Blackjack Appendix 8: Side Bets

Last update: Mar. 28, 2008

• 2 Run 21
• 2 Through 6
• 21+3
• 21 to the River
• Blackjack only
• Bonanza Blackjack
• Bonus Blackjack
• Bonus Spin
• Bust It
• Casino Surrender
• Field of Gold
• Hi/Low
• High Tie Bonus Blackjack
• Jack Magic
• Lucky Ladies
• Lucky Lucky
• Match the Dealer
• Over/Under 13
• Pair Square
• Perfect Pairs
• Progressive Blackjack
• Royal Match
• Straight 8's
• Streak
• Super Sevens
• Sweet 16
• Tie Bet
• Twin Blackjack
• Wheel of Madness
• Winners Option

Sign seen at the Silver Dollar casino near Seattle in June 2007. It would read "Side-bets are strictly prohibited", if it were spelled correctly.

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Super Sevens

The following is the payoff table for Super Sevens:

These awards are not cummulative, in other words if you get three sevens you don't get paid for one and two sevens as well. If the dealer gets a blackjack the player can still get paid for at least two sevens. At some casinos if the player has two sevens and the dealer gets a blackjack a third card will be dealt to the player for the chance to get three sevens.

The following probability table 1 shows the probability, payoff, and expected return of each hand. This table assumes (1) a third card is not dealt if the player has two sevens and the dealer gets a blackjack and (2) six decks.

The following probability table 2 shows the probability, payoff, and expected return of each hand. This table assumes (1) a third card is dealt if the player has two sevens and the dealer gets a blackjack and (2) six decks.

The tables above show a house edge of 12.61% if the player does not get a third card if the dealer gets a blackjack and a house edge of 11.40% if the player is guaranteed to get three cards.

Below are the derivations of the table 1 probabilities where n is the number of decks. The combin(x,y) function is the number of ways to arrange y cards out of x. For example combin(52,5)=2598960, the number of possible five card poker hands from a single deck. Let p₂ denote the probability that dealer will get a blackjack if the player's first two cards are sevens. Let p₃ denote the probability that dealer will get a blackjack if the player's first three cards are sevens. The combin(x,y) function can be used in Excel, by the way.

Probability of 1 seven: (1/13)*(48*n/(52*n-1))

Probability of 2 unsuited sevens: [combin(4n,2)-4*combin(n,2)]/combin(52*n,2) * [(48*n)/(52*n-2) * (1-p₂) + p₂]

Probability of 2 suited sevens: 4*combin(n,2)/combin(52*n,2) * [(48*n)/(52*n-2) * (1-p₂) + p₂]

Probability of 3 unsuited sevens: [combin(4n,3)-4*combin(n,3)]/combin(52*n,3) * (1-p₃)

Probability of 3 suited sevens: 4*combin(n,3)/combin(52*n,3) * (1-p₃)

p₂ = 4*(4*n)² / combin(52*n-2,2)

p₃ = 4*(4*n)² / combin(52*n-3,2)

Below are the probabilties for table 2 where the player is guaranteed to get a third card.

Probability of 1 seven: (1/13)*(48*n/(52*n-1))

Probability of 2 unsuited sevens: [combin(4n,2)-4*combin(n,2)]/combin(52*n,2)

Probability of 2 suited sevens: 4*combin(n,2)/combin(52*n,2) * (48*n)/(52*n-2)

Probability of 3 unsuited sevens: [combin(4n,3)-4*combin(n,3)]/combin(52*n,3)

Probability of 3 suited sevens: 4*combin(n,3)/combin(52*n,3)

Royal Match

The royal match is a simple bet that pays a bonus if the first two cards are suited (an easy match) and a top bonus for a suited king and queen (a royal match). Below are probability tables for two versions I have seen based on a single deck game.

The following table displays the house edge for each version given the number of decks used.

In the unlikely event you ever see version 2 at a table with 4 or more decks be sure to play it hard because the player will have the advantage.

At the Isle of Capri casino in Natchez, Mississippi, they use version 1 of the royal match with 6 decks. In the event both the player and dealer have a royal match the player wins an additional $1000. This lowers the house edge from 6.66% to 6.00%, assuming a $1 bet.

The probabilties for the royal match are easy to derive. Lets use n for the number of decks of cards. The number of two card combinations is combin(52*n,2). The number of ways to make a royal match is 4*n². This is because there are 4 suits and n ways to choose the queen and n ways to choose the king. The number of ways to make an easy match is 4*(combin(13*n,2)-n²). The 4 is the number of suits and combin(13*n,2) is the number of ways to arrange 2 cards from a given suit. You must also subtract the number of ways to make a royal match.

