Card Counting the Blazing 7’s and Heavenly 9’s Baccarat Side Bets

I was recently made aware of the collection of side bets known as “5 Treasures Baccarat” after an email from a reader. A quick search showed that Mike at WizardofOdds.com had already done the combinatorial analysis: here.

One of the five side bets is the well known Dragon 7 (Banker winning three card 7 pays 40-to-1) which is rebranded as the Fortune 7. Another one is the Panda 8 (Player winning three card 8 pays 25-to-1) which has been rebranded as the Golden 8. I have previously analyzed both of these.

In this post, I am going to look at two new side bets found in 5 Treasures Baccarat, Blazing 7’s and Heavenly 9’s.

Blazing 7’s

Blazing 7’s pays as follows

  • 7-7 Tie, Player and Banker each have 2 cards pays 50-to-1.
  • 7-7 Tie, Player and Banker each have 3 cards pays 200-to-1.
  • Otherwise the wager loses.

Blazing 7’s wins if the hand ends in a 7-7 tie and the Banker hand and Player hand have the same number of cards.  I have previously analyzed a 7-7 Tie under UR Way Egalite and found the 7-7 Tie to be the most vulnerable of that collection, returning 2.65 units per 100 hands. Intuitively, a shoe rich in 7’s will be good for the AP and that is exactly what the analysis shows.

A combinatorial analysis shows:

  • a house edge of 7.7797%
  • a standard deviation of 10.7651

Computing the EOR’s leads to the card counting system: (1,0,-1,-1,-1,0,-6,2,2,1), that is,

  • 8,9 = 2
  • A, T, J, Q, K = 1
  • 2, 6 = 0
  • 3, 4, 5 = -1
  • 7 = -6

A simulation of  one hundred million (100,000,000) eight-deck shoes counting Blazing 7’s with the cut card at 14 cards gives the following:

  • Trigger true count: +4
  • Wager frequency: 19.68%
  • Average edge: 10.44%
  • Win(in units) per 100 hands: 2.05
  • Win (in units) per shoe: 1.67

This side bet is certainly highly vulnerable to card counting and should be adequately protected.

Heavenly 9’s

Heavenly 9’s pays as follows:

  • Player and Banker both have a three card total of 9 pays 75-to-1.
  • Player or Banker (but not both) has a three card total of 9 pays 10-to-1.
  • Otherwise the wager loses.

Heavenly 9’s wins if the Player or Banker hand ends in a three card total of 9.  Like Blazing 7’s, intuitively a shoe rich in 9’s should be good for this bet. But, with more 9’s, the chance of a hand-ending natural 9 works against the AP.  For that reason, Heavenly 9’s does not have a significant card counting vulnerability.

A combinatorial analysis shows:

  • a house edge of 9.3105%
  • a standard deviation of 4.3977

Computing the EOR’s leads to the card counting system: (1,1,0,-1,-1,-1,-1,0,-2,1), that is,

  • A, 2, T, J, Q, K = +1
  • 3, 8 = 0
  • 4, 5, 6, 7 = -1
  • 9 = -2

A simulation of one hundred million (100,000,000) eight-deck shoes counting Heavenly 9’s with the cut card at 14 cards gives the following:

  • Trigger true count: +7
  • Wager frequency: 4.01%
  • Average edge: 6.70%
  • Win (in units) per 100 hands: 0.269
  • Win (in units) per shoe: 0.218

It’s clear from these numbers that card counting is not a realistic threat against this bet.

Team Play

Certainly two card counters working together against 5 Treasures Baccarat could have a lot of fun.  One AP will be counting the Dragon 7 (called the Fortune 7), the other counting Blazing 7’s.  When either makes their wager, the other follows suit.  In this way both counters get the advantage of playing against both bets simultaneously. Team play is absolutely something to be on guard against from the casino side.