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DJ Wild
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Introduction
DJ Wild is a unique poker-inspired game where the deuces and a joker act as wild cards. Players begin by placing Ante and Blind bets, after which they face a choice to either raise or fold. The player's hand is then compared to the dealer's, and the winner is determined by who holds the higher-ranking hand.
I was introduced to this game during the 2014 Global Gaming Expo. Subsequently, I came across it at the New York New York casino in Las Vegas on April 23, 2015. Since then, I have heard about its appearances in other venues. Here’s everything I know as of April 27, 2015:
- Las Vegas: New York New York
- Michigan: Greektown casino
- Ohio: Cleveland Horseshoe
- California: Unknown
- United Kingdom: Unknown
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Rules
- A standard 53-card deck that includes one joker is utilized.
- The ranking of hands is structured as follows, starting from the highest to lowest:
- Five wilds
- Royal flush
- Five of a kind
- Straight flush
- Four of a kind
- Full house
- Flush
- Straight
- Three of a kind
- Two pair
- Pair
- Ace high or less
- Gameplay commences with the player placing equal bets on the Ante and Blind. An optional side bet called Trips can also be placed.
- The dealer is responsible for dealing five cards each to both the player and themselves, with the dealer's cards facing down.
- After looking at their cards, players can decide to either fold or place a Play bet, which must equal twice the amount of their Ante bet.
- Once both players have made their decisions, the dealer reveals their cards and compares their hand to the player's hand, with the higher-ranking hand being declared the winner.
- If the dealer ends up with the stronger hand, the player will lose their Ante, Blind, and Play bets.
- In the event of a tie, the Ante, Blind, and Play bets will remain unchanged (push).
- If the player's hand is stronger, they will receive even money on their Ante and Play bets, while the Blind bet will payout according to the outlined pay table. All payouts are calculated on a 'to one' basis.
- The payout for the Trips bet depends solely on the poker hand value of the player's hand. More details about the Trips bet can be found at the end of this page.
Blind Bet Pay Table
| Player Hand | Pays |
|---|---|
| Five Wilds | 1000 |
| Royal Flush | 50 |
| Five of a Kind | 10 |
| Straight Flush | 9 |
| Four of a Kind | 4 |
| Full House | 3 |
| Flush | 2 |
| Straight | 1 |
| Three of a Kind or Less | Push |
Analysis
The table below presents the number of possible combinations, their probabilities, and how they contribute to the expected return from various scenarios.
DJ Wild — Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player wins with five wilds | 1003 | 1,712,304 | 0.00000035 | 0.00034952 |
| Player wins with royal flush | 53 | 1,719,017,200 | 0.00034984 | 0.01854133 |
| Player wins with five of a kind | 13 | 2,396,963,100 | 0.00048781 | 0.00634147 |
| Player wins with straight flush | 12 | 6,243,236,040 | 0.00127056 | 0.01524670 |
| Player wins with four of a kind | 7 | 88,035,952,768 | 0.01791616 | 0.12541313 |
| Player wins with full house | 6 | 25,233,599,448 | 0.00513528 | 0.03081168 |
| Player wins with flush | 5 | 31,727,826,728 | 0.00645692 | 0.03228459 |
| Player wins with straight | 4 | 138,585,030,624 | 0.02820338 | 0.11281354 |
| Players win with three of a kind or fewer. | 3 | 1,944,630,013,152 | 0.39575088 | 1.18725263 |
| Tie | 0 | 560,641,504 | 0.00011410 | 0.00000000 |
| Player folds | -2 | 1,507,375,457,280 | 0.30676538 | -0.61353075 |
| Dealer wins | -4 | 1,167,263,654,092 | 0.23754936 | -0.95019744 |
| Total | 4,913,773,104,240 | 1.00000000 | -0.03467361 |
In the bottom right corner of the table, an expected loss of 3.47% per unit is shown. This indicates that if a player wagers one unit each on the Ante and Blind, they can anticipate a loss of 3.47% of either amount. For example, if they start betting $10 on both, an average loss of $10 × 3.47% = 35¢ is expected per hand.
The house advantage stands at 3.47% concerning the Ante bet alone, or 1.73% when considering both the Ante and Blind bets together.
An essential factor to assess the game's value is the Element of Risk, calculated as the expected loss relative to the total amount wagered. On average, players tend to raise 69.32% of the time, leading to an average bet of 2 plus 69.32×2, equating to 3.39 units total. Thus, the Element of Risk is 3.47%/3.39 = 1.02%.
Relative to the Ante bet, the standard deviation is noted to be 3.44.
In terms of where the house advantage concentrates, the Blind bet wins only 5.98% of the time, resulting in an expected player loss of 38.2%.
