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Last Updated: December 7, 2016

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



  1. The side bet is based on the use of ordinary 52-card decks.
  2. Winning hands are based on three cards — the initial two player cards and the dealer up card.
  3. 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


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%







Written by: Michael Shackleford

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