3 Card Draw Poker

Rules

1. A single 52-card deck is used.
2. As in standard poker, all cards and hands are ranked accordingly. The hierarchy of hands is as follows:
   • Straight flush
   • Three of a kind
   • Straight
   • Flush
   • Pair
   • All other
3. The game kicks off with the player placing an Ante bet. At this point, there is also an optional side bet known as the First 3 Bonus that players may choose to make.
4. Every player receives three cards while the dealer is dealt four cards, all of which are kept face down.
5. After assessing their own hand, the player can choose from several options:
   • Place a Raise bet that matches the Ante bet and remain in the game
   • Place a Raise equal to the Ante bet, then exchange one card for the next available card from the deck.
   • Fold
6. If the player chooses to discard, the new card will be compared separately from the other two cards for the adjudication of the First 3 Bonus side bet.
7. Once the player has made their decision, the dealer will reveal their cards and select the three that create the highest-ranking poker hand.
8. The player’s hand is then compared with the dealer’s, with the higher hand declared the winner.
9. If the player holds a superior hand, both the Ante and Raise bets will pay out at even money.
10. However, if the dealer’s hand is stronger, the player will lose both the Ante and Raise bets.
11. In the event of a tie, neither the Ante nor Raise bets will win or lose.
12. If the player successfully achieves a straight or a better hand, they will receive the 'In to Win Bonus.' Interestingly, it is not necessary to surpass the dealer to qualify for this bonus. There are two different pay tables available, which can be found below.
13. The First 3 Bonus will be determined based on the player's original three cards. If the player chose to stand, their hand will be clear. If they drew new cards, the only eligible win for the First 3 Bonus will be a pair. It’s reasonable to assume the dealer considers the player would have stood if they had a flush or higher. A pay table for the First 3 Bonus is provided below.

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

Here is the pay table for the First 3 Bonus, as demonstrated in the video below. All winnings are expressed as 'to one'.

Atlantic City Rules Analysis

The following table illustrates the probability and expected return for all possible outcomes based on the Atlantic City pay table for the In to Win Bonus.

The table corner indicates a house edge of 3.20%. On average, players will raise approximately 92.8326% of the time, leading to an average final bet of 1.928326 units. Consequently, the Element of Risk, defined as the expected player loss relative to total bets, calculates to a player value of 3.2018% divided by 1.928326, resulting in 1.66%.

United Kingdom Rules Analysis

The next table provides the probability and return contribution for all potential outcomes according to the United Kingdom pay table for the In to Win Bonus.

The lower right corner of this table shows a house edge of 1.04%. Players will raise about 92.8326% of the time, leading to an average final wager of 1.928326 units. Therefore, the Element of Risk yields a player value of 1.04% divided by 1.928326, which equals 0.54%.

First 3 Bonus Analysis

The next table outlines the probability and return contribution for all possible events under the First 3 Bonus.

The house edge indicated in the lower right corner of this table is 4.20%.

Strategy

The following strategy outlines how to play every initial hand. This guide was crafted by Gordon Michaels, who deserves thanks for allowing me to share it.

• For a 3-card straight, 3-card flush, or 3-of-a-kind — always place a BET and stand firm with your three cards.
• If you have a Pair — place a BET, discard the unpaired card, and draw to enhance your pair. The sole exception is with 2-2-A when the ace is suited to one of the deuces; in that scenario, discard the unsuited deuce.
• The drawing strategy for different hands can be complex and is explained in detail below. The betting strategy, however, is straightforward: raise with any of the following hands, or else fold:
  • With Q98 or higher, or
  • Two suited cards, or
  • Consecutive cards (such as an open-ended straight draw), or
  • J-9 or T-8

The next section covers the drawing strategy when holding three different suited cards.

• AKx, AQx: Draw to the 2 highest cards
• With hands like AJx – QTx: If possible, draw to any two cards of adjacent ranks. If not, aim for A3 or A2. Lastly, draw to the two highest cards. An exception exists when holding K32; in this case, it is preferable to draw to K3 instead of 32.
• For Q9x – 53x: Strive to draw to any two adjacent rank cards if possible. The second best option is to aim for J9 or T8. If neither is available, FOLD. Drawing strategy for a high-card hand with two suited cards.

When you have a high card accompanied by two suited cards, always place a bet, discard one, and draw. Generally, you want to draw to your two suited cards; however, on occasion, it may be advantageous to draw to two high cards (like Ax, Kx) or to two unsuited cards that create a straight draw. Here are the strategic guidelines:

• Always attempt to draw to a straight flush when feasible, unless you have the following two specific hands: A53 with a suited 53, or A42 with a suited 42; in these instances, draw to A3o or A2o, respectively.

When you have no straight flush draw:

• For AKx, AQx: Always aim to draw to the two highest cards unless you have the option to draw to AJs, ATs, or A9s.
• When holding AJx-A4x: Draw to any suited Ax. The second choice should be a straight draw to A3o or A2o, followed by the two highest cards.
• KQx: Always draw to the KQ.
• For KJx - QTx: Draw to any suited Kx or Qx. If those aren't available, prioritize drawing to the two highest cards.
• Q9x- 532: Always draw to the 2 suited cards.

Differences in Strategy: Atlantic City Compared to the United Kingdom

In most cases, the strategy remains consistent regardless of whether you’re playing under United Kingdom or Atlantic City rules. The few exceptions stem from the Atlantic City paytable, which offers less motivation to aim for a straight flush. When the two lowest cards are suited, your approach should vary based on the regulatory framework.

AQT, A86, A75, A64

Under Atlantic City Rules, discard the lowest card and draw to the two highest. Conversely, under United Kingdom rules, it’s wiser to pursue a straight flush with the two lowest cards.

The Borderline Hand

In terms of betting versus folding with an unsuited high card hand, Q97 (unsuited) sits at a critical juncture. Of course, folding this hand results in an EV of -1.0. There are two distinct methods to draw to Q97, and surprisingly here are the EVs:

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

If the earlier instructions weren’t clear enough, I’ll provide strategy tables outlining which card to hold from Q32 to AKQ.

Video

Included is a video by the game’s creator detailing how to play.

Be aware that around the 6:22 mark, incorrect advice is given suggesting that one should fold on a J92 offsuit. This strategy is incorrect; it is actually advisable to retain the J9.

Acknowledgements

I’d like to express gratitude to Daniel Dale and Gordon Michaels for their insightful analysis of the game, and to Gordon Michaels for sharing his strategy. Both of these talented individuals are recognized as CrystalMath and gordon888 on my forum at Wizard of Vegas .

External Links

• Discussion This platform offers mathematically sound strategies and information covering casino games like blackjack, craps, roulette, among countless others.

Written by: Michael Shackleford