# Super Three Card

## Introduction

Super Three Card has the betting structure of Ultimate Texas Hold 'Em, but based on a three-card as in Three Card Poker. But wait, there's more, the game is played with a six- or eight-deck shoe. All due credit to Galaxy Gaming for trying something new. I first noticed that game at the Rampart casino in Las Vegas on January 28, 2019.

## Rules

1. Six or eight ordinary 52-card decks are used.
2. Three-card poker hands are ranked as follows:
• Royal flush (suited A-K-Q)
• Suited three of a kind
• Straight flush
• Three of a kind (unsuited)
• Straight
• Flush
• Pair
• Ace high or less
3. Play starts with the player making equal wagers on the Ante and Odds bets. At this time the player may make side bets, as explained later.
4. The dealer deals two cards two the player and one face up card to the dealer.
5. The player has two choices, raise or surrender:
• If the player raises, then he must make a Play wager, equal to the Ante bet.
• If the player surrenders, then he loses his Ante bet and his Odds bet is returned.
6. The dealer deals one more card to the player and two more to himself.
7. The poker-value of the player's hand is compared to the dealer's hand, the higher hand wins.
8. If the player has the higher hand or there is a tie, then the Ante and Play wagers pay even money, while the Odds bet pays according to one of the pay tables below.
9. If the dealer has the higher hand, then the Ante, Odds, and Play wagers all lose.
10. One side bet is titled the Big Hand Bonus and pays based on the poker value of the initial three cards dealt (two to the player and one to the dealer). There are various pay tables, as shown below.
11. There is another side bet whose name is not clear, so I'll call it the Progressive Bet. It is a flat \$1 bet and also pays according to the same three cards as the Big Hand Bonus. The pay table is also below.

Following are three pay tables available for the Odds bet.

### Odds Bet Pay Table

Hand Pay Table 1 Pay Table 2 Pay Table 3
Royal flush 50 60 100
Suited three of a kind 10 30 50
Straight flush 5 10 15
Three of a kind 4 5 5
Straight 3 3 3
Suited pair 2 2 2
Flush 2 1.5 1
Pair of jacks or better 1 1 1
All other Push Push Push

Following are six pay tables available for the Big Hand Bonus bet.

### Big Hand Bonus Pay Table

Hand Pay Table 1 Pay Table 2 Pay Table 3 Pay Table 4 Pay Table 5 Pay Table 6
Three suited aces 1000 500 1000 1000 1000 1000
Royal flush 150 150 150 150 100 75
Suited three of a kind 100 100 100 100 50 50
Straight flush 50 50 40 50 40 40
Three of a kind 30 30 30 30 30 30
Straight 6 6 6 5 6 6
Suited pair 4 4 4 4 4 4
Flush 3 3 3 3 3 3
All other Loss Loss Loss Loss Loss Loss

Following is the only known pay table available for the Bonus Jackpot bet. Wins are on a "for one" basis.

### Bonus Jackpot Pay Table

Hand Pays
Suited three of a kind (J-K) Jackpot
Suited three of a kind (all other) \$125
Straight flush \$25
Three of a kind (unsuited) \$20
Straight \$6
Flush \$2

If these rules were not clear, please see if scans of the rule card help. Click either image for a larger version.

## Base Game Six Deck Analysis

The following three tables show my analysis of the base game under the three different Odds bet pay tables.

The following table is for Odds bet pay table 1 (that goes 50-10-5-4-3-2-2-1) and six decks. The lower right cell shows that the house edge is 2.54%, relative to the Ante bet. The average bet by the end of the hand is 2.77 units. This makes the element of risk, defined as the ratio of the expected loss to total amount bet 2.54%/2.77 = 0.92%.

