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Wheel Poker Deluxe
Introduction
Wheel Poker Deluxe is a video poker variant I noticed at the Red Rock casino in March 2010. It can also be played for free at VideoPoker.com.
The game can be played like conventional 3-play or 5-play video poker. However, for the price of an additional 5-coin bet, on top of already betting 5 coins on each hand, a bonus feature will be enabled. Specifically, if the player gets any hand containing a three of a kind (including a full house and four of a kind) on the deal with the five-coin bet, the player gets to play the bonus.
The bonus involves a spinning wheel which will stop on one of eleven possible video poker starting hands. The player will then play out that hand and get paid according to the outcome and special bonus pay tables.
Example
Let's look at an example taken from screenshots from VideoPoker.com.
Here I was playing 3-play Bonus Poker, with the bonus feature enabled. I received a three of a kind on the deal, so I earned the bonus.
After playing out the hand, the game asked me to press the "spin" button to spin the wheel.
This is a picture of the spinning wheel, which is why it looks blurry. It stopped on triple-play, holding the A234 of spades.
There is no decision making in regards to what cards to hold; the selection is automatic. The tables at the top show the possible wins. Note the callout box in the lower left that says "Only highest category paid per bonus."
I made one flush, which paid 150. Some of the fields in the image above are missing because they were blinking, and I grabbed the screenshot at the wrong moment.
Bonus Rules
Like many prize wheels, not all stops are equally likely. The following table shows the possible outcomes of the prize wheel, with the associated weight for each stop. The probability of each outcome on the wheel is proportional to the weighting.
Wheel Poker Deluxe Prize Wheel
Number Hands | Cards | Weight |
---|---|---|
3 | AKQ suited | 4 |
3 | A234 suited | 3 |
3 | AKQJ suited | 1 |
5 | AKQ suited | 3 |
5 | 8877 | 4 |
5 | KKK | 3 |
10 | AA | 3 |
10 | AKQ suited | 3 |
10 | 258T suited | 3 |
50 | 258T suited | 3 |
100 | 8877 | 3 |
The next table shows the possible wins for landing on 3-play suited AKQ.
3-play Suited AKQ Pay Table
Number | Pair, 2P, or 3K | Flsh or Str | Royal |
---|---|---|---|
0 | 0 | 0 | 0 |
1 | 125 | 125 | 4000 |
2 | 325 | 3000 | 8000 |
3 | 800 | 3000 | 12000 |
The next table shows the possible wins for landing on 3-play suited A234.
3-play Suited AKQ Pay Table
Number | Pair, Str, or Flsh | Str. Flsh. |
---|---|---|
0 | 0 | 0 |
1 | 150 | 1000 |
2 | 400 | 4000 |
3 | 900 | 4000 |
The next table shows the possible wins for landing on 3-play AKQJ suited.
3-play Suited AKQJ Pay Table
Number | Pair, Str, or Flsh | RF |
---|---|---|
0 | 0 | 0 |
1 | 0 | 4000 |
2 | 25 | 8000 |
3 | 50 | 12000 |
The next table shows the possible wins for landing on 5-play AKQ suited.
5-play Suited AKQ Pay Table
Number | Pair, Str, or Flsh | RF |
---|---|---|
0 | 0 | 0 |
1 | 50 | 4000 |
2 | 150 | 4000 |
3 | 300 | 4000 |
4 | 800 | 4000 |
5 | 1500 | 4000 |
The next table shows the possible wins for landing on 5-play two pair.
5-play Two Pair Pay Table
Number | FH |
---|---|
0 | 50 |
1 | 400 |
2 | 900 |
3 to 5 | 4000 |
The next table shows the possible wins for landing on 5-play three of a kind.
5-play Three of a Kind Pay Table
Number | FH or 4K |
---|---|
0 | 50 |
1 | 300 |
2 | 900 |
3 | 2500 |
4 or 5 | 4000 |
The next table shows the possible wins for landing on 10-play pair.
