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Last Updated: June 10, 2018

Premium Hold 'Em

Introduction

Premium Hold 'Em is a poker variant marketed by AGS. The first placement, that I'm aware of, was at Harrah's Rincon near San Diego in early 2018. It later got a field trial placement at the Mont Bleu in Lake Tahoe on May 31, 2018.

The game can most easily be compared to Ultimate Texas Hold 'Em. In both games, the player must make two equal bets to start. It also shares the same kind of betting structure as Ultimate Texas Hold 'Em, except it has two opportunities to raise instead of three. It does differ in that it gives the player and dealer three hole card each and a four-card flop. All things considered, the element of risk, assuming optimal player strategy, is a low 0.595%.

Rules

  1. A single 52-card deck is used.
  2. Hands are scored as in conventional Texas Hold 'Em, which I assume the reader is familiar with.
  3. Play begins with the player making equal bets on the Ante and the X-Tra Bonus. At this time, the player may make optional side bets on the Player Bonus and Dealer Bonus.
  4. The player and dealer shall each receive three hole cards face down. The player may inspect his own cards.
  5. The player may either check or make a Play bet equal to three times the Ante.
  6. The dealer shall deal four community cards face up, known as the flop.
  7. If the player did not make the Play bet before the flop, then the The player may bet 1x or 2x hit Ante bet or fold. If the player did make the Play bet before the flop, then play continues with no decision to be made at this point.
  8. The dealer shall reveal his own hole cards.
  9. The dealer qualifies with a pair of threes of better. If the dealer does not qualify, then remaining Ante bets shall push, before any hand comparison.
  10. The best five-card hand of both player and dealer shall be compared, the higher hand winning.
  11. The Ante bet, if still live, and the X-Tra Bonus shall pay even money if the player has the higher hand, push on a tie, and lose if the dealer has the higher hand.
  12. The X-Tra Bonus bet shall pay according to the pay table below if the player has the higher hand, push on a tie, and lose if the dealer has the higher hand.
  13. The Player Bonus and Dealer Bonus bets shall pay based on the poker value of the hand bet on only. Wins are shown in the pay table below.

The pay table below shows the win for winning X-Tra Bonus hands (which must beat the dealer), the Player Bonus and Dealer Bonus.

Blind Bet Pay Table

Hand X-Tra
Bonus
Player &
Dealer Bonus
Royal flush 500 50
Straight flush 100 30
Four of a kind 10 10
Full house 3 6
Flush 1.5 4
Straight 1 3
Three of a kind Push 2
Two pair (jacks up or better) Push 1
All other Push Loss

Analysis

The following table shows the win, number of combinations, probability, and contribution to the return for all possible events in Premium Hold 'Em, assuming optimal strategy. The numbers in this table are quoted with permission from the outstanding web site Discount Gambling.