The probability of an easy match is 4*(combin(13*n,2)-n²)/combin(52*n,2).

The probability of a royal match is 4*n²/combin(52*n,2).

In a third version there is a separate pay for a suited blackjack as follows.

• Royal Match pays 25 to 1
• Suited Blackjack pays 5 to 1
• Easy Match pays 5 to 2

The following table shows the expected value for a 6-deck game is -3.70%.

The next table shows the house edge for various number of decks for version 3.

The Shufflemaster TMS 300 is an electronic blackjack game, played facing a giant video screen of a dealer. It features a Royal Match side bet, adding a pay for the player and dealer both having a royal match. Following is the return table for six decks.

The next table shows the house edge by number of decks.

Streak

Streak is an optional blackjack side bet I noticed at Caesars in Atlantic City in April of 2000. Since that time I have seen it displayed at the Global Gaming Expo, where I have been given rule updates. Streak is a simple bet on winning a specified number of consecutive bets. If the player splits then it is the net win that counts toward whether the hand as a whole won or lost. For example if the player split and won one hand and pushed the other the hand would count as a net win. In the event of a push or breaking even after a split the hand would not count for purposes of the side bet, neither advancing the number of consecutive wins nor breaking the winning streak. The player may bet on a winning streak from 2 to 5, or as many of these as desired.

My blackjack appendix 4 addresses the probability of a net win or loss. However that table includes surrender, which is usually not offered, and a player may decline to take anyway, if a Streak bet were on the line. So I reran my simulation with the following rules: six decks, dealer stands on soft 17, no surrender, player may split up to four hands, double on any two cards, double after split allowed, resplit aces not allowed, cut card used. Here are the results of the simulation.

The lower right cell shows a house edge of 0.4521%. This may look a bit high for the rules, especially against my blackjack calculator. Most house edge figures, including those of my calculator are based on a continuously shuffled game. The use of a cut card, as was the case in this simulation, adds 0.02% to the house edge with six decks. For more information on the cut card effect please see my blackjack appendix 10.

Adding up the wins and losses we get the following.

The probability of winning n hands in a row is simply 0.4751ⁿ. The following return tables show the pay table, probability of winning, and return for all four streak bets, under both the new and old rules.

The table above shows that under the new, more liberal, rules the best bet is on a streak of 4, with a house edge of 3.20%.

Over/Under 13

This pair of side bets pay even money if the player can correctly bet if the sum of the player's first two cards will be over or under 13. Aces count as 1. The following is the house edge according to the number of decks.

Pair Square

"Pair Square" is a blackjack side bet I have seen in Tunica and Reno that wins if the player's first two cards are of the same rank. A suited pair is best and pays more than an unsuited pair. The following table displays the pay off according to the number of decks and the corresponding house edge.

Tie

Caesars Palace in Las Vegas at one time offered a side bet on a tie at two of their blackjack tables. If the player and dealer do tie the side bet pays 10 to 1. The player may bet no more than 50% of their original blackjack wager on the side bet. If the player splits he must also split the side bet. The following table shows the proper basic strategy assuming the maximum side bet is played.

The combined house edge of the blackjack wager and the side bet is about 0.5% of the blackjack wager. For example if the player bets $100 on the blackjack wager and $50 on the side bet the total expected loss is 50 cents. This is based on 8 decks and the dealer hitting a soft 17.

21+3

Version 1 of 21+3 I noticed at the Las Vegas Hilton in April, 2001. The side bet pays based on the player's first two cards and the dealer's up card. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. The following table shows the probability of each hand in a six-deck game, as played at the Hilton.

The house edge under these rules is 3.24%.

At the Regent in Las Vegas all hands listed above, plus a pair, pay 5 to 2. I'll call this version 2. Two decks are used in this version. The following table shows a house edge under these rules of 2.78%.

I have an uncomfirmed report that Internet casinos using Wagerworks software use the following pay table, which I will call "Version 3."

Although Wager Works only uses six decks in their blackjack game, as far as I know, here is the house edge for 3 to 8 decks.

Sweet Sixteen

Sweet Sixteen is a blackjack side bet I noticed at the Las Vegas Club in April 2001. It is played with a six-deck shoe and pays based on the player's first two cards. The following table shows each paying hand, the probability, payoff, and contribution to the total return.

The lower right cell shows a return of 97.43%, for a house edge of 2.57%. Here is the house edge for other numbers of decks.

