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Five Play Draw Poker Game. What’s better than a single hand of video poker? How about playing several of them at the same time? That’s the concept behind multihand machines, which give players the chance to play more than once each time they get dealt a new set of cards.

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.

External Links

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

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15 members have voted

I just heard that the Atlantic City Tropicana is hosting the game 3 Card Draw Poker. Here is a video on how to play:

Direct link: https://www.youtube.com/watch?v=FfxCdhALKDM
I can't justify analyzing this game over just one placement but will keep an eye out for it should it grow. Seems to me that poker variants with a draw option have not done well in general. Then again, almost every new game idea does not get far. Anyone know of other placements?
The question for the forum is would you play 3 Card Draw Poker?Interesting . This is another poker game in which the dealer has more cards than the player from which to make a poker hand. Similar to Four Card Poker and Discard Inferno.
1. Can anyone read the two payout tables in the video? I could not read a couple of the lines.
2. Are you limited to drawing a maximum of 1 card? Or, could you draw 2 cards to an ace?

Interesting . This is another poker game in which the dealer has more cards than the player from which to make a poker hand. Similar to Four Card Poker and Discard Inferno.
1. Can anyone read the two payout tables in the video? I could not read a couple of the lines.
2. Are you limited to drawing a maximum of 1 card? Or, could you draw 2 cards to an ace?

Their website scoregaming.com has all the payouts, it says you can only draw one card.Thanks. Their website says that the main game, the ante bet, has a HE of 1.04% That is quite attractive.
The bonus bet is stated to have a house edge of 2.21%.
Over and above winning or losing, the Ante Payout Table on the ante bet is:
Straight: 1 to 1
Trips: 3 to 1
Str Flush: 10 to 1
Mini Royal: 20 to 1
The optional First 3 Bonus Wager has this payout table:
Pair: 1 to 1
Flush: 3 to 1
Straight: 6 to 1
Trips: 30 to1
Str Flush: 60 to 1
Mini Royal: 100 to 1
Pretty puny payout on the mini-royal.

That's some complicated payouts the dealer has to remember. I cant' see this doing well.

Dealers don't 'remember' any of the payouts on these types of games. Rather, they just look at the paytable on the felt and pay it off, oftentimes incorrectly. :)
I think the game is pretty cool. It makes sense, very straightforward, and seems simple enough to play.
With a 1% HE game and a 2% HE side bet, the casino isn't going to be making much money, especially when you consider it's not likely a game for big bettors. Other games either have a low HE (like BJ) but move very fast.....or have a big house edge and move slowly (UTH, MS, etc.)....or like baccarat, which doesn't move particularly fast, has a small house edge, but has huge bets.
I don't know what the strategy is for this game, but IF you usually hold 2 cards to a flush (which I doubt) is the proper play, then I'm not seeing much room for player mistakes drastically increasing the HE (ie: like idiots not shoving with AK in UTH).
This game will move slowly, have small bets, and has a small HE.

Would also be time consuming for each hand. The dealer has to wait for each player to make their decision in order and many times the player has to decide whether to go for the straight, flush , high card or Straight Flush(like the first hand dealt in the video).

I think that is a big reason draw games don't do well. Table game management put a huge emphasis on hands per hour.Just for chuckles, here what I calculate for the distribution of hands that a dealer will make, as dealt from a fresh 52-card deck:
Dealer hand distribution, 52 card deck
Mini-Royal: 0.0635%
Str Flush: 0.789%
Trips: 0.946%
Straight: 10.73%
Flush: 15.28%
Pair: 26.52%
Hi Card: 45.66%
High Card hands are distributed as:
A-High: 14.47%
K-High: 11.15%
Q-High: 7.91%
J-High: 5.35%
Lower: 6.78%
*****************************************
I do think the strategy is complicated and that there will be lots of player errors. For the strategy, you will need to determine what the minimum hand to hit is in each of these categories:
Drawing to 2 unpaired cards:
- No flush draw, no straight draw
- No flush draw, 1-gap straight draw

4 Card Poker Casino Game

- No flush draw, open-ended straight draw (do you draw to a 23, holding J32? with K32 should you draw to K3 or 32?)
- Flush draw, no straight draw
- Flush draw or 1-gap straight draw (example: QsTh2s or AsQh5s
That doesn't cover it all. What will customers do with these hands? What would you do?
As2s2h? Draw to 2s2h or As2s?
As4s4h? Draw to 4s4h or As4s?

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