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TriLux
Introduction
TriLux is a blackjack side bet based on the first two player cards and the dealer up card. It is similar to the 21+3 side bet, except adds a fixed bonus for the dealer on any winning hand.
Rules
- The side bet is based on the use of ordinary 52-card decks.
- Winning hands are based on three cards — the initial two player cards and the dealer up card.
- There are three tables, as shown below. They show the pay table for the player, which is based on the bet amount, as usual. They also show the "Lucky George," which is a flat win paid to the dealer, regardless of the bet amount.
You may be wondering why the award to the dealer is called a "Lucky George bonus." All I know for sure is that a good tipper is called a "George." Meanwhile, a stingy tipper is called a "stiff." One theory is that a dollar bill features George Washington, and at the time that the saying caught on $1 was still a good tip.
Following are three known pay tables and Lucky George bonuses.
Pay Table 1
Event | Player Wins |
Lucky George |
---|---|---|
Straight flush | 8 to 1 | $1 |
Three of a kind | 8 to 1 | $1 |
Straight | 8 to 1 | $1 |
Flush | 8 to 1 | $1 |
Pay Table 2
Event | Player Wins |
Lucky George |
---|---|---|
Straight flush | 25 to 1 | $10 |
Three of a kind | 15 to 1 | $5 |
Straight | 8 to 1 | $2 |
Flush | 5 to 1 | $1 |
Pay Table 3
Event | Player Wins |
Lucky George |
---|---|---|
Straight flush | 25 to 1 | $10 |
Three of a kind | 15 to 1 | $5 |
Straight | 10 to 1 | $2 |
Flush | 5 to 1 | $1 |
The following pay table 4 I noticed at the 7 Cedars casino in Washington on July 28, 2021. I don't recall seeing a Lucky George bonus, so will assume it does not have one.
Pay Table 4
Event | Player Wins |
---|---|
Straight flush | 35 to 1 |
Three of a kind | 33 to 1 |
Straight | 10 to 1 |
Flush | 5 to 1 |
The following pay table 5 I heard was seen at the Silver Sevens casino in Las Vegas on May 17, 2023.
Pay Table 5
Event | Player Wins |
---|---|
Mini royal | 9 to 1 |
Straight flush | 9 to 1 |
Three of a kind | 9 to 1 |
Straight | 9 to 1 |
Flush | 9 to 1 |
Analysis — Pay Table 1
Following is my analysis of the player's expected return of pay table 1 and six decks. The lower right cell shows a house advantage of 12.91%.
Pay Table 1 — Player Analysis
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | 8 | 10,368 | 0.002068 | 0.016545 |
Three of a kind | 8 | 26,312 | 0.005248 | 0.041987 |
Straight | 8 | 155,520 | 0.031021 | 0.248171 |
Flush | 8 | 292,896 | 0.058424 | 0.467388 |
Loser | -1 | 4,528,224 | 0.903239 | -0.903239 |
Total | 5,013,320 | 1.000000 | -0.129147 |
Following is my analysis of the Lucky George bonus of pay table 1 and six decks. The lower right cell shows the dealer can expect to get ¢9.68 for every hand played.
Pay Table 1 — Lucky George Analysis
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | $1 | 10,368 | 0.002068 | $0.002068 |
Three of a kind | $1 | 26,312 | 0.005248 | $0.005248 |
Straight | $1 | 155,520 | 0.031021 | $0.031021 |
Flush | $1 | 292,896 | 0.058424 | $0.058424 |
Total | 5,013,320 | 1.000000 | $0.096761 |
The next table shows the expected return for both the player and dealer by number of decks under pay table 1.
Pay Table 1 — House Edge
Decks | Player Return |
Dealer Return |
---|---|---|
2 | -0.165356 | $0.092738 |
4 | -0.138195 | $0.095756 |
5 | -0.132766 | $0.096359 |
6 | -0.129147 | $0.096761 |
8 | -0.124624 | $0.097264 |
Analysis — Pay Table 2
Following is my analysis of the player's expected return of pay table 2 and six decks of cards. The lower right cell shows a house advantage of 23.25%.
Pay Table 2 — Player Analysis — Six Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | 25 | 10,368 | 0.002068 | 0.051702 |
Three of a kind | 15 | 26,312 | 0.005248 | 0.078726 |
Straight | 8 | 155,520 | 0.031021 | 0.248171 |
Flush | 5 | 292,896 | 0.058424 | 0.292118 |
Loser | -1 | 4,528,224 | 0.903239 | -0.903239 |
Total | 5,013,320 | 1.000000 | -0.232521 |
Following is my analysis of the Lucky George bonus of pay table 2 with six decks. The lower right cell shows the dealer can expect to get ¢16.74 for every hand played.
Pay Table 2 — Lucky George Analysis — Six Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | $10 | 10,368 | 0.002068 | $0.020681 |
Three of a kind | $5 | 26,312 | 0.005248 | $0.026242 |
Straight | $2 | 155,520 | 0.031021 | $0.062043 |
Flush | $1 | 292,896 | 0.058424 | $0.058424 |
Total | 5,013,320 | 1.000000 | $0.167389 |
The next table shows the expected return for both the player and dealer by number of decks under pay table 2.
