Last Updated: July 9, 2019

# 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.

### Magic Deal -- Available Games and Pay Tables

Game Pay
Table
Prob. One
Magic Card
Prob. Two
Magic Cards
Prob. Three
Magic Cards
Base Game
Return
Return with
Feature
Double Double Bonus 9-6 8.400% 1.000% 0.100% 98.981% 99.398%
Double Double Bonus 9-5 8.400% 1.000% 0.100% 97.873% 98.778%
Double Double Bonus 8-5 8.300% 1.000% 0.100% 96.786% 97.898%
Double Double Bonus 7-5 8.000% 1.000% 0.100% 96.497% 96.497%
Double Double Bonus 7-5 7.800% 1.000% 0.100% 95.712% 95.966%
Triple Double Bonus 9-6 2.960% 1.000% 0.100% 98.154% 99.045%
Triple Double Bonus 9-6 2.710% 1.000% 0.100% 98.154% 98.232%
Triple Double Bonus 9-5 2.712% 1.000% 0.100% 97.020% 97.645%
Triple Double Bonus 8-5 2.610% 1.000% 0.100% 95.969% 96.770%
Triple Double Bonus 7-5 2.459% 1.000% 0.100% 94.918% 95.739%
Bonus Poker 7-5 10.800% 2.000% 0.200% 98.015% 99.079%
Bonus Poker 7-5 10.600% 2.000% 0.200% 98.015% 98.739%
Bonus Poker 6-5 10.100% 2.000% 0.200% 96.869% 97.229%
Bonus Poker 6-5 9.920% 2.000% 0.200% 96.869% 96.926%
Double Bonus 10-6-5 9.600% 1.000% 0.145% 98.885% 99.317%
Double Bonus 9-6-5 9.630% 1.000% 0.145% 97.806% 98.766%
Double Bonus 9-6-4 9.640% 1.000% 0.145% 96.375% 97.793%
Double Bonus 9-5-4 9.650% 1.000% 0.130% 95.274% 96.091%
Double Bonus 8-5-4 9.640% 1.000% 0.130% 94.190% 95.443%
Jacks or Better 8-6 10.850% 2.600% 0.200% 98.393% 99.055%
Jacks or Better 8-5 10.900% 2.600% 0.200% 97.298% 98.428%
Jacks or Better 7-5 10.900% 2.600% 0.200% 96.147% 97.747%
Jacks or Better 7-5 10.900% 2.500% 0.200% 96.147% 96.849%
Jacks or Better 6-5 10.950% 2.400% 0.200% 94.996% 95.344%
Bonus Poker Deluxe 8-6 9.300% 1.000% 0.110% 98.493% 99.134%
Bonus Poker Deluxe 8-5 9.300% 1.000% 0.110% 97.401% 98.520%
Bonus Poker Deluxe 7-5 9.300% 1.000% 0.100% 96.253% 97.172%
Bonus Poker Deluxe 7-5 9.120% 1.000% 0.100% 96.253% 96.697%
Bonus Poker Deluxe 6-5 9.020% 1.000% 0.100% 95.361% 95.921%
Deuces Wild 25-15-9 12.000% 2.400% 0.200% 98.913% 99.229%
Deuces Wild 20-12-10 12.100% 2.400% 0.200% 97.579% 98.203%
Deuces Wild 25-16-13 12.000% 2.300% 0.200% 96.765% 97.747%
Deuces Wild 25-16-13 12.000% 2.220% 0.200% 96.765% 96.988%
Deuces Wild 25-15-10 12.000% 2.200% 0.200% 94.818% 95.411%
Deuces Wild Bonus 13-4-3-3 11.600% 2.000% 0.200% 98.803% 99.464%
Deuces Wild Bonus 10-4-3-3 11.600% 2.000% 0.200% 97.364% 98.429%
Deuces Wild Bonus 10-4-3-3 11.600% 1.900% 0.200% 97.364% 97.401%
Deuces Wild Bonus 12-4-3-2 11.600% 1.850% 0.200% 96.218% 96.478%
Deuces Wild Bonus 10-4-3-2 11.600% 1.850% 0.200% 95.337% 95.826%

## 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.

### Zero Magic Cards

Event Pays Combinations Probability Return
Royal flush 800 488,567,700 0.000025 0.019608
Straight flush 50 2,184,917,880 0.000110 0.005481
4 aces + 2-4 400 1,227,691,500 0.000062 0.024636
4 2-4 + A-4 160 2,854,370,052 0.000143 0.022911
4 aces + 5-K 160 3,460,011,120 0.000174 0.027773
4 2-4 + 5-K 80 7,662,444,216 0.000384 0.030752
4 5-K 50 32,494,582,452 0.001630 0.081509
Full house 9 216,474,969,996 0.010860 0.097740
Flush 6 226,412,247,120 0.011359 0.068151
Straight 4 254,472,741,540 0.012766 0.051065
3 of a kind 3 1,500,277,164,324 0.075265 0.225795
Two pair 1 2,453,055,008,724 0.123064 0.123064
Jacks or better 1 4,212,339,758,244 0.211322 0.211322
Nothing 0 11,019,826,042,332 0.552837 0.000000
Total   19,933,230,517,200 1.000000 0.989808

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.

