3 Card Draw Poker Online

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The dealer replaces it with a draw card. The dealer turns his four cards face up and arranges to show his best three card hands. Hand rankings are the same as in Three Card Poker. Going from low to high, rankings are high card, pair, flush, straight, three of a kind, straight flush, mini-royal.

Introduction

3 Card Draw Poker could be compared to conventional Three Card Poker but with the option to switch a card. In addition, the dealer always qualifies. The take-back is that the dealer starts with four cards and makes his best three-card hand out of them.

The game appeared at the Tropicana in Atlantic City in late 2017 and I hear has also been seen in the United Kingdom somewhere.

Rules

1. A single 52-card deck is used.
2. All cards and hands are scored as in poker. The order of hands is as follows:
   • Straight flush
   • Three of a kind
   • Straight
   • Flush
   • Pair
   • All other
3. Play begins with the player making an Ante bet. There is also an optional First 3 Bonus side bet that may be made at this time.
4. All players receive three cards and the dealer four cards, all face down.
5. After checking his own hand, the player has the following options:
   • Make a Raise bet, equal to the Ante bet, and stand
   • Make a Raise, equal to the Ante bet, and exchange one card for the next card in the deck.
   • Fold
6. If the player discards, the new card will be kept separate from the other two, for purposes of adjudicating the First 3 Bonus side bet.
7. The dealer will turn over his cards and select the three that form the hand of the highest poker value.
8. The player and dealer hands shall be compared, the higher hand wins.
9. If the player has the higher hand, then the Ante and Raise bets shall pay even money.
10. If the dealer has the higher hand, then the Ante and Raise bets shall lose.
11. If the player and dealer tie, then the Ante and Raise bets shall push.
12. If the player has a straight or higher, then he shall win the 'In to Win Bonus.' Note that it is not required to beat the dealer to qualify for this bonus. There are two known pay tables, as shown below.
13. The First 3 Bonus will be adjudicated according to the player's initial three cards. If the player stood, it will be obvious what they were. If the player drew, then the only possible First 3 Bonus win will be a pair. I assume the dealer will assume the player would have stood with a flush or higher. A pay table for the First 3 Bonus appears below.

Following are the In to Win Bonus pay tables for both the United Kingdom and Atlantic City.

In to Win Bonus

Following is the First 3 Bonus pay table as seen in the video below. All wins are on a 'to one' basis.

First 3 Bonus

Atlantic City Rules Analysis

The following table shows the probability and contribution to the return for all possible events under the Atlantic City pay table on the In to Win Bonus.

Atlantic City Rules Analysis

The lower right cell in the table above reflects a house edge of 3.20%. On average, the player will raise 92.8326% of the time, for a final average wager of 1.928326 units. This makes the Element of Risk, defined as the ratio of the expected player loss to the total amount bet, what I think is a good measurement of player value, 3.2018%/1.928326 = 1.66%.

United Kingdom Rules Analysis

The following table shows the probability and contribution to the return for all possible events under the United Kingdom pay table on the In to Win Bonus.

United Kingdom Rules Analysis

The lower right cell in the table above reflects a house edge of 1.04%. On average, the player will raise 92.8326% of the time, for a final average wager of 1.928326 units. This makes the Element of Risk, defined as the ratio of the expected player loss to the total amount bet, what I think is a good measurement of player value, 1.04%/1.928326 = 0.54%.

First 3 Bonus Analysis

The following table shows the probability and contribution to the return for all possible events of the First 3 Bonus.

First 3 Bonus

The lower right cell in the table above reflects a house edge of 4.20%.

Strategy

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The following strategy show how to play each initial hand. It was developed by Gordon Michaels, to whom I thank for letting me publish it.

• 3-card straight, 3-card flush, 3-of-a-kind — Always BET and stand on your three cards.
• Pair — BET, and always discard your unpaired card and draw to you pair. The only exception is with 2-2-A, where the ace is suited to one of the deuces, in which case discard the unsuited deuce.
• The drawing strategy for all other hands is rather involved and explained below. The betting strategy is easier, which is to raise with any of the following, otherwise fold:
  • With Q98 or higher, or
  • Two suited cards, or
  • Two consecutive cards (i.e. open-ended straight draw), or
  • J-9 or T-8

Following is the drawing strategy with three singletons of different suits.

• AKx, AQx: Draw to the 2 highest cards
• AJx – QTx: If you can, draw to any two cards of adjacent rank. Second priority is draw to any A3 or A2. Otherwise, draw to the 2 highest cards. Exception: with K32 it is better to draw to K3 than to 32.
• Q9x – 53x: If you can, draw to any two cards of adjacent rank. Second priority is draw to a J9 or T8. Otherwise FOLD. Drawing to a High-Card Hand with 2 suited cards.

Given a high card with two suited cards, you will always bet, and discard and draw a card. In general you want to draw to the 2-suited cards but sometimes it is better to draw to two very high cards (Ax, Kx) or to 2 unsuited cards that comprise a straight draw. Here are the strategy rules:

• Always draw to a straight flush when possible, except for these two hands; A53 with a suited 53, or A42 with a suited 42; with these hands you should draw to the A3o or A2o respectively.

When you have no straight flush draw:

• AKx, AQx: – Always draw to the 2 highest cards except when you can draw to AJs, ATs, A9s
• AJx-A4x: - Draw to any suited Ax. Second priority is a straight draw to an A3o or A2o. Third priority is drawing to the 2 highest cards.
• KQx: Always draw to the KQ.
• KJx - QTx: Draw to any suited Kx or Qx. Otherwise draw to the 2 highest cards.
• Q9x- 532: Always draw to the 2 suited cards.

