Introduction

In both online and land-based casinos the wagering options a player has are numerous. There is a core set of games that are easily recognized and understood by the player.  Consequently, players more readily gravitate to those types of games. Some of these games favor the player more while other games favor the casino more. However, in the casinos’ ongoing attempt to extract more and more money from the player they offer variations of a commonly known game. This is done most often in the game of 21

The axiom of any advantage player is: “Given the right circumstances, any game is beatable.” And this holds true for the blackjack variations, where it is easy to keep track of what cards have been played.  One such blackjack variation is the Blazing 7s Blackjack game. Here we will be taking a closer look at the Blazing 7s Blackjack game and discuss its vulnerabilities’.

Playing Blazing 7s

Before we get into the Blazing 7s vulnerabilities we have to know what the objectives and rules of the game are.  Blazing 7s Blackjack is a new take on the traditional game of 21. It’s played just like traditional blackjack; the game offers an additional side bet that has some astonishingly high payouts.

The Blazing 7 side bet pays out based on the number of sevens in the player's first three cards. If you place your bet and draw a seven, you're a winner. Payouts start with just one seven in the players’ first two cards, and increase all the way up to a progressive jackpot that hits when three suited sevens or three sevens in diamonds are dealt to the player.

A payout is also incurred when a 6,7,8 is dealt to the player.  What payouts are had depends on what version of the game is being played. In some cases the games are linked across multiple casinos and the progressive jackpots can get quite high.   

Bonuses come in a 1-unit bonus or a 5-unit bonus, depending on which version you are playing.  The following chart shows the value in units of the payouts. It’s important to remember that these payouts are rare events and the percentages are over the lifetime of the game. The short-term payouts are much greater as we will see below. This means when you actually hit one of the payable bonuses in your playing session.

Hand 1 Unit Bonus 5 Unit Bonus
Any 678 0.17% 1.15%
Any 777 0.02%  0.11%
Suited 678 0.01%  0.05%
Suited 777 0% 0%

Blazing 7s Rules

There are two versions of the Blazing 7s side bet. Each one has slightly different nuances but the objective remains the same. They variations are as follows:

  • Version 1: Wins are based on the first three player cards. Wins for one or two sevens are based on the first two cards only. If the player hits, the first additional card shall count as the third card. If the player splits, then the first card dealt to the first hand shall count as the third card. If the dealer has a blackjack, then the player is capped at two cards. 
  • Version 2: Wins are based on the first two player cards and the dealer up card. Wins for one or two sevens are based on the player cards only

Further complicating things, there are two pay tables as well. Pay table 1 below is for version 1 and pay table 2 is for version 2. 

Pay Table 1

  • Three suited sevens: 100% of jackpot.
  • Three sevens of the same color: 10% of jackpot. 
  • Three sevens 200 for 1. 
  • Two sevens 25 for 1. 
  • One seven 2 for 1. 

Pay Table 2 

  • Three sevens in diamonds: 100% of jackpot.
  • Three suited sevens: 10% of jackpot.
  • Three sevens of the same color: 500 for 1. 
  • Three sevens 200 for 1. 
  • Two sevens 25 for 1. 
  • One seven 2 for 1.
Side Bets

Probability and Percentages 

There are four permutations of the game when you consider the two versions and two pay tables. Here we assume that we are using a six-deck shoe for all variations. For all payouts the player does not get his original bet back on a win. Bets can range from $1 to $5, but for simplicity we use a $1 side wager. The player can easily multiply the results by 2,3,4 or 5 to get those values. 

The following table is the return table is for Version 1 and Pay Table 1. 

Version 1 Pay-Table 1

Event Payout Combinations Probability Return
3 Suited 7 100% Jackpot 21,735,360 0.000015 Jackpot Dependent
Three 7s same color 10% Jackpot 97,809,120 0.000068 Jackpot Dependent
Three 7s 200 430,360,128 0.000301 0.060132
Two 7s 25 7,593,011,712 0.005305 0.132617
One 7 2 203,926,947,840 0.142468  0.284937
Loss 0 1,219,313,208,960 0.851843 0
Total   1,431,383,073,120 1.0 0.477686

The following insights on the Version 1 pay table 1 are from Mike Shackelford and the Wizard of Odds website.

  • Fixed wins = 47.77% 
  • Return per $1000 in meter ($1) = 2.20% 
  • Return per $1000 in meter ($5) = 2.44% 
  • 1% in meter ($1) = $454.17 
  • 1% in meter ($5) = $2,270.86 
  • Break-even ($1) = $23,722.09 
  • Break-even ($5) = $118,610.45

The following return table is for Version 1 and Pay Table 2.