10-play Pair Pay Table
Number | 2P to FH | 4K |
---|---|---|
0 | 0 | 0 |
1 | 0 | 4000 |
2 | 100 | 4000 |
3 or 4 | 100 | 12000 |
5 or 6 | 450 | 12000 |
7 or 8 | 1000 | 12000 |
9 or 10 | 2000 | 12000 |
The next table shows the possible wins for landing on 10-play suited AKQ.
10-play Suited AKQ Pay Table
Number | Pair to Fl. | RF |
---|---|---|
0 | 0 | 0 |
1 | 0 | 4000 |
2 or 3 | 90 | 4000 |
4 or 5 | 180 | 4000 |
6 or 7 | 450 | 4000 |
8 to 10 | 1000 | 4000 |
The next table shows the possible wins for landing on 10-play suited 258T.
10-play Suited 258T Pay Table
Number | flush |
---|---|
0 | 0 |
1 | 30 |
2 | 60 |
3 | 90 |
4 | 1000 |
5 to 10 | 4000 |
The next table shows the possible wins for landing on 50-play suited 258T.
50-play Suited 258T Pay Table
Number | Flush |
---|---|
0 to 5 | 0 |
6 to 10 | 100 |
11 to 15 | 450 |
16 to 20 | 1100 |
21 to 50 | 4000 |
The next table shows the possible wins for landing on 100-play two pair.
100-play Two Pair Pay Table
Number | FH |
---|---|
0 to 4 | 60 |
5 to 9 | 120 |
10 to 15 | 900 |
16 to 17 | 4000 |
18 to 19 | 8000 |
20 to 100 | 20000 |
Bonus Analysis
The next 11 tables show the probability and return for each possible win for all 11 bonus hands. I won't bother to introduce each table, just look at the table headers. The average win of each bonus game is in the lower right cell of the table. For example, if you get the 3-play suited AKQ bonus, the average win is 218.51.
3-Play Suited AKQ Return Table
Win | Probability | Return |
---|---|---|
0 | 0.223806 | 0.000000 |
125 | 0.433508 | 54.188440 |
325 | 0.275985 | 89.695061 |
800 | 0.057847 | 46.277619 |
2500 | 0.001556 | 3.889557 |
3000 | 0.004749 | 14.248469 |
4000 | 0.002547 | 10.186735 |
12000 | 0.000002 | 0.026016 |
Total | 1.000000 | 218.511898 |
3-Play Suited A234 Return Table
Win | Probability | Return |
---|---|---|
0 | 0.324951 | 0.000000 |
150 | 0.413574 | 62.036133 |
400 | 0.175456 | 70.182292 |
900 | 0.024812 | 22.330729 |
1000 | 0.059923 | 59.922960 |
4000 | 0.001284 | 5.135995 |
Total | 1.000000 | 219.608109 |
3-Play Suited AKQJ Return Table
Win | Probability | Return |
---|---|---|
0 | 0.484375 | 0.000000 |
25 | 0.344401 | 8.610026 |
50 | 0.110017 | 5.500850 |
4000 | 0.059923 | 239.691840 |
8000 | 0.001275 | 10.199653 |
12000 | 0.000009 | 0.108507 |
Total | 1.000000 | 264.110876 |
5-Play Suited AKQ Return Table
Win | Probability | Return |
---|---|---|
0 | 0.082500 | 0.000000 |
50 | 0.266334 | 13.316717 |
150 | 0.343922 | 51.588290 |
300 | 0.222056 | 66.616812 |
800 | 0.071686 | 57.348927 |
1500 | 0.009257 | 13.885428 |
4000 | 0.004244 | 16.977904 |
Total | 1.000000 | 219.734079 |
5-Play 8877 Return Table
Win | Probability | Return |
---|---|---|
50 | 0.647228 | 32.361392 |
400 | 0.294194 | 117.677791 |
900 | 0.053490 | 48.140914 |
4000 | 0.005088 | 20.351080 |
Total | 1.000000 | 218.531178 |
5-Play KKK Return Table
Win | Probability | Return |
---|---|---|
50 | 0.583825 | 29.191270 |
300 | 0.331719 | 99.515692 |
900 | 0.075391 | 67.851608 |
2500 | 0.008567 | 21.417806 |
4000 | 0.000498 | 1.991325 |
Total | 1.000000 | 219.967701 |
5-Play AA Return Table
Win | Probability | Return |
