938843 0.951165 0.970784
Deuces Wild 25-15-9-4-4-3 0.976864 0.989131 0.989367
Deuces Wild 20-12-10-4-4-3 0.963761 0.975791 0.977638
Deuces Wild 20-12-9-4-4-3 0.958529 0.970554 0.973716
Deuces Wild 25-16-13-4-3-2 0.955600 0.967651 0.969844
Deuces Wild 20-10-8-4-4-3 0.947612 0.959638 0.959694
Deuces Wild 25-15-10-4-3-2 0.936144 0.948182 0.950030
Deuces Wild Bonus 13-4-3-3 0.975604 0.988025 0.989621
Deuces Wild Bonus 10-4-3-3 0.961235 0.973644 0.978363
Deuces Wild Bonus 12-4-3-2 0.950119 0.962183 0.970475
Deuces Wild Bonus 10-4-3-2 0.941334 0.953368 0.955013
Super Bonus Deuces Wild 25-12-9-4-3-2 0.976371 0.988366 0.989076
Super Bonus Deuces Wild 25-10-8-4-3-2 0.966703 0.978713 0.981152
Super Bonus Deuces Wild 25-10-6-4-3-2 0.959182 0.971234 0.975064
Super Bonus Deuces Wild 20-10-8-4-3-2 0.957598 0.969435 0.970216
Joker Poker (kings or better) 940-200-100-50-16-7-5 0.963596 0.975929 0.975965
Joker Poker (kings or better) 100-800-100-16-8-5 0.935541 0.971923 0.972836
Joker Poker (kings or better) 940-200-100-50-15-7-5 0.955063 0.967435 0.968741
Joker Poker (kings or better) 800-200-100-50-15-7-5 0.955063 0.963848 0.966036
Joker Poker (kings or better) 800-200-100-40-20-5-4 0.948029 0.954570 0.958935

I spot checked some of these returns. With six-coins bet, I sometimes agreed and sometimes was a little off. For example, with 6-5 Double Double Bonus, I get a six-coin return of 0.966385. VideoPoker.com claims it is 0.966735. My return is 0.000351 less. Following is my return table for that game.

### 6-5 Double Double Bonus Return Table

Win Pays Combinations Probability Return
Royal Flush 4,000 41,290,830 0.000025 0.016572
Straight Flush 250 169,472,231 0.000107 0.004458
Four Aces with any 2,3,4 2,427.80 103,036,197 0.000061 0.024683
Four 2s, 3s, 4s with any A,2,3,4 1,227.80 246,396,238 0.000147 0.030081
Four Aces 1,227.80 290,627,040 0.000173 0.035402
Four 2s, 3s, 4s 827.80 663,837,093 0.000395 0.054497
Four 5s thru Ks 677.80 2,870,923,896 0.001724 0.194755
Full House 30 13,783,328,064 0.008236 0.041180
Flush 25 17,301,948,709 0.011108 0.046283
Straight 20 20,820,426,543 0.014139 0.047130
Three of a Kind 15 131,380,864,501 0.078340 0.195850
Two Pair 5 182,864,573,055 0.108699 0.090583
Jacks or Better 5 375,020,716,704 0.221894 0.184912
All Other 0 915,545,101,999 0.554952 0.000000
Totals   1,661,102,543,100 1.000000 0.966385

## Acknowledgements

I would like to thank VideoPoker.com for sharing their list of games and returns as well as permission to use the screen shots seen above.