I noticed another new AGS game in my nearby Harrah’s Casino, called Premium Hold’Em, extending their products of 3-hole card poker games against the dealer. I kind of enjoy squeezing these hole cards, catching minimal glimpses of colors and symbols, and making (correct) decisions without knowing my full hand. Sometimes, this leaves me with emergency outs after seeing the dealer’s hand.
Plus, once you’ve played enough Ultimate Texas Hold’Em (UTH), all those decisions become automatic, and all you seem to notice is that string of miracle dealer hands which constantly scoop the table. UTH can be boring *and* painful.
So, what’s new with AGS’s Premium Hold’Em? Well, first, there’s the novelty and the squeezing of your three hole cards. Next, the all-in preflop raise is lowered to 3x, which should reduce the variance a bit (from UTH’s 4x). Then, the entire community board is dealt out at once as a four card “flop”. Finally, you can either 2x, 1x, or fold after seeing your entire hand! (Compare to UTH’s 2x decision before the turn+river.) Of course, the dealer has three unseen hole cards, but the 2x option is still more favorable than in UTH. Overall, these advantages are offset by the lowered 3x preflop raise, and the higher pair-of-treys Dealer qualifier. Bottom lime, the house edge of Premium Hold’Em is lower than UTH, at 2.06% of an Ante.
Oh, and the bonus side bet pays down to Jacks Up (two pairs), and has a low house edge of 4.87%. Again, this offers lower variance than the UTH Trips side bet.
Basic Strategy
I wanted to try out the game, so I worked out a Basic Strategy. I worked it down to the detail that I like, using hand features that make sense to me. The table is organized by the two decision points, and divided into mutually exclusive categories for the Player hand, and also for the board. For each determined sub-category, the selected betting rules should be followed top-down, looking for the first matched condition, or else falling through to the bottom action.
The betting rules are meant to be concise and unambiguous, but I’ll elaborate on some of them below, to clarify with examples.
The Basic Strategy is sub-optimal by only 0.28% from the ideal 2.06% house edge.
You can practice the game for free at the AGS website.
Premium Hold’Em Basic Strategy
Decision
Player Hand
Board
Prioritized Betting Rules
Preflop
(3x All-In
or
Check)
Trips
3x all Three-of-a-Kind hands.
Pair
3x pair of FIVE’s or better, else
check all others.
3-Suited
3x A-T-x all suited or higher, else
3x three suited cards all NINE or higher, else
check all others.
other
3x A-J-T ranks or all higher, else
check all others.
River
(2x, 1x, or Fold)
Royal Flush,
Straight Flush
2x all hands
Four-of-a-Kind
quads on board
2x with 1st or 2nd nut kicker, else
1x with 7th nut kicker or better, else
fold all others
other
2x all hands
Full House
2x all Full Houses
Flush
2x all Flushes
Straight
4-flush
1x Straight against 4-flush board
other
2x all Straights
Three-of-a-Kind
trips on board
2x trips on board with nut kicker in the hole, else
1x trips on board with 2nd or 3rd nut kicker in the hole, else
fold all others
4-flush
1x Three-of-a-Kind against scare flush
other
2x all hands
Two Pairs
double-paired
2x two better pairs, else
2x nut kicker, else
1x 2nd or 3rd nut kicker, else
fold all others
paired
2x “top pair” or “overpair”, else
2x “bottom pair” with 3rd nut or better kicker, else
1x all others
4-flush or
open-ended
1x all hands vs scare board
other
2x all hands
One Pair
pair on board
1x with nut kicker in the hole, else
1x with 2nd nut kicker in the hole and 2-flush max board, else
fold all others
4-flush or
open-ended
1x 2nd pair or better, else
fold all others
gutshot
1x bottom pair or better, else
fold all other underpairs
other
2x 2nd pair or better, when SIX’s or better, else
1x bottom pair or better, else
1x qualifying underpair, else
Fold all other underpairs
High Card
4-flush or
4-straight
Fold all hands
other
1x Ace-King with nut kicker in the hole vs rainbow board, else
fold all others
Typical play is actually pretty easy, and the Basic Strategy is intuitive and easy to learn. The top part of the table tells you what the 3x preflop raising hands are. They occur about 15.7% of the time, and are easy to remember.