### Odds Bet Pay Table 1 — Six Decks

Hand Pays Combinations Probability Return
Player wins with mini royal 52 864 0.000172 0.008962
Player wins with suited three of a kind 12 1,040 0.000208 0.002492
Player wins with straight flush 7 9,492 0.001893 0.013253
Player wins with unsuited three of a kind 6 25,154 0.005017 0.030105
Player wins with straight 5 136,794 0.027286 0.136431
Player wins with suited pair 4 176,643 0.035235 0.140939
Player wins with flush 4 209,648 0.041818 0.167273
Player wins with pair 3 198,984 0.039691 0.119073
Player wins with less than pair 2 1,448,155 0.288861 0.577723
Fold -1 1,147,536 0.228897 -0.228897
Dealer wins -3 1,659,009 0.330920 -0.992761
Total   5,013,319 1.000000 -0.025408

The following table is for Odds bet pay table 2 (that goes 60-30-10-5-3-2-1.5-1) and six decks. The lower right cell shows that the house edge is 2.58%, relative to the Ante bet. The average bet by the end of the hand is 2.67 units. This makes the element of risk, defined as the ratio of the expected loss to total amount bet 2.58%/2.677 = 0.97%.

### Odds Bet Pay Table 2 — Six Decks

Hand Pays Combinations Probability Return
Player wins with mini royal 62 864 0.000172 0.010685
Player wins with suited three of a kind 32 1,040 0.000207 0.006638
Player wins with straight flush 12 9,492 0.001893 0.022720
Player wins with unsuited three of a kind 7 25,154 0.005017 0.035122
Player wins with straight 5 136,794 0.027286 0.136431
Player wins with suited pair 4 176,209 0.035148 0.140593
Player wins with flush 4 206,952 0.041280 0.144482
Player wins with pair 3 198,984 0.039691 0.119073
Player wins with less than pair 2 1,446,684 0.288568 0.577136
Fold -1 1,161,936 0.231770 -0.231770
Dealer wins -3 1,649,211 0.328966 -0.986898
Total   5,013,320 1.000000 -0.025788

The following table is for Odds bet pay table 3 (that goes 100-50-15-5-3-2-1-1) and six decks. The lower right cell shows that the house edge is 2.57%, relative to the Ante bet. The average bet by the end of the hand is 2.68 units. This makes the element of risk, defined as the ratio of the expected loss to total amount bet 2.57%/2.68 = 0.96%.

### Base Game Pay Table 3 — Six Decks

Hand Pays Combinations Probability Return
Player wins with mini royal 102 864 0.000172 0.017579
Player wins with suited three of a kind 52 1,040 0.000207 0.010787
Player wins with straight flush 17 9,492 0.001893 0.032187
Player wins with unsuited three of a kind 7 25,154 0.005017 0.035122
Player wins with straight 5 136,794 0.027286 0.136431
Player wins with suited pair 4 175,262 0.034959 0.139837
Player wins with flush 3 201,064 0.040106 0.120318
Player wins with pair 3 198,066 0.039508 0.118524
Player wins with less than pair 2 1,443,840 0.288001 0.576002
Fold -1 1,193,328 0.238031 -0.238031
Dealer wins -3 1,628,416 0.324818 -0.974454
Total   5,013,320 1.000000 -0.025699

## Base Game Eight Deck Analysis

The following three tables show my analysis of the base game under the Odds bet pay tables 2 and 3.

The following table is for pay table 2 (where the Odds bet pay table goes 60-30-10-5-3-2-1.5-1) and eight decks. The lower right cell shows that the house edge is 2.23%, relative to the Ante bet. The average bet by the end of the hand is 2.67 units. This makes the element of risk, defined as the ratio of the expected loss to total amount bet 2.23%/2.67 = 0.84%.

### Odds Bet Pay Table 2 — Eight Decks

Hand Pays Combinations Probability Return
Player wins with mini royal 62 2,048 0.000172 0.010659
Player wins with suited three of a kind 32 2,911 0.000244 0.007820
Player wins with straight flush 12 22,499 0.001889 0.022665
Player wins with unsuited three of a kind 7 61,276 0.005144 0.036008
Player wins with straight 5 324,294 0.027224 0.136119
Player wins with suited pair 4 438,216 0.036787 0.147149
Player wins with flush 4 489,389 0.041083 0.143791
Player wins with pair 3 470,372 0.039487 0.118460
Player wins with less than pair 2 3,422,164 0.287283 0.574566
Fold -1 2,754,816 0.231261 -0.231261
Dealer wins -3 3,924,175 0.329426 -0.988278
Total   11,912,160 1.000000 -0.022301

The following table is for Odds bet pay table 3 (that goes 100-50-15-5-3-2-1-1) and eight decks. The lower right cell shows that the house edge is 2.14%, relative to the Ante bet. The average bet by the end of the hand is 2.67 units. This makes the element of risk, defined as the ratio of the expected loss to total amount bet 2.14%/2.67 = 0.80%.