• 1 deck: 3.62%
• 2 decks: 2.99%
• 4 decks: 2.68%
• 8 decks: 2.52%

Dare any Pair

Dare any Pair is a side bet I noticed at the Lady Luck in April 2001. It simply pays 11 to 1 if the player's first two cards are a pair. Six decks are used. The probability of a pair is 0.073954984 for a house edge of 11.25%. Here is the house edge for other numbers of decks.

• 1 deck: 29.41%
• 2 decks: 18.45%
• 4 decks: 13.04%
• 8 decks: 10.36%

Lucky Ladies

This is a common side bet found in many casinos such as the Wizard's Casino (nice name) in Seattle. Any player 20-point hand wins something. There are three possible pay tables, A-C, as follows:

The next table is an analysis of pay table C with six decks.

The lower right cell shows a return of 75.29%, or a house edge of 24.71%.

The lower right cell shows a house edge of 29.89%.

The final Lucky Ladies table shows the house edge according to the pay table and number of decks. Note that the top hands with pay table A and B are impossible with 1 deck.

Bonus Blackjack

This is a simple pair of side bets that the player and/or dealer will get a blackjack. The player may bet on a player blackjack, dealer blackjack, or both. If the player bets both and the player gets a blackjack composed of an ace and jack of spades then the player will win a progressive bonus.

As the number of decks increases the probability of a blackjack decreases, making the player's odds worse. The following table shows pertinent information about this bet as explained below.

First column: Number of decks
Second column: House edge if just one bet is made
Third column: Overal reduction in house edge for each $100 in meter if both bets are made
Fourth column: Point meter must reach for bet to have zero house edge.

Progressive Blackjack

As the name implies this is a blackjack side bet with a progressive jackpot. For an optional $1 the blackjack player may see back $3 to the progressive jackpot, which starts at $25,000. I saw this side bet at the New York New York casino where they had three tables tied into the same progressive. On July 30, 2001, the jackpot meter was at $35537.36. At this time I was told they recently put it in place and nobody had hit the jackpot yet. On August 11 the meter had risen to $37746.28.

Just like in Caribbean Stud the player puts the $1 for the Progressive side bet in a slot. Before dealing a new hand the dealer presses a button, the dollars vanish, and a light designates who made the bet. The following table shows what each winning hand pays, the probability (based on six decks), and the contribution to the return.

The following table shows the return based on a meter of $35537.36, the amount the last time I observed it.

The above table shows an expected return of 56.10% per dollar bet, or a house edge of 43.90%. The general formula for the return is 47.01% plus 2.56% for each $10,000 in the meter. To have no house edge the meter would need to reach $207287.85. Also note there are no basic strategy deviations for this side bet. If the player gets two aces he should split anyway, which guarantees two more cards.

It is unclear to me what events cause the meter to go up and down. Sometimes the meter goes up by 28 cents for each $1 bet made. According to the Mikohn's web site the house edge is 22%. If this is the case then the meter contribution rate is 24.60%. Mikohn also mentions that part of each dollar goes to a higher reseed of the next jackpot. So 24.60% would be divided between the current meter and the next one. Based on this contribution rate the average jackpot when won would be $121,225.86.

Mikohn, the owners of this side bet, keep a list of casinos that offer this side bet here.

Twin Blackjack

Twin blackjack is not a side bet, but a variation of the game of blackjack. I saw the game at the Stardust in August, 2001. Each position has two betting spots. If the player makes a bet in both of them he will play out two hands against the dealer's up card. In the event the player gets two blackjacks (called twin blackjacks) they both shall pay 2-1. If the player gets two identical blackjacks (called identical twin blackjacks) both shall pay 4-1.

The following table shows what this is worth to the player.

The lower right cell in the table shows the twin blackjack rules add about 0.1133% to the players return. However as usual with novelty games you give more than you get back. In this case the player may NOT double after a split and the number of splits per hand is lowered from 3 to 2. Under the normal Stardust 6-deck rules the house edge is 0.4066%. Under these rules, not including the twin blackjack bonuses, the house edge is 0.5527%. Overall the house edge is 0.4394%, 0.0328% higher than the conventional rules.

Perfect Pairs

Perfect Pairs is a blackjack side bet found in casinos in Australia and London. It pays if the player's first two cards are a pair. The following table shows the specifics. A "perfect pair" is two identical cards (like two ace of spades). A "colored pair" is two cards of the same rank and color (like the ace of spades and ace of clubs). There are two pay tables, which are referred to as A and B. The following two tables show how the expected return is calculated for each pay table based on an 8 deck game.