### One Magic Card

Event Pays Combinations Probability Return
Royal flush 800 143,426,496 0.000681 0.544544
Straight flush 50 523,794,192 0.002486 0.124292
Four A + 2-4 400 253,219,560 0.001202 0.480696
Four 2-4 + A-4 160 727,804,620 0.003454 0.552648
Four A + 5-K 160 604,322,040 0.002868 0.458883
Four 2-4 + 5-K 80 1,544,961,420 0.007332 0.586572
Four 5-K 50 5,345,057,340 0.025367 1.268340
Full house 9 6,135,845,580 0.029120 0.262078
Flush 6 4,969,881,612 0.023586 0.141518
Straight 4 11,185,328,112 0.053084 0.212335
Three of a kind 3 96,146,990,820 0.456299 1.368896
Two pair 1 - 0.000000 0.000000
Jacks or better 1 72,614,497,812 0.344617 0.344617
Junk 0 10,515,552,396 0.049905 0.000000
Total   210,710,682,000 1.000000 6.345418

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.

### Two Magic Cards

Event Pays Combinations Probability Return
Royal flush 800 9,683,376 0.007927 6.341899
Straight flush 50 22,221,016 0.018191 0.909571
Four A + 2-4 400 17,543,904 0.014362 5.744983
Four 2-4 + A-4 160 57,869,016 0.047375 7.579990
Four A + 5-K 160 27,721,536 0.022694 3.631113
Four 2-4 + 5-K 80 65,443,728 0.053576 4.286083
Four 5-K 50 194,780,016 0.159458 7.972912
Full house 9 - 0.000000 0.000000
Flush 6 53,907,908 0.044132 0.264793
Straight 4 180,919,488 0.148111 0.592445
Three of a kind 3 591,421,212 0.484172 1.452515
Two pair 1 - 0.000000 0.000000
Jacks or better 1 - 0.000000 0.000000
Junk 0 - 0.000000 0.000000
Total   1,221,511,200 1.000000 38.776304

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.

### Three Magic Cards

Event Pays Combinations Probability Return
Royal flush 800 257,456 0.079249 63.399144
Straight flush 50 95,500 0.029396 1.469819
Four A + 2-4 400 293,940 0.090479 36.191707
Four 2-4 + A-4 160 316,140 0.097313 15.570043
Four A + 5-K 160 329,408 0.101397 16.223499
Four 2-4 + 5-K 80 914,736 0.281570 22.525589
Four 5-K 50 1,041,520 0.320596 16.029797
Full house 9 - 0.000000 0.000000
Flush 6 - 0.000000 0.000000
Straight 4 - 0.000000 0.000000
Three of a kind 3 - 0.000000 0.000000
Two pair 1 - 0.000000 0.000000
Jacks or better 1 - 0.000000 0.000000
Junk 0 - 0.000000 0.000000
Total   3,248,700 1.000000 171.409598

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%

### Summary

Magic
Cards
Probability Average
Win
Return
0 90.50% 0.989808 0.447888
1 8.40% 6.345418 0.266508
2 1.00% 38.776304 0.193882
3 0.10% 171.409598 0.085705
Total 100.00%   0.993982

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%.

### 9-6 Double Double Bonus Return Table

Event Pays Combinations Probability Return
Royal flush 800 47,417,469,856,104 0.000238 0.095153
Straight flush 50 103,517,300,426,688 0.000519 0.012983
Four A + 2-4 400 77,896,908,119,640 0.000391 0.078158
Four 2-4 + A-4 160 197,497,448,072,280 0.000991 0.079264
Four A + 5-K 160 144,784,006,868,640 0.000726 0.058108
Four 2-4 + 5-K 80 355,034,250,974,640 0.001781 0.071245
Four 5-K 50 1,100,572,502,657,160 0.005521 0.138032
Full house 9 2,446,677,311,632,920 0.012274 0.055235
Flush 6 2,531,927,128,521,770 0.012702 0.038106
Straight 4 3,487,042,690,521,770 0.017494 0.034987
Three of a kind 3 22,182,843,520,454,900 0.111286 0.166929
Two pair 1 22,200,147,828,952,200 0.111373 0.055686
Jacks or better 1 43,891,913,266,241,000 0.220195 0.110097
Junk 0 100,565,033,538,700,000 0.504509 0.000000
Total   199,332,305,172,000,000 1.000000 0.993982

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.

