# Wild! Wild! Wild!

## Introduction

Wild! Wild! Wild! is a video poker variant attached to multi-play video poker. If the player bets 10 credits per play, the game will randomly add one to three wild cards to the deck with certain probabilities. The price to invite this feature is 5 credits per play.

## Rules

1. Wild! Wild! Wild! is an optional feature added to multi-play video poker.
2. If the player bets one to five coins per play, the game will play like conventional multi-play video poker, which I assume the reader is familiar with.
3. If the player bets ten coins per play, he will invoke the feature. Wins will be based on five coins bet per play, with the other five coins considered a fee a pay for the feature.
4. Depending on the game and pay table, the game may add 1 to 3 wild cards to the deck. For example, in 9-6 Jacks or Better, the probabilities of added wilds are as follows:
5. The game does inform the player the player how many wilds were added.
6. If the player invokes the feature, in addition to the wild cards, the game will boost the pay table wins and add wins for a five of a kind in what are normally not wild card games.

## Example

In the image above two wilds were added to the deck.  You can tell because it says so right above the credit meter of 9280.  On the deal I got one of them.

In the image above, I choose to hold the wild card and the suited ace and king.

After the draw, two hands improve to a three of a kind, one to a flush, one to a full house and one remains a high pair.  The total "win" is 5 + 2*15 + 30 + 55 = 120 credits.  The bet amount was 5*10 = 50 credit, so the actual profit was 70 credits.

## Analysis

The following is my analysis of 9-6 Jacks or Better. First I will present four return tables, for 0 to 3 wild cards added. In each table, the return column is the produce of the win, probability and 0.5. The reason for dividing by 2 is wins are based on half the bet amount.

### 9-6 Jacks or Better — Zero Wilds Added

Event Pays Probability Return
Royal Flush 800 0.000025 0.009911
Five Aces 800 0.000000 0.000000
Five 2's, 3's, 4's 320 0.000000 0.000000
Five 5's Through K's 100 0.000000 0.000000
Straight Flush 50 0.000109 0.002714
Four of a Kind 30 0.002353 0.035294
Full House 11 0.011452 0.062984
Flush 6 0.010865 0.032596
Straight 5 0.014599 0.036499
Three of a Kind 3 0.073596 0.110394
Two Pair 2 0.127355 0.127355
Jacks or Better 1 0.207471 0.103735
Trash 0 0.552176 0.000000
Total   1.000000 0.521481

### 9-6 Jacks or Better — One Wild Added

Event Pays Probability Return
Royal Flush 800 0.000146 0.058600
Five Aces 800 0.000008 0.003078
Five 2's, 3's, 4's 320 0.000021 0.003362
Five 5's Through K's 100 0.000065 0.003265
Straight Flush 50 0.000486 0.012148
Four of a Kind 30 0.008626 0.129386
Full House 11 0.015754 0.086649
Flush 6 0.014272 0.042816
Straight 5 0.018712 0.046781
Three of a Kind 3 0.134392 0.201587
Two Pair 2 0.111222 0.111222
Jacks or Better 1 0.221151 0.110575
Trash 0 0.475144 0.000000
Total   1.000000 0.809470

### 9-6 Jacks or Better — Two Wilds Added

Event Pays Probability Return
Royal Flush 800 0.000451 0.180569
Five Aces 800 0.000040 0.016104
Five 2's, 3's, 4's 320 0.000092 0.014786
Five 5's Through K's 100 0.000295 0.014734
Straight Flush 50 0.001025 0.025623
Four of a Kind 30 0.019494 0.292415
Full House 11 0.018932 0.104127
Flush 6 0.013721 0.041164
Straight 5 0.022243 0.055608
Three of a Kind 3 0.186878 0.280317
Two Pair 2 0.097005 0.097005
Jacks or Better 1 0.237120 0.118560
Trash 0 0.402702 0.000000
Total   1.000000 1.241014

### 9-6 Jacks or Better — Three Wilds Added

Event Pays Probability Return
Royal Flush 800 0.001098 0.439188
Five Aces 800 0.000121 0.048501
Five 2's, 3's, 4's 320 0.000235 0.037537
Five 5's Through K's 100 0.000761 0.038037
Straight Flush 50 0.001621 0.040520
Four of a Kind 30 0.033008 0.495117
Full House 11 0.020270 0.111484
Flush 6 0.012974 0.038921
Straight 5 0.027422 0.068556
Three of a Kind 3 0.226116 0.339174
Two Pair 2 0.084512 0.084512
Jacks or Better 1 0.249475 0.124738
Trash 0 0.342387 0.000000
Total   1.000000 1.866286

The following table summarizes the return by the number of wilds added. The lower right cell shows a return of 99.63%.

### 9-6 Jacks or Better — Return Summary

Wilds Probability Average Win Expected Win
0 0.400000 0.521481 0.208593
1 0.190000 0.809470 0.153799
2 0.210000 1.241014 0.260613
3 0.200000 1.866286 0.373257
Total 1.000000 0.000000 0.996262

The following table also summarizes the whole game according to each paying hand. The lower right cell again shows a return of 99.63%.