The lower right cell shows a house edge of 4.10% and 3.37% respectively.

The next table shows the house edge for both pay tables according to the number of decks.

For more information visit the web site for www.tablegaming.com.

Bonanza Blackjack

Bonanza Blackjack is a side bet found on a fully electronic 6-deck game at the Boulder Station in Las Vegas. If the player has any 20 (including a soft 20) and the dealer has a 10-point card the player will win something. This is a $1 side bet, no more and no less.

The lower right cell shows a house edge of 18.19%.

Hi/Low

This is a simple pair of side bets I noticed at the Casablanca in Mesquite, Nevada. The player simply bets if his first card will be higher or lower than the dealer's up card. In the event the two cards are the same rank, except aces, the tie shall go to the dealer. Two aces push. The game I saw it on was 6-decks but here is the house edge for all numbers of decks.

2 Through 6

*: includes soft 19 and soft 20

The maximum bet allowed is the lesser of $50 and the blackjack bet.

Jack Magic

Jack Magic is a Shufflemaster side bet that has been seen at the Spirit Mountain casino in Grande Ronde, Oregon. It is played on a 5-deck blackjack game with a continuous shuffler. Wins are based on the player's initial two cards and the dealer's up card, thus no basic strategy changes are necessary. The following table shows the probability and return for each win. The lower right cell shows a house edge of 20.06%.

Match the Dealer

Match the Dealer is a side bet found in both blackjack and Spanish 21. The player wins for each of his initial two cards that match the dealer's up card. Matches in rank only pay less than a match in rank and suit. The following tables show the various versions I am aware of.

Some casinos offer a simple side bet that pays from 15 to 19 to 1 for a player blackjack. It is also possible for the bet to be based on a dealer blackjack, or both bets may be available. I have a blackjack table in my garage in which both are offered at 17 to 1. There is no particular name for this and I think it is a "common domain" bet, meaning nobody owns the idea so no royalties are required.

The following table shows the house edge for 1 to 8 decks and a payoff of 15 to 19 to 1.

Lucky Lucky is a side bet based on the player's first two cards and the dealer's up card. It is known to be played at some casinos in Alberta, Canada. The following tables shows the various winning hands, probability, payoff, and contribution to the total return, based on a six deck game. The lower right cell shows a house edge of 2.66%, one of the lowest for any side bet.

The following table shows the house edge for 1 to 8 decks and a payoff of 15 to 19 to 1.

Bonus Spin is a side bet in which the player gets to spin a wheel if he gets a blackjack. Also, a hand with at least one ace, but not a blackjack, pays 1 to 1. The prizes on the wheel are 5x, 15x, 25x, 20x, 10x, and 100x, where the x represents the bet amount. All wins are on a to one basis. Assuming all wins were equally likely the average win would be 29.17x, resulting in a player edge of 63.4%. Obviously the stops on the prize wheel where not equally weighted. I asked the table games manager what the average win was and he said it was right around 14. As the table below shows this results in a house edge of 8.63%, based on six decks.

* Based on an estimated average win.

The next table shows the house edge for 1 to 8 decks, again assuming an average win of 14.

Similar to Bonus Spin this is $1 side bet on a blackjack. If the player wins he gets to spin a prize wheel. According to Scott Brynen the average win is about 15 to 1, based on personal observation. Casinos will often allow bets of larger than $1, with a win of the product of the prize wheel and the bet made. The following table shows the probability of winning and house edge according to the number of decks, assuming an average win of 15 to 1.

This bet is vulnerable to card counting. Using indices of +1 for 2 to 9, 0 for 10-K, and -9 for aces, the odds swing in the player's favor at a true count (running count divided by decks remaining, rounding down) of 12. The next table shows how often this happens and the average advantage when it does in a 6-deck game according to the penetration, again assuming an average win of 15 to 1.

Version 1 of this is a side bet I noticed at the MGM Grand on November 26, 2005. It was played on a six-deck game.

Version 2 of this is a side bet I noticed at the Eldorado casino in Henderson on March 16, 2007. It was played on a six-deck game.

Field of Gold is a side bet I'm told can be found at the Spirit Mountain Casino in Grand Ronde, Oregon. All wins are based on the player's first two cards. For side bet purposes, aces always count as one. The following return table is based on six decks. The lower right cell shows a house edge of 5.66%.

The following table shows the house edge for various numbers of decks.

Casino Surrender is an optional rule in blackjack in which the player may force the dealer to surrender when the player has a 2-card 20 against a dealer 10. In other words the player may play out his hand or settle for a win of 50% of his bet. The option may only be invoked after the dealer checks for blacjack. The Stardust in Las Vegas has been seen offering this rule in May 2005.

