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C3: A Blackjack Side Bet

Introduction

During a visit to the Bregenz casino in Austria on March 10, 2018, I observed a side bet known as C3 that was available at all blackjack tables. There were also side bets labeled C4 and C5 for different games. Below are the rules governing these bets.

Rules

Winning outcomes are determined by the player’s first two cards along with the dealer’s visible card. If the player qualifies for multiple win scenarios, only the highest payout is awarded. The payout structure is as follows:

  • The highest hearts combination (three aces of hearts) awards a payout of 300 to 1.
  • A combination of three black jacks pays 200 to 1.
  • Trips (three of a kind) pays 50 to 1.
  • Red carpet (three red cards) pays 4 to 1.

Analysis

Presented here is my analysis for games played with six decks, indicating a house edge of 10.86% in the bottom right cell of the table.

C3 — Six Decks

Event Pays Combinations Probability Return
Highest hearts 300 20 0.000004 0.001197
Jacks in black 200 220 0.000044 0.008777
Trips 50 26,072 0.005201 0.260027
Red carpet 4 617,760 0.123224 0.492895
All other -1 4,369,248 0.871528 -0.871528
Total   5,013,320 1.000000 -0.108632

The house advantage stands at 12.90% when using four decks and drops to 9.83% with eight decks.