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Last Updated: November 16, 2017

3 Card Draw Poker

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

Event Atlantic City
Pay Table
U.K.
Pay Table
Mini Royal 20 20
Straight Flush 6 10
Trips 5 5
Straight 1 1


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

Event Pays
Mini Royal 100
Straight Flush 50
Trips 30
Straight 6
Flush 3
Pair 1


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

Event Pays Combinations Probability Return
Win, Mini Royal 22 105,779,700 0.000502 0.011044
Win, Straight Flush 8 1,125,628,080 0.005342 0.042736
Win, Trips 7 1,917,122,064 0.009098 0.063689
Win, Straight 3 15,053,855,460 0.071443 0.214330
Win, Flush 2 20,422,535,496 0.096922 0.193844
Win, Pair 2 30,486,111,084 0.144682 0.289365
Win, High Card 2 21,961,798,332 0.104227 0.208455
Lose, Mini Royal 18 - 0.000000 0.000000
Lose, Straight Flush 4 5,299,572 0.000025 0.000101
Lose, Trips 3 26,342,976 0.000125 0.000375
Lose, Straight -1 1,076,861,220 0.005111 -0.005111
Lose, Flush -2 5,158,910,832 0.024483 -0.048967
Lose, Pair -2 20,886,646,560 0.099125 -0.198250
Lose, High Card -2 77,157,616,680 0.366178 -0.732356
Push, Mini Royal 20 71,820 0.000000 0.000007
Push, Straight Flush 6 749,628 0.000004 0.000021
Push, Trips 5 - 0.000000 0.000000
Push, Straight 1 78,575,640 0.000373 0.000373
Push, Flush 0 12,828,552 0.000061 0.000000
Push, Pair 0 15,042,036 0.000071 0.000000
Push, High Card 0 116,384,988 0.000552 0.000000
Fold -1 15,102,521,280 0.071674 -0.071674
Total 210,710,682,000 1.000000 -0.032018


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

Event Pays Combinations Probability Return
Win, Mini Royal 22 105,779,700 0.000502 0.011044
Win, Straight Flush 12 1,134,919,164 0.005386 0.064634
Win, Trips 7 1,917,122,064 0.009098 0.063689
Win, Straight 3 15,070,574,952 0.071523 0.214568
Win, Flush 2 20,495,098,320 0.097267 0.194533
Win, Pair 2 30,481,490,028 0.144660 0.289321
Win, High Card 2 21,846,027,168 0.103678 0.207356
Lose, Mini Royal 18 - 0.000000 0.000000
Lose, Straight Flush 8 5,341,992 0.000025 0.000203
Lose, Trips 3 26,342,976 0.000125 0.000375
Lose, Straight -1 1,078,736,988 0.005120 -0.005120
Lose, Flush -2 5,179,699,308 0.024582 -0.049164
Lose, Pair -2 20,891,280,624 0.099147 -0.198294
Lose, High Card -2 77,152,240,740 0.366152 -0.732305
Push, Mini Royal 20 71,820 0.000000 0.000007
Push, Straight Flush 10 755,964 0.000004 0.000036
Push, Trips 5 - 0.000000 0.000000
Push, Straight 1 78,660,060 0.000373 0.000373
Push, Flush 0 12,875,652 0.000061 0.000000
Push, Pair 0 15,029,028 0.000071 0.000000
Push, High Card 0 116,114,172 0.000551 0.000000
Fold -1 15,102,521,280 0.071674 -0.071674
Total 210,710,682,000 1.000000 -0.010418


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

Event Pays Combinations Probability Return
Mini royal 100 4 0.000181 0.018100
Straight flush 50 44 0.001991 0.099548
Three of a kind 30 52 0.002353 0.070588
Straight 6 720 0.032579 0.195475
Flush 3 1,096 0.049593 0.148778
Pair 1 3,744 0.169412 0.169412
All other -1 16,440 0.743891 -0.743891
Total 22,100 1.000000 -0.041991


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

Strategy



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.

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.



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

Written by: Michael Shackleford

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