8 Deck Card Shoes

Card Counting the Buster Blackjack Side Bet, 6 Decks
April 2, 2013 – 09:02 am
4, 6, or 8 Deck Clear With

BBJ_03One of the most common blackjack side bets in California card rooms is known as Buster Blackjack (BBJ). I found this documentation online. The player who makes the BBJ wager wins if the dealer busts. The payout is then based on the total number of cards in the dealer’s busted hand. There are a lot of details to share, so I’ve decided to break up the discussion into the six-deck case and the two-deck case. This article covers card counting BBJ in a six-deck shoe game.

When I was asked about the vulnerability of BBJ to card counting by one of California’s largest banking corporations, I told them “not very.” After all, the dealer needs low cards to generate hands with lots of cards, he needs mid-cards to give stiff totals of 15 and 16, and he needs high cards to bust hands. My intuition was both right and wrong: the difference is the pay table.BBJ_04 There are eight different pay tables for BBJ that are in use or recommended. I investigated all eight and found that five of these eight are vulnerable and three are not. There is also a progressive version of BBJ that I did not investigate at all.

To begin with, I am going to focus on one specific vulnerable pay table for BBJ. This is the most common pay table used by card rooms banked by one of the largest corporations in California. The pay table is as follows:

  • Dealer busts with 8+ cards pays 200-to-1.
  • Dealer busts with 7 cards pays 100-to-1.
  • Dealer busts with 6 cards pays 30-to-1.
  • Dealer busts with 5 cards pays 6-to-1.
  • Dealer busts with 4 cards pays 3-to-1.
  • Dealer busts with 3 cards pays 1-to-1.
  • Otherwise, the player loses the BBJ bet.

BBJ_08Here is the combinatorial analysis for this pay table:

In particular,

  • The house edge is 4.724%.
  • The standard deviation is 2.724.
  • The hit frequency is 28.576%.

The following table gives the effect of removal (EOR) for each card. The EOR tells the change in house edge by removing a single card of that rank and re-computing the house edge. A positive EOR means that the edge moves towards the player side if the card is removed. A negative EOR means that the edge moves towards the house side if the card is removed.

Notice how much larger the EOR is for the cards A, 2, 3 than for any other card. With an abundance of these three cards in the shoe, the dealer is more likely to have hands with a large number of cards. Whether the dealer’s hand busts or not is beside the point to beat this pay table: the primary goal is to have multi-card hands. Removing a single deuce from a six-deck shoe moves the edge towards the house by 0.77%. That’s big. Also, an Ace never busts with fewer than four cards. Removing an Ace from the six-deck shoe moves the edge towards the house by 0.35%.

Source: apheat.net
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