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Wheel of Fortune Poker
Introduction
Wheel of Fortune Poker is a video poker variant based on multi-play machines. The game plays normally for one to five credits bet per play. For an extra five credits bet (not per play but just five in total) the player will have a chance at winning a wheel spin.
Rules
- The game is based on multi-play video poker.
- If the player bets one to five credits per play, the game plays according to conventional multi-play video poker rules, which I assume the reader is familiar with.
- For an extra five credits bet, the player will have a chance at a wheel spin. I emphasize the additional bet is five credits only and does not depend on the number of plays, as most video poker games with a bonus feature do.
- If the additional wager is made and the player gets a winning hand on the DEAL, then he will have a chance at the wheel spin. This chance depends on the game, pay table and number of plays, but is never far from 9%. The way this is shown to the player is if the player gets a winning hand on the deal, the player will get a chance at solving a word puzzle. I emphasize the player has no free will in actually solving the puzzle. About 9% of the time, the puzzle will be solved by an unseen voice and the rest of the time this voice will suggest a letter not in the puzzle and not get a wheel spin.
- The player does not need to hold the winning hand that may trigger a wheel spin. It is determined when the spin is one before the draw.
- If a spin is won, it will be awarded after the draw in the video poker game.
- In addition, if the player makes the additional five-credit wager, a dealt natural royal flush will pay 10,000 credits per play, as opposed to the usual 4,000.
- The possible prizes and weights of the wheel depend on the number of plays and are shown below.
- A probability of winning a wheel spin, given a winning hand on the deal, is shown for some games below.
The following table shows the possible prizes and weights for the Wheel Spin in 3-play mode. The lower right cell shows an average win of 264.892127 credits.
| Win | Weight | Probability | Return |
|---|---|---|---|
| 300 | 200 | 0.056038 | 16.811432 |
| 125 | 170 | 0.047632 | 5.954049 |
| 6000 | 3 | 0.000841 | 5.043430 |
| 75 | 6 | 0.001681 | 0.126086 |
| 600 | 125 | 0.035024 | 21.014290 |
| 150 | 200 | 0.056038 | 8.405716 |
| 500 | 150 | 0.042029 | 21.014290 |
| 230 | 350 | 0.098067 | 22.555338 |
| 800 | 18 | 0.005043 | 4.034744 |
| 175 | 220 | 0.061642 | 10.787335 |
| 325 | 175 | 0.049033 | 15.935836 |
| 100 | 120 | 0.033623 | 3.362286 |
| 2000 | 7 | 0.001961 | 3.922667 |
| 140 | 175 | 0.049033 | 6.864668 |
| 250 | 325 | 0.091062 | 22.765481 |
| 200 | 300 | 0.084057 | 16.811432 |
| 375 | 155 | 0.043430 | 16.286075 |
| 180 | 250 | 0.070048 | 12.608574 |
| 1000 | 10 | 0.002802 | 2.801905 |
| 105 | 160 | 0.044830 | 4.707201 |
| 750 | 100 | 0.028019 | 21.014290 |
| 225 | 350 | 0.098067 | 22.065004 |
| Total | 3569 | 1.000000 | 264.892127 |
The following table shows the possible prizes and weights for the Wheel Spin in 5-play mode. The lower right cell shows an average win of 268.254413 credits. Note the table is the same as for 3-play, except the top award is 10,000 instead of 6,000.
