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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
- Six or eight ordinary 52-card decks are used.
- 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
- 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.
- The dealer deals two cards two the player and one face up card to the dealer.
- 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.
- The dealer deals one more card to the player and two more to himself.
- The poker-value of the player's hand is compared to the dealer's hand, the higher hand wins.
- 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.
- If the dealer has the higher hand, then the Ante, Odds, and Play wagers all lose.
- 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.
- 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.
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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.
External Links
- Super Three Card — Discussion in my forum at Wizard of Vegas.