---|---|---|
0 | 0.178835 | 0.000000 |
100 | 0.681879 | 68.187900 |
450 | 0.108250 | 48.712376 |
1000 | 0.006738 | 6.738088 |
2000 | 0.000077 | 0.153796 |
4000 | 0.024220 | 96.879693 |
12000 | 0.000002 | 0.020880 |
Total | 1.000000 | 220.692733 |
10-Play Suited AKQ Return Table
Win | Probability | Return |
---|---|---|
0 | 0.050751 | 0.000000 |
90 | 0.347517 | 31.276521 |
180 | 0.440845 | 79.352115 |
450 | 0.141753 | 63.788708 |
1000 | 0.009250 | 9.250030 |
4000 | 0.009884 | 39.535273 |
Total | 1.000000 | 223.202648 |
10-Play Suited 258T Return Table
Win | Probability | Return |
---|---|---|
0 | 0.125382 | 0.000000 |
30 | 0.289342 | 8.680262 |
60 | 0.300471 | 18.028237 |
90 | 0.184905 | 16.641450 |
1000 | 0.074673 | 74.673172 |
4000 | 0.025228 | 100.910244 |
Total | 1.000000 | 218.933365 |
50-Play Suited 258T Return Table
Win | Probability | Return |
---|---|---|
0 | 0.073079 | 0.000000 |
100 | 0.596476 | 59.647643 |
450 | 0.312950 | 140.827307 |
1100 | 0.017369 | 19.106118 |
4000 | 0.000125 | 0.501223 |
1.000000 | 1.000000 | 220.082291 |
100-Play 8877 Return Table
Win | Probability | Return |
---|---|---|
60 | 0.073266 | 4.395985 |
120 | 0.605125 | 72.614964 |
200 | 0.193651 | 38.730132 |
400 | 0.089964 | 35.985790 |
900 | 0.029453 | 26.507731 |
4000 | 0.007063 | 28.251968 |
8000 | 0.001278 | 10.222293 |
20000 | 0.000200 | 3.998760 |
Total | 1.000000 | 220.707622 |
Now that we know the probability and expected return from each bonus hand, we can find the expected win of the overall bonus, as shown in the table below. The lower right cell shows the bonus is worth, on average, 221.24 coins.
Bonus Return Table
Hands | Bonus Hand | Weight | Probability | Average Win | Expected Return |
---|---|---|---|---|---|
3 | Three to a Royal Flush | 4 | 0.121212 | 218.511898 | 26.486291 |
3 | Four to a Straight Flush | 3 | 0.090909 | 219.608109 | 19.964374 |
3 | Four to a Royal Flush | 1 | 0.030303 | 264.110876 | 8.003360 |
5 | Three to a Royal Flush | 3 | 0.090909 | 219.734079 | 19.975825 |
5 | Two Pair | 4 | 0.121212 | 218.531178 | 26.488628 |
5 | Three of a Kind | 3 | 0.090909 | 219.967701 | 19.997064 |
10 | One Pair | 3 | 0.090909 | 220.692733 | 20.062976 |
10 | Three to a Royal Flush | 3 | 0.090909 | 223.202648 | 20.291150 |
10 | Four to a Flush | 3 | 0.090909 | 218.933365 | 19.903033 |
50 | Four to a Flush | 3 | 0.090909 | 220.082291 | 20.007481 |
100 | Two Pair | 3 | 0.090909 | 220.707622 | 20.064329 |
Total | 1.000000 | 221.244510 |
Game Analysis
We can see from my page on probabilities in poker that the bonus probability is (54,912 + 3,744 + 624)/2,598,960 = 0.022809, or once every 43.84 hands. With an average win of 221.24, the expected win from the bonus before the deal is 0.022809 × 221.24 = 5.046393. The cost of enabling the bonus is 5 coins, making it a good bet. The expected return on the bonus feature is 5.046393/5 = 1.009279. In other words, the additional bonus wager has almost a 1% player advantage. However, the main game still carries a negative expected value. Combining the two, the following table shows the overall return, with and without the bonus wager.