Strategy Changes: Atlantic City Vs. United Kingdom

With only a few exceptions, the strategy is the same for United Kingdom and Atlantic City rules. The few exceptions arise from the fact that the Atlantic City paytable provides less incentive to draw to a straight flush. When the lowest two cards are suited, the following hands should be played differently, depending upon the rules.

AQT, A86, A75, A64

With Atlantic City Rules, you should discard the lowest card and draw to the two highest cards. With United Kingdom rules, it is best to draw to the straight flush with the two lowest cards.

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The Borderline Hand

The hand that forms the borderline between betting and folding an unsuited high card hand is Q97 (unsuited.) Of course, folding this hand has an EV = -1.0. There are two potential ways to draw to Q97 and remarkably enough, here are the EVs:

• Discard the 7, draw to Q9: EV = -1.0148106.
• Discard the Q, draw to 97: EV = - 1.0002618.

If the above isn't clear, I also present the following strategy tables on which card to hold with Q32 to AKQ.

Video

Following is a video by the game maker on how to play.

Please not that at about the 6:22 point the advice given incorrectly to fold on a J92 offsuit. This is not the correct strategy. It is correct to hold the J9.

Acknowledgements

I would like to thank Daniel Dale and Gordon Michaels for their analysis of the game and Gordon Michaels for the strategy. The two geniuses are known respectively as CrystalMath and gordon888 in my forum at Wizard of Vegas.

External Links

• Discussion about 3 Card Draw Poker in my forum at WizardOfVegas.com.

Draw Poker games are any games where players get at least one opportunity to discard a certain number of cards from their hand in exchange for new cards from the deck. It gives each player the chance to get rid of cards that are doing nothing to help their overall hand and hope for something better. The draw of cards also allows the possibility for other players to guess what kind of hand that player has. A player who draws one card, for example, is probably trying to complete a flush or straight, as opposed to a poker player who draws three cards who is probably only holding a pair, but one can only guess.

Drawing:
The dealer determines how many cards players will be allowed to draw from the deck, and how many opportunities players will have to draw cards from the deck. “Two draws of two cards”, for example, means that players will have two opportunities throughout the course of the game to draw as many as two new cards from the deck each time. “One of three, one of one” would mean that on the first draw, each player can draw as many as three new cards from the deck, and on the second draw, as many as one new card. When determining draws of cards, the dealer must make sure that there will be enough cards in the deck should each player choose to exercise their maximum allowed number of cards on each draw.

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Wild cards:
The sky is the limit with Draw Poker games. The dealer can designate that any card of his or her choice (before looking at his or her hand, of course) is wild. “Twos and Threes are wild”, for example. A player dealt a Two or a Three can make that card any of the 52 cards in the deck he or she chooses. The point to bear in mind is that the more wild cards there are, the better a hand will need to be in order to have a fighting chance in the game.

‘Deuces Wild’ will produce some fairly modest hands, whereas ‘Acey Deucey One-Eyed Jacks, and the Man with the Battleaxe’ (count ’em, that’s 11 wild cards in total, out of a deck of 52 cards), or worse yet ‘Pregnant Threes’ (TWELVE wild cards altogether) will produce some very competitive hands where, most likely, nothing less than a four of a kind will cut it. In Roll Your Own, each poker player chooses which card in his or her hand will be wild. In Kings and Little Ones, Kings and the smallest card in each player’s hand is wild.

Betting:
Typical poker Draw games involve at least two betting rounds, one before and one after each draw. Two draws would involve three rounds of betting, one before the first draw, one between draws, and one after the second draw. There is always one more betting round than there are draws. Because the dealer can call any stipulation he or she likes, some tables play Draw games with only one betting round, after the draw. However, betting rounds are what keep players “honest” and make sure they are paying their dues in order to stay in the game…you can rarely bluff or scare somebody out of a game with one betting round only.

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Pay for Your Draw:
This is a feature that can be added to any Draw poker game. It helps increase the pot and tends to keep hands lower, which is especially helpful in draw games that include wild cards. When the dealer calls this feature, he or she also calls the price of each card drawn. If, for example, the price of each drawn card is a quarter, and a player decides to draw 3 cards at the appropriate point in the game, then that player would have to throw 75 cents into the pot. A maximum draw can still be called by the dealer, but players must now pay for each card that they wish to draw from the deck.

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Roll ‘Em:
When this feature is added to a Draw poker game, the game is played as normal up until the showdown. At that point, each player lays their hand face-down before them. On the count of three, each player reveals one card of their hand. The highest card showing opens a betting round. On the count of three again, each player reveals a second card from their hand. Best hand showing opens a betting round. This continues for a third and a fourth card, after which the best hand showing opens the fourth and final betting round.

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In essence, this adds a Stud element to the Draw game. As this adds four betting rounds to the game, it is best used in poker games that do not have enough betting rounds, such as Pass the Trash. One variation of Roll ‘Em is that less than the entire hand is rolled off; for example, the dealer may specify that each player only roll off 3 of the 5 cards in their hand. Yet another variation is Seven Card Draw, where each player rolls off five of their seven cards; the cards that they roll off need not necessarily be ones that they use in their five card hand at the showdown.