Pay Table 2 — House Edge
Decks | Player Return |
Dealer Return |
---|---|---|
2 | -0.266529 | $0.159338 |
4 | -0.241138 | $0.165330 |
5 | -0.235977 | $0.166562 |
6 | -0.232521 | $0.167389 |
8 | -0.228185 | $0.168430 |
Analysis — Pay Table 3
Following is my analysis of the player's expected return of pay table 3. The lower right cell shows a house advantage of 17.05%.
Pay Table 3 — Player Analysis — Six Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | 25 | 10,368 | 0.002068 | 0.051702 |
Three of a kind | 15 | 26,312 | 0.005248 | 0.078726 |
Straight | 10 | 155,520 | 0.031021 | 0.310214 |
Flush | 5 | 292,896 | 0.058424 | 0.292118 |
Loser | -1 | 4,528,224 | 0.903239 | -0.903239 |
Total | 5,013,320 | 1.000000 | -0.170479 |
Following is my analysis of the Lucky George bonus of pay table 3 and six decks. The lower right cell shows the dealer can expect to get ¢16.74 for every hand played.
Pay Table 3 — Lucky George Analysis — Six Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | $10 | 10,368 | 0.002068 | $0.020681 |
Three of a kind | $5 | 26,312 | 0.005248 | $0.026242 |
Straight | $2 | 155,520 | 0.031021 | $0.062043 |
Flush | $1 | 292,896 | 0.058424 | $0.058424 |
Total | 5,013,320 | 1.000000 | $0.167389 |
The next table shows the expected return for both the player and dealer by number of decks under pay table 3.
Pay Table 3 — House Edge
Decks | Player Return |
Dealer Return |
---|---|---|
2 | -0.203268 | $0.159338 |
4 | -0.178794 | $0.165330 |
5 | -0.173814 | $0.166562 |
6 | -0.170479 | $0.167389 |
8 | -0.166292 | $0.168430 |
Combined Casino Cost
Although this site usually looks at games from the player's perspective, I will break from that with the following tables. They show the expected profit according to the amount of the player's bet and the pay table for six and two decks. These figures are lower than the house edge figures in the tables above because the casino must pay the player winnings and the Lucky George bonus.
House Edge from Casino Perspective — Six Decks
Bet | Pay Table 1 |
Pay Table 2 |
Pay Table 3 |
---|---|---|---|
$100 | 12.82% | 23.08% | 16.88% |
$50 | 12.72% | 22.92% | 16.71% |
$25 | 12.53% | 22.58% | 16.38% |
$20 | 12.43% | 22.42% | 16.21% |
$15 | 12.27% | 22.14% | 15.93% |
$10 | 11.95% | 21.58% | 15.37% |
$5 | 10.98% | 19.90% | 13.70% |
$3 | 9.69% | 17.67% | 11.47% |
$2 | 8.08% | 14.88% | 8.68% |
$1 | 3.24% | 6.51% | 0.31% |
House Edge from Casino Perspective — Two Decks
Bet | Pay Table 1 |
Pay Table 2 |
Pay Table 3 |
---|---|---|---|
$100 | 16.44% | 26.49% | 20.17% |
$50 | 16.35% | 26.33% | 20.01% |
$25 | 16.16% | 26.02% | 19.69% |
$20 | 16.07% | 25.86% | 19.53% |
$15 | 15.92% | 25.59% | 19.26% |
$10 | 15.61% | 25.06% | 18.73% |
$5 | 14.68% | 23.47% | 17.14% |
$3 | 13.44% | 21.34% | 15.02% |
$2 | 11.90% | 18.69% | 12.36% |
$1 | 7.26% | 10.72% | 4.39% |
Analysis — Pay Table 4
The following table shows my analysis of pay table 4, based on six decks. The lower right cell shows a house edge of 4.41%.
Pay Table 4 — Pay Table 4 Analysis — Six Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Mini Royal | 100 | 864 | 0.000172 | 0.017234 |
Straight flush | 35 | 9,504 | 0.001896 | 0.066351 |
Three of a kind | 33 | 26,312 | 0.005248 | 0.173198 |
Straight | 10 | 155,520 | 0.031021 | 0.310214 |
Flush | 5 | 292,896 | 0.058424 | 0.292118 |
Loser | -1 | 4,528,224 | 0.903239 | -0.903239 |
Total | 5,013,320 | 1.000000 | -0.044124 |
With eight decks and the same pay table, version 4 would have a house edge of 3.71%.
Analysis — Pay Table 5
The following table shows my analysis of pay table 5, based on eight decks. The lower right cell shows a house edge of 2.74%.
Pay Table 5 Analysis — Eight Decks
Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Mini Royal | 9 | 2,048 | 0.000172 | 0.001547 |
Straight flush | 9 | 22,528 | 0.001891 | 0.017021 |
Three of a kind | 9 | 64,480 | 0.005413 | 0.048717 |
Straight | 9 | 368,640 | 0.030947 | 0.278519 |
Flush | 9 | 700,928 | 0.058841 | 0.529572 |
Loser | -1 | 10,753,536 | 0.902736 | -0.902736 |
Total | 11,912,160 | 1.000000 | -0.027360 |
With six decks, pay table 5 has a house edge of 3.24%.
External Links
- Wizard of Vegas — Discussion of this side bet.