Magic Deal

Introduction

Magic Deal is a video poker variant that is placed on top of conventional three-play, five-play, and ten-play video poker machines. The player can play those games normally or pay a fee equal to the maximum bet amount of five coins per line to invoke the Magic Deal feature. If the feature is active, the game will randomly give the player one to three Magic Deal cards on the deal, and they function like wild cards.

Rules

 

1. Magic Deal can play like conventional three-, five-, or ten-play video poker. In addition, if the player pays a fee equal to the total bet amount if playing without the feature, then he will invoke the Magic Deal feature.
2. If the Magic Deal feature is active, then according to the probabilities in the table below, the player can get one, two, or three Magic Cards on the deal. They are always automatically held. Additional Magic Cards never appear on the draw.
3. Magic Cards serve much the same function as wild cards. However, unlike wild cards, they must take the form of a specific card the player doesn't already have on the draw. The game will figure out which card is the most beneficial. If multiple cards tie for the greatest win, the game seems to pick one arbitrarily.
4. If the player discarded a card on the deal, a Magic Card can still assume its value on the draw.
5. The Magic Card probabilities were carefully chosen to offer a better value with the feature than without it, assuming optimal player strategy. The probabilities tend to be higher in bottom-heavy games like Jacks or Better and lower in top-heavy games like Double Double Bonus.

 

Example

 

The example below shows a game based on 3-play Jacks or Better. On the deal I was dealt two Magic Cards and three junk cards.

 

I threw away all three junk cards. The image below shows I was dealt an ace, 2, and 5 on the top hand. The best use of the two Magic Cards were a 3 and 4 to form a straight. In the middle hand I was dealt two aces and a 6. The best use of the magic cards was two more aces, for a four of a kind. In the bottom hand I was dealt a king, 5, and 2. Here the best I could do was a three of a kind. The game could have given me a pair of kings, fives, or twos. It arbitrarily chose kings.

 

The "8-6" pay table was used, although in this case it didn't matter. The straight paid 4 per coin bet on the top hand, the four of a kind paid 25 per coin bet on the middle hand, and the three of a kind paid 3 per coin bet on the bottom hand. Five coins were bet on each line, so the total "win" was 5×(4+25+3) = 160 credits. I bet 5×3×2 = 30 credits, so my net win was 130 credits.

Available Games and Magic Card Probabilities

 

The following table shows the games available with Magic Deal, the pay tables, probabilities of 1, 2, and 3 Magic Cards, the return without the feature, and the return with it. The list is the same for 3-, 5-, and 10-play. The information was kindly provided to me by VideoPoker.com, the creator of the game.

 

Analysis

 

The following analysis is based on 9-6 Double Double Bonus. As a reminder, the Magic Card probabilities are:

• 0 Magic Cards: 90.5%
• 1 Magic Card: 8.4%
• 2 Magic Cards: 1.0%
• 3 Magic Cards: 0.1%

 

The way I did the analysis was to break it up into four parts, one for each possible number of Magic Cards. Then I took the dot product of the probability of each number of Magic Cards and the average win to get the overall average win.

First, here is the return table for no Magic Cards, which is the same as for conventional 9-6 Double Double Bonus.

 

Second, here is the return table for one Magic Card. The lower right cell shows the average win with one Magic Card is 6.345418 times the amount bet per hand, not including the additional fee to invoke the Magic Card feature.

 

Third, here is the return table for two Magic Cards. The lower right cell shows the average win with two Magic Cards is 38.776304 times the amount bet per hand, not including the additional fee to invoke the Magic Card feature.

 

Fourth, here is the return table for three Magic Cards. The lower right cell shows the average win with three Magic Cards is 171.409598 times the amount bet per hand, not including the additional fee to invoke the Magic Card feature.

 

The next table shows the probability of each number of Magic Cards, the average win given that number, and contribution to the return. The contribution to the return is defined as the product of the second and third columns and 0.5. The reason for dividing by 2 is wins are based on only half of the total amount bet. The lower right cell shows an overall return of 99.398%

 

The next table summarizes the whole game in a different way, by the final hand, as opposed to the number of Magic Cards. Combinations are given to 15 decimal places only (blame Excel). As in the table above, the return column is the product of the win, probability and 0.5. The lower right cell also shows a return of 99.398%.

 

Here are some statistics from the tables above:

• Standard deviation = 8.43.
• Hit frequency = 49.55%.
• Royal frequency = 1 in 4,204 hands.

 

To keep this page from running too long, I present below just the final return table of the most liberal pay table of some of the other games available. Again, combinations are given to 15 decimal places only because that is all Excel will display.

         

External Links

 

• Magic Deal -- Discussion in my forum at Wizard of Vegas.
• Analyzing Magic Deal -- Discussion in my forum at Wizard of Vegas.
• 9-6 Double Double Bonus strategy -- from a forum post by alpax at VideoPoker.com. The strategy looks sound to me.

Written by: Michael Shackleford