Blazing 7's ™

Introduction

Blazing 7's™ is a blackjack side bet that pays based on the number of sevens in the player's first three cards. Pays start with just one seven in the first two cards and go up to a progressive jackpot for three suited sevens or three sevens in diamonds, depending on the version.

Note: Blazing 7's is trademarked by Bally Gaming.

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Rules

I have heard of two versions of this side bet, 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.

To make matters more complicated, not only are there two versions but two pay tables as well, as follow.

Pay Table 1

Three suited sevens: 100% of jackpot.
Three colored sevens: 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 colored sevens: 500 for 1.
Three sevens 200 for 1.
Two sevens 25 for 1.
One seven 2 for 1.

Analysis

Between the two versions and two pay tables, there are four possible combinations. For my analysis of all four combinations, six decks of cards is assumed. All wins are on a "for one" basis, meaning the player does not get his original bet back on a win. I have heard of bet amounts of $1 and $5. For statistics where the bet amount matters, I will present them for both a $1 and $5 bet.

Version 1 — Pay Table 1

The following return table is four Version 1 and Pay Table 1.

Version 1 — Pay Table 1 — Six Decks

Event	Pays	Combinations	Probability	Return
Three suited sevens	100% of Jackpot	21,735,360	0.000015	?
Three colored sevens	10% of Jackpot	97,809,120	0.000068	?
Three sevens	200	430,360,128	0.000301	0.060132
Two sevens	25	7,593,011,712	0.005305	0.132617
One seven	2	203,926,947,840	0.142468	0.284937
Loser	0	1,219,313,208,960	0.851843	0.000000
Total		1,431,383,073,120	1.000000	0.477686 + ?

Here is some more information about Version 1 and Pay Table 1.

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

Version 1 — Pay Table 2

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

Version 1 — Pay Table 2 — Six Decks

Event	Pays	Combinations	Probability	Return
Three sevens in diamonds	100% of Jackpot	5,433,840	0.000004	?
Three suited sevens	10% of Jackpot	16,301,520	0.000011	?
Three colored sevens	500	114,110,640	0.000080	0.039860
Three sevens	200	430,360,128	0.000301	0.060131
Two sevens	25	7,593,011,712	0.005305	0.132615
One seven	2	203,926,947,840	0.142467	0.284934
Loser	0	1,219,313,208,960	0.851833	0.000000
Total		1,431,399,374,640	1.000000	0.517540 + ?

Here is some more information about Version 1 and Pay Table 2 for both $1 and $5 bets.

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

Version 2 — Pay Table 1

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

Version 2 — Pay Table 1 — Six Decks

Event	Pays	Combinations	Probability	Return
Three suited sevens	100% of Jackpot	480	0.000016	?
Three colored sevens	10% of Jackpot	2160	0.000072	?
Three sevens	200	9504	0.000316	0.063192
Two sevens	25	158976	0.005285	0.132128
One seven	2	4285440	0.142468	0.284937
Loser	0	25623360	0.851843	0.000000
Total		30079920	1.000000	0.480257 + ?

Here is some more information about Version 2 and Pay Table 1 for both $1 and $5 bets.

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

Version 2 — Pay Table 2

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

Version 2 — Pay Table 2 — Six Decks

Event	Pays	Combinations	Probability	Return
Three sevens in diamonds	100% of Jackpot	120	0.000004	?
Three suited sevens	10% of Jackpot	360	0.000012	?
Three colored sevens	500	2160	0.000072	0.035904
Three sevens	200	9504	0.000316	0.063192
Two sevens	25	158976	0.005285	0.132128
One seven	2	4285440	0.142468	0.284937
Loser	0	25623360	0.851843	0.000000
Total		30079920	1.000000	0.516161 + ?