Wheel Poker Deluxe Return Table
Base Game | Pay Table | No Bonus | Bonus 3-Play | Bonus 5-Play |
---|---|---|---|---|
Bonus Poker | 8/5 | 0.991660 | 0.996064 | 0.994596 |
Bonus Poker | 7/5 | 0.980147 | 0.987430 | 0.985002 |
Bonus Poker | 6/5 | 0.968687 | 0.978835 | 0.975452 |
Bonus Deluxe | 9/6 | 0.996417 | 0.999632 | 0.998561 |
Bonus Deluxe | 9/5 | 0.985495 | 0.991441 | 0.989459 |
Bonus Deluxe | 8/6 | 0.984928 | 0.991016 | 0.988987 |
Bonus Deluxe | 8/5 | 0.974009 | 0.982827 | 0.979887 |
Double Bonus | 9/7/5 | 0.991065 | 0.995618 | 0.994100 |
Double Bonus | 9/6/5 | 0.978062 | 0.985866 | 0.983265 |
Double Bonus | 9/7/4 | 0.977414 | 0.985380 | 0.982725 |
Double Bonus | 9/6/4 | 0.963754 | 0.975135 | 0.971341 |
Double Double Bonus | 9/6 | 0.989808 | 0.994676 | 0.993053 |
Double Double Bonus | 8/6 | 0.978949 | 0.986531 | 0.984004 |
Double Double Bonus | 9/5 | 0.978729 | 0.986367 | 0.983821 |
Double Double Bonus | 8/5 | 0.967861 | 0.978216 | 0.974764 |
Triple Double Bonus | 9/7 | 0.995778 | 0.999153 | 0.998028 |
Triple Double Bonus | 9/6 | 0.981540 | 0.988475 | 0.986163 |
Triple Double Bonus | 9/5 | 0.970204 | 0.979972 | 0.976716 |
Deuces Wild | 25/16/10/4/4/3 | 0.997283 | 1.000282 | 0.999282 |
Deuces Wild | 25/15/9/4/4/3 | 0.989131 | 0.994168 | 0.992489 |
Deuces Wild | 20/12/10/4/4/3 | 0.975791 | 0.984163 | 0.981373 |
Deuces Wild | 25/16/13/4/3/2 | 0.967651 | 0.978058 | 0.974589 |
Bonus Deuces Wild | 9/4/4/3 | 0.994502 | 0.998196 | 0.996964 |
Bonus Deuces Wild | 8/4/4/3 | 0.990625 | 0.995288 | 0.993734 |
Bonus Deuces Wild | 13/4/3/3 | 0.988025 | 0.993339 | 0.991567 |
Bonus Deuces Wild | 12/4/3/3 | 0.982835 | 0.989446 | 0.987242 |
The highest return is on 16-10 deuces wild with the bonus enabled in 3-play at 100.03%.
The next pay table shows the best pay tables available at the Red Rock casino. The best game there is the 99.42% deuces wild.
Red Rock Pay Tables
Base Game | Pay Table | No Bonus | Bonus 3-Play | Bonus 5-Play |
---|---|---|---|---|
Bonus Poker | 7/5 | 0.980147 | 0.987430 | 0.985002 |
Bonus Deluxe | 8/5 | 0.974009 | 0.982827 | 0.979887 |
Double Bonus | 9/6/5 | 0.978062 | 0.985866 | 0.983265 |
Double Double Bonus | 9/5 | 0.978729 | 0.986367 | 0.983821 |
Deuces Wild | 25/15/9/4/4/3 | 0.989131 | 0.994168 | 0.992489 |
Triple Double Bonus | 9/6 | 0.981540 | 0.988475 | 0.986163 |
Strategy
- Find the best pay table you can.
- If trying to maximize the return, you should pick triple-play. If the casino has a generous player-reward program, pushing the game over 100%, then the hourly expected profit may be greater playing 5-play.
- Always make the bonus bet.
- Hold the cards the same way as in conventional video poker.
Acknowledgements
- J.B. for digging up the rules at VideoPoker.com and for the math analysis.
- VideoPoker.com for the screenshots of the example hand.
- IGT for confirming the average bonus win.
- Bob Dancer for his comments and corrections.