### Base Game Pay Table 3 — Eight Decks

Hand Pays Combinations Probability Return
Player wins with mini royal 102 2,048 0.000172 0.017536
Player wins with suited three of a kind 52 2,911 0.000244 0.012707
Player wins with straight flush 17 22,499 0.001889 0.032109
Player wins with unsuited three of a kind 7 61,276 0.005144 0.036008
Player wins with straight 5 324,294 0.027224 0.136119
Player wins with suited pair 4 436,041 0.036605 0.146419
Player wins with flush 3 476,506 0.040002 0.120005
Player wins with pair 3 468,326 0.039315 0.117945
Player wins with less than pair 2 3,416,014 0.286767 0.573534
Fold -1 2,823,765 0.237049 -0.237049
Dealer wins -3 3,878,479 0.325590 -0.976770
Total   11,912,159 1.000000 -0.021437

## Big Hand Bonus Analysis

There are six known pay tables for the Big Hand Bonus bet. In the interests of brevity, I will show the full breakdown of pay table 2 only, the one used by the Rampart casino, for both six and eight decks. The one below is for six decks. The lower right cell shows a house edge of 6.36%.

### Big Hand Bonus Pay Table 2 — Six Decks

Hand Pays Combinations Probability Return
Three suited aces (other suit) 500 80 0.000016 0.007979
Royal flush 150 864 0.000172 0.025851
Suited three of a kind 100 960 0.000191 0.019149
Straight flush 50 9,504 0.001896 0.094787
Three of a kind 30 25,272 0.005041 0.151229
Straight 6 155,520 0.031021 0.186128
Suited pair 4 224,640 0.044809 0.179235
Flush 3 236,736 0.047221 0.141664
All other -1 4,359,744 0.869632 -0.869632
Total   5,013,320 1.000000 -0.063610

The following table shows my analysis of Pay Table 2 of the Big Hand Bonus for eight decks. The lower right cell shows a house edge of 4.54%.

### Big Hand Bonus Pay Table 2 — Eight Decks

Hand Pays Combinations Probability Return
Three suited aces 500 224 0.000019 0.009402
Royal flush 150 2,048 0.000172 0.025789
Suited three of a kind 100 2,688 0.000226 0.022565
Straight flush 50 22,528 0.001891 0.094559
Three of a kind 30 61,568 0.005169 0.155055
Straight 6 368,640 0.030947 0.185679
Suited pair 4 559,104 0.046936 0.187742
Flush 3 561,152 0.047107 0.141322
All other -1 10,334,208 0.867534 -0.867534
Total   11,912,160 1.000000 -0.045420

The following table shows the house edge for all six pay tables for six and eight decks.

### Big Hand Bonus House Edge Summary

Hand Pay Table 1 Pay Table 2 Pay Table 3 Pay Table 4 Pay Table 5 Pay Table 6
Three suited aces 1000 500 1000 1000 200 100
Royal flush 150 150 150 150 100 75
Suited three of a kind 100 100 100 100 50 50
Straight flush 50 50 40 50 40 40
Three of a kind 30 30 30 30 30 30
Straight 6 6 6 5 6 6
Suited pair 4 4 4 4 4 4
Flush 3 3 3 3 3 3
Six Decks 5.56% 6.36% 7.46% 8.67% 10.55% 11.15%
Eight Decks 3.60% 4.54% 5.49% 6.70% 8.99% 9.60%

## Bonus Jackpot Analysis

This side bet is also found on some blackjack games. For my analysis of that, please see my page on Bonus Jackpot.

## Acknowledgements

I would like to thank Galaxy Gaming for sharing with me their BMM math report for this game, for my which my analysis of the base game is based. I did my own work for the Big and Bonus and Bonus progressive.