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Last Updated: January 12, 2016

Poker with a Joker

Introduction



Poker with a Joker is a poker-based game that made its casino appearance at the Green Valley Ranch in Las Vegas in early 2015.

Rules



  1. A 53-card deck is used, including one fully-wild joker.
  2. Play begins with the player making equal Ante and Bonus wagers. The player may also make optional Wild 5 and Wild 7 side bets.
  3. The player and dealer shall each receive five cards face down. There will also be two community cards dealt face down.
  4. After examining his cards, the player has the following options:
    • Fold and forfeit the Ante and Bonus bets.
    • Make a Play bet equal to 1 to 3 times the Ante bet.
  5. If the player makes the Play bet, then he may keep his original five cards or discard one. If the player discards, then he shall be able to include the two community cards with his hand.
  6. After all players have acted, the dealer shall reveal his own five cards and play them according to the following house way:
    • If the dealer has a pat five-card hand (straight, flush, full house, straight flush, royal flush, or five of a kind), then he shall stand.
    • If the dealer has a two pair, three of a kind, or four of a kind, then he shall discard the lowest singleton.
    • If the dealer has four to a flush or outside straight, then the dealer shall discard the fifth card. If the dealer has both of these hands, then he shall keep the four to a flush.
    • Otherwise, if the dealer has a pair or five singletons, then he shall discard the lowest singleton.
  7. The dealer shall reveal the two community cards.
  8. Both the player and dealer shall be allowed to include the two community cards in his own hand if he discarded.
  9. The dealer shall determine the poker value of both hands.
  10. If the dealer's hand is a pair or better, then the dealer shall qualify.
  11. The player and dealer hands shall be compared. The Ante, Bonus, and Play bets shall be adjudicated as follows:
    • If the dealer does not qualify, then the Ante bet shall automatically push.
    • The Ante and Play wagers pay 1 to 1 if the player has the higher hand, push on a tie, and lose if the dealer has the higher hand.
    • The Bonus wager shall pay according to the following pay table if the player has the higher hand, push on a tie, and lose if the dealer has the higher hand. All wins are on a "to one" basis.

      Bonus Wager Pay Table

      Hand Pays
      Five of a kind 100
      Royal flush 50
      Straight flush 10
      Four of a kind 5
      Full house 3
      Flush 2
      Straight 1
      All other Push



  12. The Wild 5 side bet is paid based on the player's original five cards and the following pay table. All wins are on a "to one" basis.

    Wild 5 Pay Table

    Hand Pays
    Five of a kind 1000
    Royal flush 500
    Straight flush 250
    Four of a kind 100
    Full house 50
    Flush 25
    Straight 10
    Three of a kind 5
    Two pair 5
    All other Loss


  13. The Wild 7 side bet is paid based on the player's original five cards plus the two community cards and the following pay table. The top two awards are based on a progressive jackpot. The bet is always $1. All wins are on a "for one" basis.

    Wild 7 Pay Table

    Hand Pays
    Seven-card straight flush 100% of Jackpot
    Five aces 10% of Jackpot
    Five of a kind (2-K) $500
    Royal flush $250
    Straight flush $100
    Four of a kind $20
    Full house $4
    All other $0




Strategy



The following is known as the "Station Casinos Strategy" and is available on the rack cards at the Green Valley Ranch. I'm told it results in a house edge 1% higher than optimal strategy, or about 3.84%.

  1. With a pat hand (five card flush, straight, full house, Royal, Five of a kind) — Keep hand and raise 3x.
  2. Four to a flush or outside straight, or a pair of 8's or better — Keep the high pair on the draw and raise 3x.
  3. Four to an inside straight, or a pair of 7's down to a Queen high with no draw — Call 1x.
  4. Jack-high or less and there is no draw — Fold.


The next strategy I call the "Steve How" strategy. If you're not familiar with the name, he is the genius behind the site Discount Gambling. I assume this strategy is near optimal.