The following table shows the player's expected return with a 20 agaisnt a dealer 10, after the dealer checks for blackjack, according to the number of decks and composition of the 20.

The table shows the player always stands to win 55.46% to 58.53% of his bet by playing out the hand. In a typical 6-deck game the player will give up 5.91% of his bet with a 10,10 and 5.46% with an A,9 by invoking the surrender option. The bottom line is taking dealer surrender is a mistake and the player should go for the full win.

"Bust It" is a side bet seen at the Taj Majal in Atlanic City in April, 2007. The side bet can not exceed the lesser of the blackjack bet and $25. It wins if the dealer busts on the third card. The side bet is available on ordinary blackjack and Double Attack Blackjack, which use a Spanish deck. It does not matter whether dealer hits or stands on soft 17, because either way busting with three cards is impossible. Card counters may be interested to know that the dealer is more likely to bust when the count is high. So at some positive count the odds would swing to the player's favor.

The following return table is for ordinary blackjack with eight decks. The lower right cell shows a house edge of 6.814%.

The next table shows the house edge for the pay table above and rules above for one to eight decks.

The following return table is for eight Spanish decks. The lower right cell shows a house edge of 8.006%.

The next table shows the house edge for the pay table above and rules above for one to eight Spanish decks.

"Straight 8's" is a blackjack side bet seen in Calgary in March 2007. Like the Lucky Lucky, it pays based on the player's first two cards and the dealer's up card.

The following return table is based on six decks. The lower right cell shows a house edge of 2.696%.

The next table shows the house edge for the pay table above and rules above for one to eight decks.

2 Run 21 is a blackjack side bet I noticed at the Silver Dollar casino in Seattle on June 5, 2007. It pays based on the player's first two cards, and the dealer's first two cards.

The following return table is based on six decks. The lower right cell shows a house edge of 10.236%.

The next table shows the house edge for the pay table above and rules above for one to eight decks.

In May 2008 I had an unconfirmed report that the above table is no longer the one in use. The writer claims the side bet is now based on only the player’s first two cards, and the dealer’s up card.

Winners Option is a side bet seen at the Las Vegas Hard Rock in August, 2007. In addition to playing blackjack normally, the player may bet on the dealer's hand. Unfortunately, you can't deliberately lose your own hand, in this case. If you bet on the dealer, as indicated on the table by a "D" arrow, then you must play according to the same rules as the dealer, never doubling or splitting, and hitting to hard 17 or soft 18. In the event both player and dealer bust, the bet will lose half.

I was not told how many decks were used, so I analyzed it by random simulation for all number of decks from one to eight. Here are the results. The right column shows the expected player loss. In a six-deck game, for example, the house edge would be 4.09%.

Winners Option web site.

21 to the River is a blackjack side bet I noticed at the Hard Rock in Las Vegas on March 27, 2008. The rules are as follows.

1. Player makes a blackjack and poker bet.
2. The blackjack bet shall be adjudicated according to conventional blackjack rules. In the case of the Hard Rock, these rules were six decks, dealer hits soft 17, double after split allowed, no surrender, and no resplitting aces.
3. In the event the blackjack hand busts, a five-card poker hand will be created using the card that busted the player, and the next four cards in the shoe.
4. If the poker hand shall pay according to the return table below.
5. If the player does not bust, then the poker bet will push.
6. If the player splits, the first hand, if any, that busts will start the poker hand. If none bust, the poker bet will push.

The first step to analyze this game is to determine the probability that the blackjack hand will bust, and if so, with what card. To answer this, I ran the following simulation. My simulation treats all 10-point cards the same way, so I divided that total between the four 10-point cards.

The total probability of busting comes to 13.29%. This is higher than other places on my site, which say it is 13.00%. This is because of the rule the splitting rule.

The next table shows the probability of each poker hand, with six decks, according to the first card dealt in the hand.

The next table combines the probability of each bust card, by the poker probabilities starting with that card.

The lower right cell shows a house edge of 1.29%, per bet made. The probability of the bet resolving with a win or loss is 10.96%. The house edge, per bet resolved, is thus 1.29%/10.96% = 11.76%.

If you are interested in the analysis of blackjack side bets, please see my Gaming Math course notes on that topic. Here are some links.

• blackjack side bets part 1.
• blackjack side bets part 2.
• March 8, 2005 homework questions..
• March 8, 2005 homework answers..
• March 15, 2005 homework questions..
• March 15, 2005 homework answers..

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