Version 1 Pay Table 2 

Event Payout Combinations Probability Return
3 Suited 7 diamonds 100% of Jackpot 5,433,840 0.000004 Jackpot Dependent
Three 7s suited 10% of Jackpot 16,301,520 0.000011 Jackpot Dependent
Three 7s same color 500 114,110,640 0.000080 0.039860
Three 7s 200 430,360,128 0.000301 0.060131
Two 7s 25 7,593,011,712 0.005305 0.132615
One 7 2 203,926,947,840 0.142467 0.284934
Loss 0 1,219,313,208,960 0.851833 0.000000
Total   1,431,399,374,640 1.000000 0.517540

The following insights on the Version 1 pay table 2 are from Mike Shackelford and the Wizard of Odds website.

  • Fixed wins = 51.75% 
  • Return per $1000 in meter ($1) = 0.49% 
  • Return per $1000 in meter ($5) = 0.10% 
  • 1% in meter ($1) = $2,026.33 
  • 1% in meter ($5) = $10,131.66 
  • Break-even ($1) = $97,762.40 
  • Break-even ($5) = $488,812.02 

The following table is the return table for Version 2 and Pay Table 1.

Version 2 Pay Table 1

Event Payout Combinations Probability Return
Three suited 7s 100% of Jackpot 480 0.000016 Jackpot Dependent
Three 7s same color 10% of Jackpot 2160 0.000072 Jackpot Dependent
Three 7s 200 9504 0.000316 0.063192
Two 7s 25 158976 0.005285 0.132128
One 7 2 4285440 0.142468 0.284937
Loser 0 25623360 0.851843 0.000000
Total   30079920 1.000000 0.480257

The following insights on the Version 2 pay table 1 are from Mike Shackelford and the Wizard of Odds website.

  • Fixed wins = 48.03% 
  • Return per $1000 in meter ($1) = 2.31% 
  • Return per $1000 in meter ($5) = 0.46% 
  • 1% in meter ($1) = $432.18 
  • 1% in meter ($5) = $2,160.91 
  • Break-even ($1) = $22,462.41 
  • Break-even ($5) = $112,312.07

The following return table is for Version 2 and Pay Table 2.

Version 2 Pay Table 2

Event Payout Combinations Probability Return
3 Suited 7 diamonds 100% of Jackpot 120 0.000004 Jackpot Dependent
Three 7s suited 10% of Jackpot 360 0.000012 Jackpot Dependent
Three 7s same color 500 2160 0.000072 0.035904
Three 7s 200 9504 0.000316 0.063192
Two 7s 25 158976 0.005285 0.132128
One 7 2 4285440 0.142468 0.284937
Loss 0 25623360 0.851843 0.000000
Total   30079920 1.000000 0.516161

  
The following insights on the Version 2 pay table 1 are from Mike Shackelford and the Wizard of Odds website.

  • Fixed wins = 48.03% 
  • Return per $1000 in meter ($1) = 0.52% 
  • Return per $1000 in meter ($5) = 0.10% 
  • 1% in meter ($1) = $1,928.20 
  • 1% in meter ($5) = $9,641.00 
  • Break-even ($1) = $100,216.92 
  • Break-even ($5) = $501,084.62 
Blackjack Players

Vulnerability

Because 21 is a game with memory and we have direct knowledge of what cards have been removed from the deck, it is reasonable to determine that the Blazing 7s game is beatable. Mostly because the effect of removal can be calculated for each card, which is why card counting is so effective.

Because there are six decks per shoe there are a total of 24 7s in the shoe. If we keep track of the 7s in the shoe that have been played and normalize the number of remaining 7s into the number of decks that remain to be played we can get a value.

Consider that no 7s have been played and there are four shoes that are still to be played, we will get a normalized value of 1.5 (24/4 = 6, this means there are 6 7s per remaining deck and then 6/4 decks remaining = 1.5).

At this value, it is a positive game for the player. 1.5 would be the minimum normalized value I would play for this game.  The higher the normalized number the greater the advantage for the player.  

Conclusion

The Blazing 7s side bet is beatable for the player. At normalizations of values of 7s greater than 1.5, it gives a positive expectation for the player. It takes exceptional patience for the player to get to the 1.5 value. When it does arrive you should max bet the side bet and hope for the best.  Sooner or later it will hit and you will get paid off in a big way.

About the Author
By

Nicholas is a 17 year veteran of the casino gaming industry. He is former player manager with the infamous MIT Blackjack teams and is a regular attendee of the Blackjack Ball, a gathering of the world’s top professional gamblers.

He is the Managing Director of the Alea Consulting Group, a leading gaming consultant company with a focus on gaming economics and, is a frequent contributor to world class business publications like Forbes and Entrepreneur magazines’ and over 15 gaming trade publications. He is also the founder of Casino Exploits a player centric casino gaming site.