All the river decisions for hands Three-of-a-Kind and higher are simple and intuitive. Thankfully, you should 2x bet *all* full houses and flushes, independent of the board. The only time you slow down with a straight is when you 1x it against a 4-flush board. Notice you still 2x the idiot end straight against an open-ended board, and you still 2x a baby flush against a 4-flush board. And you still 2x a flush against a double-paired board.
You’ll slow down with Three-of-a-Kind when they’re on board. You will 2x them with a nut (best) kicker in the hole. For example, say you’re holding Kh 9s 6h, and there’s trips on board with 8s 8c 8h Ad. You have the nut (best) kicker in the hole (Kh), so you can still 2x your hand. However, if your hole cards were Qh 9s 6h, you should only 1x the hand since your Qh is only 2nd nut kicker. You could still 1x call with Jh 9s 6h (3rd nut kicker), but you would fold with anything lower than the 3rd nut kicker.
If you have Three-of-a-Kind and the board is a scare flush (4-flush), then you can still 1x your hand. For example, if your hole cards were 7d 3s 3h and the board was 3c Kc Jc 6c, you’d only 1x your trip 3’s.
You’ll generally 2x your two pairs, unless the board is dangerous. So, against a scare flush (4-flush) or a scare straight (open-ended) board, you’ll just 1x your two pairs. You should 2x raise your two pairs any time you can beat a double-paired board, or even if you just have the nut kicker. If the board is paired, you’ll 2x raise your top pair or over pair. You can 2x raise with bottom pair, just as long as you have 3rd nut kicker or better. You’ll never fold two pairs when you beat the board. The only time you’ll fold with two pairs is when you’re playing the board, and don’t have 4th nut kicker or better.
Note: “bottom pair” on a paired board means you’ve paired the lowest singleton on the board. For example, say the board is 3s 3h Kd 7h. If you’re holding a 7, you’ve made bottom pair on the board. If you’re holding a K, you’ve made top pair on the board. If you have a pair of wired Aces, they’d be an over pair to the board. If you have a pair of wired Deuces, they’d be an under pair to the board. Also, if you held a pair of wired Fives in the hole, they’d be an under pair to the board too (lowest board singleton is a Seven).
There are a few occasions when you can 2x raise one pair against a safe board (no 4-flush or 4-straight board, including gutshot board). Against a safe board, you can 2x raise one pair if it’s an over pair, top pair, or second pair.
Generally speaking, you’ll at least 1x call any pair made with the board. You will fold 3rd or bottom pair against a scare board. You’ll only call a wired under pair to the board if it’s qualifying, and there’s no 4-flush or 4-straight on board.
You can 1x call playing one pair on board, if you have the nut kicker. You can also 1x call the pair on board if you hold the 2nd nut kicker, and the board is 2-flush or less.
There’s only one case to 1x bet a no-pair hand on the river. You should 1x play an Ace-King high hand against a rainbow flop when holding the nut kicker, and the board isn’t 4-cards to a straight. For example, if your hole cards were Qh 8d 3s and the board was Ac Kh 9d 4s, then you should 1x your hand, because your Qh hole card is the nut kicker.
Collusion Analysis
The game is not vulnerable to even 5 confederates colluding at a full-table sharing perfect information. Ideal decisions using all known player hole cards (15 of them at a full table) yield only about a +1.4% improvement over Basic Strategy (about +0.5% from counter-strategy pre-flop decisions, and about +0.9% from counter-strategy river decisions).
Bonus Side Bet
An optional bonus on your final hand, or the Dealer’s final hand, is available before the hand begins. The table below shows the payouts and their frequencies and returns. The house edge is a reasonable 4.87%, and it pays down to Jacks Up (two pairs), instead of the UTH Trips or better bonus.