| Win | Weight | Probability | Return |
|---|---|---|---|
| 300 | 200 | 0.056038 | 16.811432 |
| 125 | 170 | 0.047632 | 5.954049 |
| 10000 | 3 | 0.000841 | 8.405716 |
| 75 | 6 | 0.001681 | 0.126086 |
| 600 | 125 | 0.035024 | 21.014290 |
| 150 | 200 | 0.056038 | 8.405716 |
| 500 | 150 | 0.042029 | 21.014290 |
| 230 | 350 | 0.098067 | 22.555338 |
| 800 | 18 | 0.005043 | 4.034744 |
| 175 | 220 | 0.061642 | 10.787335 |
| 325 | 175 | 0.049033 | 15.935836 |
| 100 | 120 | 0.033623 | 3.362286 |
| 2000 | 7 | 0.001961 | 3.922667 |
| 140 | 175 | 0.049033 | 6.864668 |
| 250 | 325 | 0.091062 | 22.765481 |
| 200 | 300 | 0.084057 | 16.811432 |
| 375 | 155 | 0.043430 | 16.286075 |
| 180 | 250 | 0.070048 | 12.608574 |
| 1000 | 10 | 0.002802 | 2.801905 |
| 105 | 160 | 0.044830 | 4.707201 |
| 750 | 100 | 0.028019 | 21.014290 |
| 225 | 350 | 0.098067 | 22.065004 |
| Total | 3569 | 1.000000 | 268.254413 |
The following table shows the possible prizes and weights for the Wheel Spin in 10-play mode. The lower right cell shows an average win of 276.660129 credits. Note the table is the same as for 3-play, except the top award is 20,000 instead of 6,000.
| Win | Weight | Probability | Return |
|---|---|---|---|
| 300 | 200 | 0.056038 | 16.811432 |
| 125 | 170 | 0.047632 | 5.954049 |
| 20000 | 3 | 0.000841 | 16.811432 |
| 75 | 6 | 0.001681 | 0.126086 |
| 600 | 125 | 0.035024 | 21.014290 |
| 150 | 200 | 0.056038 | 8.405716 |
| 500 | 150 | 0.042029 | 21.014290 |
| 230 | 350 | 0.098067 | 22.555338 |
| 800 | 18 | 0.005043 | 4.034744 |
| 175 | 220 | 0.061642 | 10.787335 |
| 325 | 175 | 0.049033 | 15.935836 |
| 100 | 120 | 0.033623 | 3.362286 |
| 2000 | 7 | 0.001961 | 3.922667 |
| 140 | 175 | 0.049033 | 6.864668 |
| 250 | 325 | 0.091062 | 22.765481 |
| 200 | 300 | 0.084057 | 16.811432 |
| 375 | 155 | 0.043430 | 16.286075 |
| 180 | 250 | 0.070048 | 12.608574 |
| 1000 | 10 | 0.002802 | 2.801905 |
| 105 | 160 | 0.044830 | 4.707201 |
| 750 | 100 | 0.028019 | 21.014290 |
| 225 | 350 | 0.098067 | 22.065004 |
| Total | 3569 | 1.000000 | 276.660129 |
The following table is a sampling of the probability of solving the puzzle (and thus spinning the Wheel) given a winning hand on the draw. Please note there are many other games and pay tables available. Note the probability ranges from 8.72% to 9.83%. There is a negative correlation between the number of plays and the probability. This makes sense because the dealt royal flush feature is more valuable according to the number of plays.
| Game | Weight | Plays | Probability |
|---|---|---|---|
| Bonus Poker | 8-5 | 3 | 0.090890 |
| Deuces Wild | 25-15-10-4-3-2 | 3 | 0.098289 |
| Double Bonus | 9-7-5 | 3 | 0.090872 |
| Jacks or Better | 7-5 | 3 | 0.088347 |
| Joker Poker | 40-20-5-4-3-2 | 3 | 0.092772 |
| Super Double Bonus | 6-5 | 3 | 0.089009 |
| Super Double Bonus | 7-5 | 3 | 0.089833 |
| Super Double Bonus | 8-5 | 3 | 0.090671 |
| Super Double Bonus | 9-5 | 3 | 0.091319 |
| Super Double Double Bonus | 6-5 | 3 | 0.089763 |
| Super Double Double Bonus | 8-5 | 3 | 0.091307 |
| Triple Double Bonus | 9-5 | 3 | 0.089146 |
| Bonus Poker | 8-5 | 5 | 0.089823 |
| Bonus Poker | 7-5 | 5 | 0.089108 |
| Joker Poker | 40-20-5-4-3-2 | 5 | 0.091990 |
| Double Double Bonus | 9-6 | 10 | 0.087596 |
| Jacks or Better | 9-5 | 10 | 0.087220 |
| Jacks or Better | 9-6 | 10 | 0.087600 |
| Joker Poker | 40-20-5-4-3-2 | 10 | 0.090118 |
Example
The following example is based on 9-6 Jacks or Better 5-play.