### 8-6 Jacks or Better Return Table

Event Pays Combinations Probability Return
Royal flush 800 107,813,216,050,980 0.000541 0.216349
Straight flush 50 241,340,738,393,964 0.001211 0.030269
Four of a kind 25 3,112,932,512,699,990 0.015617 0.195210
Full house 8 2,705,048,854,165,550 0.013571 0.054282
Flush 6 2,888,760,663,929,320 0.014492 0.043477
Straight 4 4,075,201,207,922,060 0.020444 0.040889
Three of a kind 3 24,752,759,280,902,900 0.124178 0.186268
Two pair 2 22,251,616,497,966,200 0.111631 0.111631
Jacks or better 1 44,721,980,874,036,000 0.224359 0.112179
Junk 0 94,474,851,325,932,900 0.473957 0.000000
Total   199,332,305,172,000,000 1.000000 0.990552

### 7-5 Bonus Poker Return Table

Event Pays Combinations Probability Return
Royal flush 800 95,677,866,475,440 0.000480 0.191997
Straight flush 50 198,220,933,309,296 0.000994 0.024861
Four aces 80 352,899,863,657,232 0.001770 0.070816
Four 2-4 40 580,097,605,307,184 0.002910 0.058204
Four 5-K 25 1,855,939,020,485,230 0.009311 0.116385
Full house 7 2,695,193,302,116,530 0.013521 0.047324
Flush 5 2,600,927,214,354,860 0.013048 0.032620
Straight 4 3,870,268,005,575,380 0.019416 0.038832
Three of a kind 3 24,426,720,184,136,700 0.122543 0.183814
Two pair 2 22,416,648,077,181,600 0.112459 0.112459
Jacks or better 1 45,238,153,508,438,000 0.226948 0.113474
Junk 0 95,001,559,590,962,600 0.476599 0.000000
Total   199,332,305,172,000,000 1.000000 0.990786

### 8-6 Bonus Poker Deluxe Return Table

Event Pays Combinations Probability Return
Royal flush 800 57,027,285,366,036 0.000286 0.114437
Straight flush 50 96,752,131,716,048 0.000485 0.012135
Four of a kind 80 1,993,968,131,473,480 0.010003 0.400129
Full house 8 2,508,869,831,157,610 0.012586 0.050345
Flush 6 2,497,079,643,549,460 0.012527 0.037582
Straight 4 3,593,843,565,824,440 0.018029 0.036059
Three of a kind 3 22,724,632,679,242,400 0.114004 0.171006
Two pair 1 22,920,972,431,308,200 0.114989 0.057494
Jacks or better 1 44,712,580,189,323,900 0.224312 0.112156
Junk 0 98,226,579,283,038,400 0.492778 0.000000
Total   199,332,305,172,000,000 1.000000 0.991342

### 10-6-5 Double Bonus Return Table

Event Pays Combinations Probability Return
Royal flush 800 63,549,827,401,974 0.000319 0.127525
Straight flush 50 115,342,685,579,526 0.000579 0.014466
Four aces 160 247,615,894,520,184 0.001242 0.099378
Four 2-4 80 462,075,285,435,198 0.002318 0.092725
Four 5-K 50 1,320,977,570,047,160 0.006627 0.165675
Full house 10 2,637,952,295,359,990 0.013234 0.066170
Flush 6 2,511,876,178,798,080 0.012601 0.037804
Straight 5 4,314,478,769,385,490 0.021645 0.054112
Three of a kind 3 22,592,218,856,815,600 0.113339 0.170009
Two pair 1 22,526,918,485,699,600 0.113012 0.056506
Jacks or better 1 43,375,157,153,811,600 0.217602 0.108801
Junk 0 99,164,142,169,145,700 0.497482 0.000000
Total   199,332,305,172,000,000 1.000000 0.993172

### 9-6 Triple Double Bonus Return Table

Event Pays Combinations Probability Return
Royal flush 800 2,701,372,178,996 0.000163 0.065050
Straight flush 50 5,980,061,265,302 0.000360 0.009000
Four A + 2-4 800 6,649,286,529,432 0.000400 0.160117
Four 2-4 + A-4 400 15,933,028,931,430 0.000959 0.191837
Four A + 5-K 160 7,964,216,681,580 0.000479 0.038356
Four 2-4 + 5-K 80 22,758,022,374,432 0.001370 0.054802
Four 5-K 50 65,519,804,539,176 0.003944 0.098609
Full house 9 180,782,012,611,494 0.010883 0.048975
Flush 6 219,571,969,092,000 0.013218 0.039655
Straight 4 267,329,686,862,230 0.016094 0.032187
Three of a kind 2 1,493,762,049,557,470 0.089926 0.089926
Two pair 1 1,934,878,537,339,960 0.116482 0.058241
Jacks or better 1 3,444,942,062,276,700 0.207389 0.103694
Junk 0 8,942,253,320,759,810 0.538332 0.000000
Total   16,611,025,431,000,000 1.000000 0.990450