# 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%.