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C3: A Blackjack Side Bet
Introduction
I noticed a side bet in blackjack called the C3 at the Bregenz casino in Austria on March 10, 2018. It seemed to be on every blackjack table. Other bets, called the C4 and C5, were on other games. Following are the rules.
Rules
Wins are based on the player's initial two cards and the dealer's up card. In the event the player qualifies for a win more than one way, only the higher pay will be paid. The pay table is as follows:
- Highest hearts (three ace of hearts) pays 300 to 1.
- Jacks in black (three jacks in the color black) pays 200 to 1.
- Trips (three of a kind) pays 50 to 1.
- Red carpet (three red cards) pays 4 to 1.
Analysis
The following table shows my analysis for six decks. The lower right cell shows a house edge of 10.86%.
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 edge with four decks is 12.90% and with eight decks is 9.83%.