In the image above I am dealt a paying hand of a two pair. The puzzle is automatically solved for me, which has about an 8.8% chance of happening.
Before I spin the wheel for solving the puzzle, I finish playing out the hand. I hold the two pair and discard the singleton.
Four of the plays do not improve and one does to a full house.
After playing out my video poker hand, I spin the wheel, which lands on 200 credits.
In the end, I win 10 credits for each of 4 two pairs, 45 for one full house, and 200 for the wheel spin, for a total win of (4*10) + 45 + 200 = 285.
8-5 Bonus Poker Analysis
The way I look at this game is it is a side bet on top of conventional multi-play video poker. So, my analysis is mostly of the side bet by itself, since video poker has already been analyzed. Much like I usually don't have to reanalyze blackjack in an analysis of a blackjack side bet.
For my analysis, I shall look at 5-play 8-5 Bonus Poker.
In this game, the probability of solving the puzzle, given that the player has a winning hand on the deal, is 0.089823. The probability of being dealt a winning hand in any jacks or better based game is 0.206275. The average wheel spin in any 5-play game is 268.254413. This makes the value of the expected win of the side bet equal to prob(winning hand on deal) × prob(solving the puzzle) × average Wheel award = 0.206275 × 0.089823 × 268.254413 = 4.970278.
There is also the value of the additional win of 10,000 per play for a dealt royal. The probability of a dealt royal is 4/2,598,960. The additional win per play is 10,000 - 4,000 = 6,000. The number of plays is 5. Thus, the value of this feature is (4/2,598,960) × 6,000 × 5 = 0.046172.
The total value of the side bet is 4.970278 + 0.046172 = 5.016450. Divided by the five-credit bet cost, the RTP (Return to Player) of the side bet is 5.016450/5 = 1.003290.
The RTP of 8-5 Bonus Poker without the feature is 0.991660. The overall RTP, considering the side bet is 1/6 of the total bet, is (5/6)×0.991660 + (1/6)×1.003290 = 0.993598. Note this is an increase of 0.19% compared to the same game without the feature.
25-15-10-4-3-2 3-Play Deuces Wild Analysis
In this game, the probability of solving the puzzle, given that the player has a winning hand on the deal, is 0.098289. The probability of being dealt a winning hand in any deuces wild based game is 0.184394. The average wheel spin in any 3-play game is 264.892127. This makes the value of the expected win of the side bet equal to prob(winning hand on deal) × prob(solving the puzzle) × average Wheel award = 0.184394 × 0.098289 × 264.892127 = 4.800873.
There is also the value of the additional win of 10,000 per play for a dealt royal. The probability of a dealt royal is 4/2,598,960. The additional win per play is 10,000 - 4,000 = 6,000. The number of plays is 3. Thus, the value of this feature is (4/2,598,960) × 6,000 × 3 = 0.027703.
The total value of the side bet is 4.800873 + 0.027703 = 4.828576. Divided by the five-credit bet cost, the RTP (Return to Player) of the side bet is 4.828576/5 = 0.965715.
The RTP of 25-15-10-4-3-2 Deuces Wild without the feature is 0.948182. The overall RTP, considering the side bet is 1/4 of the total bet, is (3/4)×0.948182 + (1/4)×0.965715 = 0.952565. Note this is an increase of 0.44% compared to the same game without the feature.