Outcome
Combinations
Frequency
Payout
Return
ROYAL_FLUSH
4,324
0.000032
50
0.001616
STRAIGHT_FLUSH
37,260
0.000279
30
0.008355
FOUR_OF_A_KIND
224,848
0.001681
10
0.016807
FULL_HOUSE
3,473,184
0.025961
6
0.155766
FLUSH
4,047,644
0.030255
4
0.121020
STRAIGHT
6,180,020
0.046194
3
0.138581
THREE_OF_A_KIND
6,461,620
0.048299
2
0.096597
Two Pairs (J’s Up+)
173,854,08
0.129951
1
0.129951
other
95,970,252
0.717349
-1
-0.717349
total
133,784,560
1.000000
-0.048656
expected
133,784,560
Detailed Stats
The total outcomes for every possible starting hand, for every possible flop, and every possible dealer hole cards are shown in the table below, following optimal decisions. The player will 3x about 15.7% of his hands, will 2x about 37.4% of his hands, will 1x about 23.9% of the hands, and will fold about 23.0% of the hands.
Outcome
Combinations
Frequency
Net
Return
Win 3x Play w/ ROYAL_FLUSH vs. qualified dealer
879,320,772
0.000013
504
0.006670
Win 3x Play w/ STRAIGHT_FLUSH vs. qualified dealer
2,149,315,348
0.000032
104
0.003364
Win 3x Play w/ FOUR_OF_A_KIND vs. qualified dealer
55,353,208,088
0.000833
14
0.011663
Win 3x Play w/ FULL_HOUSE vs. qualified dealer
602,898,278,304
0.009074
7
0.063516
Win 3x Play w/ FLUSH vs. qualified dealer
237,450,980,932
0.003574
5.5
0.019655
Win 3x Play w/ STRAIGHT vs. qualified dealer
191,445,164,564
0.002881
5
0.014406
Win 3x Play w/ THREE_OF_A_KIND vs. qualified dealer
575,993,062,524
0.008669
4
0.034675
Win 3x Play w/ TWO_PAIRS vs. qualified dealer
2,246,740,264,764
0.033814
4
0.135256
Win 3x Play w/ ONE_PAIR vs. qualified dealer
1,066,642,147,548
0.016053
4
0.064213
Lose 3x Play vs. qualified dealer
3,231,042,644,372
0.048628
-5
-0.243140
Tie 3x Play vs. qualified dealer
30,011,251,504
0.000452
0
0.000000
Win 3x Play w/ ROYAL_FLUSH vs. non-qualified dealer
201,445,188
0.000003
503
0.001525
Win 3x Play w/ STRAIGHT_FLUSH vs. non-qualified dealer
430,781,892
0.000006
103
0.000668
Win 3x Play w/ FOUR_OF_A_KIND vs. non-qualified dealer
3,718,604,400
0.000056
13
0.000728
Win 3x Play w/ FULL_HOUSE vs. non-qualified dealer
87,580,605,564
0.001318
6
0.007909
Win 3x Play w/ FLUSH vs. non-qualified dealer
65,138,805,780
0.000980
4.5
0.004412
Win 3x Play w/ STRAIGHT vs. non-qualified dealer
62,396,153,160
0.000939
4
0.003756
Win 3x Play w/ THREE_OF_A_KIND vs. non-qualified dealer
292,929,250,596
0.004409
3
0.013226
Win 3x Play w/ TWO_PAIRS vs. non-qualified dealer
508,732,581,216
0.007657
3
0.022970
Win 3x Play w/ ONE_PAIR vs. non-qualified dealer
1,045,415,883,192
0.015734
3
0.047201
Win 3x Play w/ HIGH_CARD vs. non-qualified dealer
71,345,648,256
0.001074
3
0.003221
Lose 3x Play vs. non-qualified dealer
22,949,828,544
0.000345
-4
-0.001382
Tie 3x Play vs. non-qualified dealer
1,115,495,892
0.000017
0
0.000000
Win 2x Play w/ ROYAL_FLUSH vs. qualified dealer
902,421,300
0.000014
503
0.006832
Win 2x Play w/ STRAIGHT_FLUSH vs. qualified dealer