### 9-6 Jacks or Better — Overall Return Table

Event Pays Probability Return
Royal Flush 800 0.000352 0.140855
Five Aces 800 0.000034 0.013667
Five 2's, 3's, 4's 320 0.000070 0.011251
Five 5's Through K's 100 0.000226 0.011322
Straight Flush 50 0.000675 0.016879
Four of a Kind 30 0.013275 0.199131
Full House 11 0.015604 0.085820
Flush 6 0.012534 0.037602
Straight 5 0.019551 0.048877
Three of a Kind 3 0.139441 0.209161
Two Pair 2 0.109347 0.109347
Jacks or Better 1 0.224697 0.112349
Trash 0 0.464193 0.000000
Total   1.000000 0.996262

The following set of tables show the pay tables available for each game, the probabilities for 1 to 3 wilds, the 5-coin return and 10-coin return. You can see the 10-coin return is always a little higher.

### Triple Triple Bonus

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-6 33.8% 16.2% 1.0% 0.997516 0.998125
9-5 34.2% 15.8% 1.0% 0.986087 0.988065
8-5 34.5% 15.5% 1.0% 0.975516 0.978888
7-5 35.0% 15.0% 1.0% 0.964948 0.967663
6-5 35.5% 14.5% 1.0% 0.954392 0.956614

### Double Double Bonus

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-6 22.0% 24.0% 5.0% 0.989808 0.992654
9-5 23.0% 23.0% 5.0% 0.978729 0.979416
8-5 23.0% 23.0% 5.0% 0.967861 0.973390
7-5 24.0% 22.0% 5.0% 0.957120 0.960078
6-5 24.0% 22.0% 5.0% 0.946569 0.954316

### Triple Double Bonus

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-7 32.9% 14.1% 4.0% 0.995778 0.997753
9-6 33.8% 13.2% 4.0% 0.981540 0.982452
9-5 34.0% 13.0% 4.0% 0.970204 0.974809
8-5 34.7% 12.3% 4.0% 0.959687 0.962143
7-5 35.0% 12.0% 4.0% 0.949178 0.953411

The 8-5 pay table for Bonus Poker is the only one where the wild card probabilities are not exact as shown. The are based on the following weights:

• 0 wilds = 355
• 1 wild = 100
• 2 wilds = 440
• 3 wilds = 100

### Bonus Poker

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
8-5 10.0503% 44.2211% 10.0503% 0.991660 0.993538
7-5 11.5% 43.0% 10.0% 0.980147 0.980517
6-5 10.0% 43.0% 10.0% 0.968687 0.968874

### Double Bonus Poker

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-7-5 15.0% 31.0% 5.0% 0.991065 0.991211
9-6-5 15.5% 30.5% 5.0% 0.978062 0.981317
10-6-4 16.0% 30.0% 5.0% 0.974613 0.975721
9-6-4 16.5% 29.5% 5.0% 0.963754 0.966398
9-5-4 17.5% 28.5% 5.0% 0.952738 0.953866

### Jacks or Better

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-6 19.0% 21.0% 20.0% 0.995439 0.996262
9-5 19.5% 20.5% 20.0% 0.984498 0.986314
8-5 20.5% 19.5% 20.0% 0.972984 0.974251
7-5 19.5% 20.5% 20.0% 0.961472 0.963206
6-5 20.0% 20.0% 20.0% 0.949961 0.953392

### Bonus Poker Deluxe

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9-6 20.8% 25.2% 5.0% 0.996417 0.997437
9-5 21.5% 24.5% 5.0% 0.985495 0.986541
8-5 22.0% 24.0% 5.0% 0.974009 0.977041
7-5 24.0% 22.0% 5.0% 0.962526 0.962659
6-5 24.5% 21.5% 5.0% 0.953611 0.958094

### Deuces Wild

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
20/12/9/5/3 18.0% 22.0% 20.0% 0.989378 0.992907
25/15/10/4/3 15.5% 24.5% 20.0% 0.989131 0.990747
25/15/10/4/3 16.0% 24.0% 20.0% 0.975791 0.975823
25/16/13/4/3 16.8% 23.2% 20.0% 0.967651 0.968383
25/15/10/4/3 18.0% 22.0% 20.0% 0.948182 0.952554

### Deuces Wild Bonus

Pay Table One Wild Two Wilds Three Wilds 5 Coin Return 10 Coin Return
9/4/4/3 19.0% 21.0% 20.0% 0.994502 0.998339
13/4/3/3 21.0% 19.0% 20.0% 0.988025 0.989615
10/4/3/3 21.0% 19.0% 20.0% 0.973644 0.978256
12/4/3/2 21.5% 18.5% 20.0% 0.962183 0.966031
10/4/3/2 21.5% 18.5% 20.0% 0.953368 0.959245

## Acknowledgements

I would like to thank VideoPoker.com for the math on this page as well as permission to use the screenshots in the example section.