  • 3x Play a pat Five-of-a-Kind, else
  • 3x Play a pat Royal Flush, else
  • 3x Play a pat Straight Flush, else
  • 3x Play a pat Full House, else
  • 3x Play Four-of-a-Kind, and discard singleton, else
  • 3x Play a Royal Flush draw or an open-ended Straight Flush draw (e.g., break a pat straight or flush), else
  • 3x Play a pat Flush or Straight, else
  • 3x Play any Straight Flush draw, else
  • 3x Play wild Three-of-a-Kind (hold singleton that maximizes straight draws), else
  • 3x Play Three-of-a-Kind (discard lowest singleton), else
  • 3x Play Two Pairs and discard singleton, else
  • 3x Play any wild flush draw, else
  • 3x Play any wild open-ended draw, else
  • 3x Play any Joker hand (discard singleton that maximizes straight draws), else
  • 3x Play a pair of 8's or better, and hold 3 suited cards or else maximize straight draws, else
  • 3x Play a flush draw (e.g., breaking a pair of 7's or lower), else
  • 3x Play a Jack-high open-ended straight draw, else
  • 3x Play an Ace-high gutshot straight draw, else
  • 1x Play an open-ended straight draw, else
  • 1x Play a pair with 3 suited cards, else
  • 1x Play a pair, holding kickers that maximize straight draws, else
  • 1x Play 3 suited cards with highest offsuit singleton, else
  • 1x Play highest 4-cards if Queen-high or better, else
  • 1x Play 4-cards with maximum number of possible straight draws, else
  • Fold all others (i.e., no possible straight draws).


Base Game Analysis



The math report by GLI states that under optimal strategy the house edge, defined as the ratio of the expected loss to the Ante bet, is 2.84%. The average wager is 3.88 units, for an Element of Risk of 0.73%.

Wild 5 Analysis



The following table shows the probability and contribution to the return of all possible outcomes of the Wild 5 bet. The lower right cell shows a house edge of 5.45%.

Wild 5 Return Table

Event Pays Combinations Probability Return
Five of a kind 1000 13 0.000005 0.004530
Royal flush 500 24 0.000008 0.004182
Straight flush 250 180 0.000063 0.015681
Four of a kind 100 3,120 0.001087 0.108723
Full house 50 6,552 0.002283 0.114159
Flush 25 7,804 0.002719 0.067987
Straight 10 20,532 0.007155 0.071548
Three of a kind 5 137,280 0.047838 0.239190
Two pair 5 123,552 0.043054 0.215271
All other -1 2,570,628 0.895788 -0.895788
Total 2,869,685 1.000000 -0.054517


Wild 7 Analysis



The following table shows the probability and contribution to the return of all possible outcomes of the Wild 7 bet under a hypothetical "break even" jackpot of $524,541.60.

Wild 7 Return Table

Event Pays Combinations Probability Return
Seven-card straight flush $524,541.60 32 0.000000 0.108894
Five aces $52,454.16 1,128 0.000007 0.383853
Five of a kind (2-K) $500.00 13,536 0.000088 0.043907
Royal flush $250.00 26,128 0.000170 0.042376
Straight flush $100.00 184,804 0.001199 0.119891
Four of a kind $20.00 1,121,024 0.007273 0.145452
Full house $4.00 5,997,144 0.038906 0.155625
All other $0 146,799,284 0.952357 0.000000
Total 154,143,080 1.000000 1.000000


Here are some more statistics on the Wild 7.

  • The return from fixed Wild 7 wins is 50.73%.
  • Each $10,000 in the meter adds 0.94% to the return.
  • Each $10,645.24 adds 1% to the return.
  • The "break even" point, where the bet is exactly fair, is $524,541.60.


Acknowledgements



I would like to thank the game owners for providing the math report by GLI, which was used for the house edge and element of risk above. I did my own analysis of the Wild 5 and Wild 7 side bets.



Wizard of Vegas — Forum discussion about Poker with a Joker.


Written by: Michael Shackleford

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