13,145,193,656
0.000198
103
0.020377
Win 2x Play w/ FOUR_OF_A_KIND vs. qualified dealer
48,452,947,496
0.000729
13
0.009480
Win 2x Play w/ FULL_HOUSE vs. qualified dealer
891,034,206,768
0.013410
6
0.080462
Win 2x Play w/ FLUSH vs. qualified dealer
1,208,401,617,832
0.018187
4.5
0.081840
Win 2x Play w/ STRAIGHT vs. qualified dealer
1,833,221,994,724
0.027590
4
0.110362
Win 2x Play w/ THREE_OF_A_KIND vs. qualified dealer
1,548,010,040,012
0.023298
3
0.069894
Win 2x Play w/ TWO_PAIRS vs. qualified dealer
5,325,367,541,112
0.080148
3
0.240444
Win 2x Play w/ ONE_PAIR vs. qualified dealer
2,347,190,713,200
0.035326
3
0.105977
Lose 2x Play vs. qualified dealer
5,884,001,322,956
0.088556
-4
-0.354223
Tie 2x Play vs. qualified dealer
356,306,998,604
0.005363
0
0.000000
Win 2x Play w/ ROYAL_FLUSH vs. non-qualified dealer
164,326,140
0.000002
502
0.001242
Win 2x Play w/ STRAIGHT_FLUSH vs. non-qualified dealer
2,738,580,240
0.000041
102
0.004204
Win 2x Play w/ FOUR_OF_A_KIND vs. non-qualified dealer
1,966,734,000
0.000030
12
0.000355
Win 2x Play w/ FULL_HOUSE vs. non-qualified dealer
49,091,947,236
0.000739
5
0.003694
Win 2x Play w/ FLUSH vs. non-qualified dealer
339,829,796,400
0.005115
3.5
0.017901
Win 2x Play w/ STRAIGHT vs. non-qualified dealer
618,260,337,144
0.009305
3
0.027915
Win 2x Play w/ THREE_OF_A_KIND vs. non-qualified dealer
144,904,859,028
0.002181
2
0.004362
Win 2x Play w/ TWO_PAIRS vs. non-qualified dealer
1,898,618,140,944
0.028575
2
0.057149
Win 2x Play w/ ONE_PAIR vs. non-qualified dealer
2,363,506,427,088
0.035571
2
0.071143
Win 1x Play w/ FOUR_OF_A_KIND vs. qualified dealer
349,955,952
0.000005
12
0.000063
Win 1x Play w/ STRAIGHT vs. qualified dealer
6,321,867,792
0.000095
3
0.000285
Win 1x Play w/ THREE_OF_A_KIND vs. qualified dealer
55,773,134,484
0.000839
2
0.001679
Win 1x Play w/ TWO_PAIRS vs. qualified dealer
677,790,208,140
0.010201
2
0.020402
Win 1x Play w/ ONE_PAIR vs. qualified dealer
1,790,737,887,912
0.026951
2
0.053902
Lose 1x Play vs. qualified dealer
10,014,543,966,612
0.150721
-3
-0.452164
Tie 1x Play vs. qualified dealer
195,881,895,144
0.002948
0
0.000000
Win 1x Play w/ STRAIGHT vs. non-qualified dealer
1,944,063,612
0.000029
2
0.000059
Win 1x Play w/ THREE_OF_A_KIND vs. non-qualified dealer
521,670,744
0.000008
1
0.000008
Win 1x Play w/ TWO_PAIRS vs. non-qualified dealer
57,782,013,408
0.000870
1
0.000870
Win 1x Play w/ ONE_PAIR vs. non-qualified dealer
2,716,947,685,944
0.040891
1
0.040891
Win 1x Play w/ HIGH_CARD vs. non-qualified dealer
218,296,927,728
0.003285
1
0.003285
Lose 1x Play vs. non-qualified dealer
142,599,511,272
0.002146
-2
-0.004292
Tie 1x Play vs. non-qualified dealer
21,633,803,136
0.000326
0
0.000000
Fold
15,265,300,263,840
0.229747
-2
-0.459493
total
66,444,101,724,000
1.000000
-0.020583
expected
66,444,101,724,000
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