There's a particular blackjack side bet known as 21+3. It includes the player's first two cards and the dealer's upcard. For this bet to work, the three cards must form a winning combination with hands like a Flush, Straight, Three of a Kind, or a Straight Flush. If any of these hands are created, the player wins. Initially, the payout for these hands was 9:1. Given this RTP, the house edge for blackjack works out to 3.2386%. More recently, updated pay tables have been introduced. They display increased volatility and higher house edges.
I want to focus on Flushes as my point of departure. Whenever there is a dramatic imbalance in the suits, this favours players. Let's consider an example as a case in point. In a situation where there are 40 cards in a deck, there are ten cards for each of the four suits. Let's not delve into the mathematics too deeply; the number of ways to formulate a three-card Flush works out to 480.
Further, let's use those 40 cards and assume a distribution of 15-10-10-5. We can now see that the number of Three Card Flushes increases to 705. By deduction, we can tell that an unbalanced distribution of suits results in a greater edge for the player.
To put this to use, we need to track the number of cards for each suit remaining in the blackjack shoe. We can do this with a card counting team. Each team member maintains a meticulous record of the suits. Alternatively, this can be completed with an experienced card counter. These card counters determine the difference between abundant and scarce suits in play. We then calculate the true count based on this difference. Once the true count is substantial, the player automatically gains a larger edge over the house. Finally, I would like to draw your attention to a simulation model I created using a six-deck shoe game of blackjack. There are 52 cards in the deck, and it has been simulated for 100 million shoes.
Based on the simulations, a card counter can enjoy a mathematical edge over the house on roughly 3.5% of hands dealt. That translates into 1.75 hands per shoe. The card counter is advised to play the 21+3 blackjack side bet every time the true count is at least eight or greater. Consider that once this bet is placed, the standard edge is a smidgen over 5%. If the table limit is C$25, a card counter who competes in a heads-up contest can expect to earn C$2.20 per shoe. We haven't evaluated the new pay tables yet.
For illustration, I conducted an experiment where I shuffled 100,000 shoes. I computed the edge once 100 cards remained in the shoe. Based on this intensive analysis, the simulation revealed an average house edge of 3.247%. This is pretty close to the theoretical value of 3.239%. The standard deviation of the house edge amounted to 3.57%. Once again, we can determine that the player edge amounts to 0.910 standard deviations above the mean. Accordingly, the player has an advantage on some 18.14% of shoes. The real challenge is to determine which ones offer the edge. Based on my simulation, the maximum player edge of 23.71% was computed with a maximum house edge of 13.55%.
Now let's turn our attention to Advantage Players. APs tend not to target the 21+3 blackjack side bet with this system. Firstly, it's complex. Secondly, there is a low return. But, there is an alternative approach that may yield better results. Let's imagine shuffle tracking, where several cards are immediately identified as abundant or deficient in a suit. When we track that through a weak card shuffle, the advantage player has a terrific opportunity to profit. I have limited knowledge of shuffle tracking technology, and I cannot definitively say that this technique has been used practically. Also, I've not contemplated whether the updated pay tables are likewise vulnerable to the 9:1 pay table.
For additional information on this exciting topic, click these links:
- Beating the 21+3 Blackjack Side Bet: Some Really Cool Graphs
- Beating the 21+3 Blackjack Side Bet: Update #1
- Perfect Play against the 21+3 Extreme Blackjack Side Bet
Take a look at my recommendations vis-a-vis 21+3:
* Keep a keen eye on individual players who place this bet at specific times during the shoe and when they make their plays. You will notice it's a maximum bet. These blackjack players tend to use a shuffle-tracking approach to their betting.
* Keep a close watch on a team of blackjack players who place maximum bets on this blackjack side bet at the same time. They might be using a card counting system.
* If, on the other hand, you are playing a hand-shuffled game, and if players can track it, consider an automatic shuffler device or a new shuffle.