40-20-5-4-3-2 10-Play Joker Poker Analysis
In this game, the probability of solving the puzzle, given that the player has a winning hand on the deal, is 0.090118. The probability of being dealt a winning hand in any joker wild kings-or-better based game is 0.195845. The average wheel spin in any 10-play game is 276.660129. This makes the value of the expected win of the side bet equal to prob(winning hand on deal) × prob(solving the puzzle) × average Wheel award = 0.195845 × 0.090118 × 276.660129 = 4.882815.
There is also the value of the additional win of 10,000 per play for a dealt royal. The probability of a dealt royal is 4/2869685. The additional win per play is 10,000 - 4,000 = 6,000. The number of plays is 10. Thus, the value of this feature is (4/2869685) × 6,000 × 10 = 0.083633.
The total value of the side bet is 4.882815 + 0.083633 = 4.966448. Divided by the five-credit bet cost, the RTP (Return to Player) of the side bet is 4.966448/5 = 0.993290.
The RTP of 40-20-5-4-3-2 Joker Wild without the feature is 0.954570. The overall RTP, considering the side bet is 1/11 of the total bet, is (10/11)×0.954570 + (1/11)×0.993290 = 0.958090. Note this is an increase of 0.35% compared to the same game without the feature.
Summary
The following table shows the return with and without the feature for some various games and pay tables. I emphasize this is just a random sampling and many others are available.
| Game | Pay Table | Plays | Return Base Game |
Return Feature |
Combined Return |
|---|---|---|---|---|---|
| Bonus Poker | 8-5 | 3 | 0.991660 | 0.998797 | 0.993444 |
| Deuces Wild | 25-15-10-4-3-2 | 3 | 0.948182 | 0.965715 | 0.952565 |
| Double Bonus | 9-7-5 | 3 | 0.991065 | 0.998600 | 0.992949 |
| Jacks or Better | 7-5 | 3 | 0.961472 | 0.971006 | 0.963856 |
| Joker Poker | 40-20-5-4-3-2 | 3 | 0.954570 | 0.967579 | 0.957822 |
| Super Double Bonus | 6-5 | 3 | 0.968710 | 0.978241 | 0.971093 |
| Super Double Bonus | 7-5 | 3 | 0.977708 | 0.987246 | 0.980092 |
| Super Double Bonus | 8-5 | 3 | 0.986863 | 0.996403 | 0.989248 |
| Super Double Bonus | 9-5 | 3 | 0.996946 | 1.003485 | 0.998581 |
| Super Double Double Bonus | 6-5 | 3 | 0.976942 | 0.986481 | 0.979327 |
| Super Double Double Bonus | 8-5 | 3 | 0.996859 | 1.003354 | 0.998483 |
| Triple Double Bonus | 9-5 | 3 | 0.970204 | 0.979738 | 0.972588 |
| Bonus Poker | 8-5 | 5 | 0.991660 | 1.003288 | 0.993598 |
| Bonus Poker | 7-5 | 5 | 0.980147 | 0.995376 | 0.982685 |
| Joker Poker | 40-20-5-4-3-2 | 5 | 0.954570 | 0.974924 | 0.957962 |
| Double Double Bonus | 9-6 | 10 | 0.989808 | 1.018254 | 0.992394 |
| Jacks or Better | 9-5 | 10 | 0.984498 | 1.013963 | 0.987177 |
| Jacks or Better | 9-6 | 10 | 0.995439 | 1.018300 | 0.997517 |
| Joker Poker | 40-20-5-4-3-2 | 10 | 0.954570 | 0.993290 | 0.958090 |
My returns agree of those kindly provided to me by VideoPoker.com, except for 9-6 Double Double Bonus 10-play. In that game, VideoPoker.com reports an RTP of 99.657%, compared to mine of 99.239%. You will have to decide for yourself whom (or is it "who") to believe.
Acknowledgement
I would like to give a big thank you to VideoPoker.com for providing me with the probabilities of solving the puzzle and tables of wheel prizes/weights. In addition, I thank them for their permission to use the screen shots above in the example section. At VideoPoker.com you may play a host of video poker games for free, although I think a paid membership is required for this premium game.