Strategy
The strategy for playing DJ Wild is straightforward and can be summarized as follows:
You should raise if you hold a pair of fours or better, except when drawing two fours and a three singleton. In all other situations, it is wise to fold.
The exception for the three singleton is logical, as a pair of fours will beat a pair of threes, especially when one of the player's cards is a three, which reduces the likelihood of the dealer obtaining a pair of threes.
If players collaborate, they may find significant advantages in this game. If you and the other players do not have any wild cards, it might be wiser to fold even if your hand is marginal. This is due to the increased likelihood that the dealer will hold one or more wild cards. Conversely, with a substantial number of wild cards in play, players should be more inclined to raise. I will defer to experts like Grosjean, Jacobson, and How to delve deeper into this aspect.
Trips
As previously mentioned in the rules, the Trips bet functions as an optional side wager that pays out based solely on the strength of the player's hand. To win this bet, the player must possess at least three of a kind. Payouts are more lucrative if the win is considered natural, lacking the assistance of a wild card. For instance, a hand with a deuce, counted legitimately (like an A2345 straight), will result in a payment categorized as a natural win.
Four separate payout tables are accessible. The table below outlines the probabilities and returns of all potential results, reflecting what I believe to be the most frequently used table. The lower right section indicates a house edge of 6.16%.
Trips Bet
| Player Hand | Wild/Natural | Pays | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Royal flush | Natural | 1,000 | 4 | 0.000001 | 0.001394 |
| Straight flush | Natural | 200 | 36 | 0.000013 | 0.002509 |
| Four of a kind | Natural | 60 | 528 | 0.000184 | 0.011040 |
| Full house | Natural | 30 | 3,168 | 0.001104 | 0.033119 |
| Flush | Natural | 25 | 4,980 | 0.001735 | 0.043385 |
| Straight | Natural | 20 | 10,176 | 0.003546 | 0.070921 |
| Three of a kind | Natural | 6 | 42,240 | 0.014719 | 0.088316 |
| Five wilds | Wild | 2,000 | 1 | 0.000000 | 0.000697 |
| Royal flush | Wild | 90 | 1,000 | 0.000348 | 0.031362 |
| Five of a kind | Wild | 70 | 1,400 | 0.000488 | 0.034150 |
| Straight flush | Wild | 25 | 3,612 | 0.001259 | 0.031467 |
| Four of a kind | Wild | 6 | 51,160 | 0.017828 | 0.106966 |
| Full house | Wild | 5 | 11,880 | 0.004140 | 0.020699 |
| Flush | Wild | 4 | 13,976 | 0.004870 | 0.019481 |
| Straight | Wild | 3 | 73,824 | 0.025725 | 0.077176 |
| Three of a kind | Wild | 1 | 415,800 | 0.144894 | 0.144894 |
| Loser | Either | -1 | 2,235,900 | 0.779145 | -0.779145 |
| Total | 2,869,685 | 1.000000 | -0.061569 |
The following table presents all three payout options, with column headings that specify the payouts for a natural four of a kind, flush, and three of a kind. The bottom row reflects the house advantage.
Trips Bet — All Pay Tables
| Player Hand | Wild/Natural | 90-25-7 | 90-30-6 | 90-25-6 | 60-25-6 |
|---|---|---|---|---|---|
| Royal flush | Natural | 1,000 | 1,000 | 1,000 | 1,000 |
| Straight flush | Natural | 200 | 200 | 200 | 200 |
| Four of a kind | Natural | 90 | 90 | 90 | 60 |
| Full house | Natural | 40 | 40 | 30 | 30 |
| Flush | Natural | 25 | 30 | 25 | 25 |
| Straight | Natural | 20 | 20 | 20 | 20 |
| Three of a kind | Natural | 7 | 6 | 6 | 6 |
| Five wilds | Wild | 2,000 | 2,000 | 2,000 | 2,000 |
| Royal flush | Wild | 100 | 100 | 100 | 90 |
| Five of a kind | Wild | 100 | 100 | 100 | 70 |
| Straight flush | Wild | 30 | 30 | 30 | 25 |
| Four of a kind | Wild | 6 | 6 | 6 | 6 |
| Full house | Wild | 5 | 5 | 5 | 5 |
| Flush | Wild | 4 | 4 | 4 | 4 |
| Straight | Wild | 3 | 3 | 3 | 3 |
| Three of a kind | Wild | 1 | 1 | 1 | 1 |
| Loser | Either | -1 | -1 | -1 | -1 |
| House edge | 0.59% | 1.19% | 3.16% | 6.16% |
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I would like to express my gratitude to Shufflemaster, the owner of the game, for sharing their mathematical report prepared by Elliot Frome. The analysis I provided aligns closely with the simulation results presented in Elliot's report. Full credit goes to Elliot for being the first to propose the strategy discussed above.