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Wild! Wild! Wild!

Introduction

Wild! Wild! Wild! is a variation of video poker associated with multi-play video poker. When betting 10 credits per hand, the game has a chance to randomly introduce one to three wild cards into the deck, depending on the probabilities set. This feature can be activated for an additional cost of 5 credits per round.

Rules

  1. The Wild! Wild! Wild! feature is an optional enhancement for multi-play video poker.
  2. When the player bets between one and five coins for each round, the game behaves like traditional multi-play video poker, which I assume most readers are already acquainted with.
  3. By betting ten coins each round, the player activates this additional feature. The payouts will be calculated based on a bet of five coins, with the other five coins covering the cost of enabling the feature.
  4. Depending on the specific game and its payout table, it might incorporate 1 to 3 wild cards into the deck. For instance, in the 9-6 Jacks or Better variant, the chances of introducing wild cards are as follows:
    • 0 added = 40%
    • 1 added = 19%
    • 2 added = 21%
    • 3 added = 20%
  5. The game does inform players about the quantity of wild cards added to the deck.
  6. When the player activates the feature, wild cards will be included, and the game will enhance winning combinations in addition to recognizing wins for five of a kind in instances where wild cards are typically not a factor.

Example

In the screenshot above, two wild cards were integrated into the deck, as noted just above the credit total of 9280. During the deal, one of these wild cards was obtained by me.

In the displayed image, I opted to retain the wild card along with the suited ace and king.

Post-draw, two of the hands evolved into three of a kind, one transformed into a flush, another into a full house, while one remained as a high pair. The cumulative 'win' totals 5 + 2*15 + 30 + 55 = 120 credits. Given that the wager was 5*10 = 50 credits, the actual profit amounted to 70 credits.

Analysis

Here is my breakdown of the 9-6 Jacks or Better game. Initially, I will provide four return tables indicating the outcomes with 0 to 3 wild cards added. In each table, the return is calculated by multiplying the win amount, its probability, and then dividing by 0.5. The rationale behind dividing by 2 is that winnings are based on half of the total bet.

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 encapsulates returns according to the number of wild cards introduced. The bottom right cell indicates a generous 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 next table also outlines the overall game according to the different winning hands. Once again, the last cell on the bottom right confirms a return of 99.63%.

Overall Return Table for 9-6 Jacks or Better

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 subsequent set of tables detail the available payout tables for each game, the likelihood of getting 1 to 3 wild cards, and the returns for both 5-coin and 10-coin bets. It is evident that the returns for 10 coins tend to be slightly superior.

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 payout structure for Bonus Poker stands out as the only one where the probabilities of wild cards do not align perfectly as displayed. They are derived from the weights indicated below:

  • 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 Acknowledgment for the calculations presented on this page, along with the allowance to utilize screenshots in the examples.

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Strategies

Full-Pay Jacks or Better:

Full-Pay Deuces Wild:

Quick Quads:

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