Ante, X-Tra Bonus, and Play Analysis

Player
Hand
Play
Bet
Dealer
Qualifies
Pays Combinations Probability Return
Royal flush 3 Yes 504 879,320,772 0.000013 0.006670
Straight flush 3 Yes 104 2,149,315,348 0.000032 0.003364
Four of a kind 3 Yes 14 55,353,208,088 0.000833 0.011663
Full house 3 Yes 7 602,898,278,304 0.009074 0.063516
Flush 3 Yes 5.5 237,450,980,932 0.003574 0.019655
Straight 3 Yes 5 191,445,164,564 0.002881 0.014406
Three of a kind 3 Yes 4 575,993,062,524 0.008669 0.034675
Two pair 3 Yes 4 2,246,740,264,764 0.033814 0.135256
One pair 3 Yes 4 1,066,642,147,548 0.016053 0.064213
Loss 3 Yes -5 3,231,042,644,372 0.048628 -0.243140
Tie 3 Yes 0 30,011,251,504 0.000452 0.000000
Royal flush 3 No 503 201,445,188 0.000003 0.001525
Straight flush 3 No 103 430,781,892 0.000006 0.000668
Four of a kind 3 No 13 3,718,604,400 0.000056 0.000728
Full house 3 No 6 87,580,605,564 0.001318 0.007909
Flush 3 No 4.5 65,138,805,780 0.000980 0.004412
Straight 3 No 4 62,396,153,160 0.000939 0.003756
Three of a kind 3 No 3 292,929,250,596 0.004409 0.013226
Two pair 3 No 3 508,732,581,216 0.007657 0.022970
One pair 3 No 3 1,045,415,883,192 0.015734 0.047201
High card 3 No 3 71,345,648,256 0.001074 0.003221
Loss 3 No -4 22,949,828,544 0.000345 -0.001382
Tie 3 No 0 1,115,495,892 0.000017 0.000000
Royal flush 2 Yes 503 902,421,300 0.000014 0.006832
Straight flush 2 Yes 103 13,145,193,656 0.000198 0.020377
Four of a kind 2 Yes 13 48,452,947,496 0.000729 0.009480
Full house 2 Yes 6 891,034,206,768 0.013410 0.080462
Flush 2 Yes 4.5 1,208,401,617,832 0.018187 0.081840
Straight 2 Yes 4 1,833,221,994,724 0.027590 0.110362
Three of a kind 2 Yes 3 1,548,010,040,012 0.023298 0.069894
Two pair 2 Yes 3 5,325,367,541,112 0.080148 0.240444
One pair 2 Yes 3 2,347,190,713,200 0.035326 0.105977
Loss 2 Yes -4 5,884,001,322,956 0.088556 -0.354223
Tie 2 Yes 0 356,306,998,604 0.005363 0.000000
Royal flush 2 No 502 164,326,140 0.000002 0.001242
Straight flush 2 No 102 2,738,580,240 0.000041 0.004204
Four of a kind 2 No 12 1,966,734,000 0.000030 0.000355
Full house 2 No 5 49,091,947,236 0.000739 0.003694
Flush 2 No 3.5 339,829,796,400 0.005115 0.017901
Straight 2 No 3 618,260,337,144 0.009305 0.027915
Three of a kind 2 No 2 144,904,859,028 0.002181 0.004362
Two pair 2 No 2 1,898,618,140,944 0.028575 0.057149
One pair 2 No 2 2,363,506,427,088 0.035571 0.071143
Four of a kind 1 Yes 12 349,955,952 0.000005 0.000063
Straight 1 Yes 3 6,321,867,792 0.000095 0.000285
Three of a kind 1 Yes 2 55,773,134,484 0.000839 0.001679
Two pair 1 Yes 2 677,790,208,140 0.010201 0.020402
One pair 1 Yes 2 1,790,737,887,912 0.026951 0.053902
Loss 1 Yes -3 10,014,543,966,612 0.150721 -0.452164
Tie 1 Yes 0 195,881,895,144 0.002948 0.000000
Straight 1 No 2 1,944,063,612 0.000029 0.000059
Three of a kind 1 No 1 521,670,744 0.000008 0.000008
Two pair 1 No 1 57,782,013,408 0.000870 0.000870
One pair 1 No 1 2,716,947,685,944 0.040891 0.040891
High card 1 No 1 218,296,927,728 0.003285 0.003285
Loss 1 No -2 142,599,511,272 0.002146 -0.004292
Tie 1 No 0 21,633,803,136 0.000326 0.000000
Fold 0 -2 15,265,300,263,840 0.229747 -0.459493
Total 66,444,101,724,000 1.000000 -0.020583

The lower right cell in the table above shows a house edge of 2.06%, measured as the ratio of the expected player loss to the Ante bet.

The following table shows the probability of each number of units bet. The lower right cell shows that by the end of the hand the player will have an average total bet equal to 3.46 times the Ante bet.

Blind Bet Pay Table

Total Bet Probability Expected Bet
5 0.156561 0.782805
4 0.374377 1.497506
3 0.239316 0.717947
2 0.229747 0.459493
Total 1.000000 3.457752

What I feel is a good measure of the value of a bet is the Element of Risk. This is defined as the ratio of the expected player loss to the average total amount bet. In the case of Premium Hold 'Em, this ratio is 2.058%/3.458 = 0.595%.

The standard deviation, based on the Ante bet, is 4.63. This is similar to Jacks or Better video poker, which is 4.42. To compare to other casino games, please see my house edge comparison.

The following table shows the probability and contribution for all possible outcomes of the Player Bonus and Dealer Bonus bets. The lower right cell shows a house edge of 4.87%, which isn't bad for a side bet.

Player & Dealer Bonus Analysis

Hand Pays Combinations Probability Return
Royal flush 50 4,324 0.000032 0.001616
Straight flush 30 37,260 0.000279 0.008355
Four of a kind 10 224,848 0.001681 0.016807
Full house 6 3,473,184 0.025961 0.155766
Flush 4 4,047,644 0.030255 0.121020
Straight 3 6,180,020 0.046194 0.138581
Three of a kind 2 6,461,620 0.048299 0.096597
Two pair (jacks up or better) 1 17,385,408 0.129951 0.129951
All other -1 95,970,252 0.717349 -0.717349
Total 133,784,560 1.000000 -0.048656

Strategy

Discount Gambling has a very detailed strategy for Premium Hold 'Em. I recommend you follow the strategy there.


Written by: Michael Shackleford

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