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Trifecta
Introduction
The Trifecta is a blackjack side bet where wins are based on the poker-value of the three-card hand consisting of the player's initial two cards and the dealer's up card. Comparisons could be easily made to the 21+3 and Lucky Lucky.
I noticed the Trifecta at the Wynn Las Vegas on June 10, 2011. On June 30, 2023, I saw it at the Golden Nugget in Laughlin, NV.
Rules
As mentioned in the introductions, wins on the Trifecta are based on the poker-value of the player's first two cards and the dealer's up card. The following is the pay table I noticed in use at the Wynn.
Pay Table
| Bet | Pays |
|---|---|
| 5,5,5 | 60 |
| Straight flush | 40 |
| Three of a kind | 30 |
| Straight | 6 |
| Flush | 4 |
| Pair of jacks or better | 2 |
Analysis
The following table shows my analysis of the pay table above, based on six decks. The lower right cell shows a house edge of 5.12%, which, for a side bet, isn't bad.
Return Table
| Bet | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 5,5,5 | 60 | 2,024 | 0.000404 | 0.024223 |
| Straight flush | 40 | 10,368 | 0.002068 | 0.082724 |
| Three of a kind | 30 | 24,288 | 0.004845 | 0.145341 |
| Straight | 6 | 155,520 | 0.031021 | 0.186128 |
| Flush | 4 | 292,896 | 0.058424 | 0.233694 |
| Pair of jacks or better | 2 | 300,672 | 0.059975 | 0.119949 |
| All other | -1 | 4,227,552 | 0.843264 | -0.843264 |
| Total | 5,013,320 | 1.000000 | -0.051204 |
Assuming the same pay table, the house edge with four decks is 6.70% and with eight decks is 4.32%.