I saw this blackjack side bet in the Venetian last month, and it looked pretty you-know-what. I forgot to post about it until now. I’m pretty sure they use 8-deck shoes at the Venetian.
|Removed Card||EOR||Balanced Count||Unbalanced Count|
Using the unbalanced taps, the bet is +EV for RC >= +34 (assuming two decks behind the cut card). This yields 16% betting opportunities, with an average edge of +2.8%/bet. The theoretical max (using full shoe composition, including suits) is 17% opportunities @ +3.0%/bet. It’s not worth much.
A reader pointed me out to Galaxy Gaming’s Bust Bonus blackjack side bet that the dealer will bust, which you make after seeing the dealer’s upcard. I figured I’d run the numbers to see if it was any good, or if it was countable. Well, it might be a fun bet on a few upcards, but it’s kind of expensive for the (offsuit) odds they offer.
*Bust Bonus wagered after dealer peeks for blackjack.
The most countable bet is against a dealer 8 upcard. It has the lowest house edge (4.9%), and has high payouts for the 888o and 888s busts. The EORs are large, and a simple unbalanced count (Eight => -8, Nine, Ten/Face, Ace, Deuce, Trey, Four => +1; bet when running count >= +24) yields an average +7.5% edge/bet on 17.3% of the dealer 8 upcard hands. Of course, a dealer 8 only occurs on 1/13th of the hands, so it’s not a very practical bet. An ideal count (using total shoe composition including suits) yields a theoretical max return of +7.5% edge/bet on 1.6% of the dealt hands.
Sadly, the standard BJ counts (like the unbalanced Knockout count) don’t correlate with the EV of any of these bets, because unlike blackjack, the Ace hurts the Bust Bonus bet. (Ace rich shoe makes it harder to bust.)
I ran across the Bust It blackjack side bet last weekend at the Palazzo in Las Vegas. It seemed countable, so I ran the numbers today. The bet is simple. You make the side bet before the hand begins, and if the dealer busts on 3 cards, you win according to the paytable. If the dealer doesn’t bust on 3 cards, you lose. The basic house edge for a 6-deck shoe game is -6.91%. The EORs are fairly high, as listed below.
|Card||EOR||Balanced Count||Unbalanced Count||Simplified Count|
If the cut card is placed after the 5th deck, then an ideal count (using perfect shoe composition) yields 14.7% betting opportunities, with an average +6.73% advatange per bet. That’s an average return of about 1.0% per dealt hand.
Practically, you’d use the unbalanced count in the table above and bet with a running count of +25 or more. This practical count yields 14.4% betting opportunities, with an average +6.1% edge per bet. That works out to an average return of +0.88% per dealt hand.
Depending on the side bet limits, counting this bet could be profitable. But, more likely, they’ll limit you to a $25 max bet. So your profit rate would be (100 hands/hr)(14.4% bets/hand)(+6.1% profit/bet)($25/bet) = $22/hr. Of course, you’ll almost certainly have to make the main bet too (e.g., the Cosmopolitan wouldn’t let me make bonus bets on my friend’s blackjack hand). If it’s only $5, and you get good rules @ -0.6%, then your cost would be (100 hands/hr)($5/hand)(-0.6%) = $3/hr, leaving you with a $19/hr job.
The unbalanced count is fairly complicated, with its multi-level taps. Unless your a very skilled counter, you’ll be better off using the simplified count above. It only uses +2 and -1 taps, and it still performs well, yielding 13.5% betting opportunities, with an average +5.3% edge per bet. Bet when the running count is +24 or more.
Also, the standard blackjack counts don’t work for this bet (there’s no correlation, I checked). You can tell that blackjack counts are very different than this specialised count, because Aces are +3 and Sixes are -2. Those are opposite to blackjack values, and they make sense. Ace-rich shoes are bad for 3-card busts. Also, sixes are valuable because of the 15:1 payouts.
Note: a reader says the Palazzo/Venetian deals out of 8-deck shoes. If that’s the case, and they place the cut card @ 6 decks, then the ideal return decreases to 10.7% frequency at an average +4.7% edge. The simplified count return decreases to 8.9% opportunities @ +3.5% edge per bet. You would bet for an RC of +32 or higher.
bust with 888 suited
bust with 888 coloured
bust with 6
bust with 7
bust with 8
bust with 9
bust with 10
no 3 card bust
I came across the Push Your Luck (PYL) blackjack sidebet yesterday (while browsing, not IRL), and I wondered if it was exploitable in any way. PYL is a simple side bet. You make the bet before you start your blackjack hand, and if you end up pushing your main bet, you win 10:1 on the side bet. The max bet is 1/2 your main bet, and its usually limited to $25.
PYL has been out there for a while, but it’s new to me. It’s pretty simple to code up in my analyzer, which finds the optimal play for the combined (main + side) bet. I don’t know why, but I always expect these bets to be +EV, or somehow exploitable. I’m kind of optimistic that way.
Well, I was very surprised to find the house edge of the side bet is very low. Even when you max the side bet (@ 1/2 your main bet), the house edge of the combined (main + side) bet is only 0.76% for a 6 deck game with good rules (DAS, SP4, SPA4, H17). That’s like a cost of 0.25%, and you’re getting 10:1 odds! Here’s the auto-generated strategy table:
With a max PYL bet, the game gets a little wild where you’re hitting the majority of your under-17 hands, even against low dealer upcards. People must have a fit at this game. But it looks kind of fun, because you’re trying to get a nice 10:1 payout. It’s a good reason to play crazy.
I thought with such a low house edge, and with a 10-to-1 multiplier, the game would be easily countable. However, the EORs are pretty tame, and are very similar to standard blackjack:
You’ll probably need the proper index plays for (not) hitting your under-17 hands on +EV counts. I looked at the strategy for a small +EV count, and the borderline decisions shift towards standard plays. If I get around to learning the lingo for index plays, I’ll post them here for PYL.
The new bust me blackjack sidebet is bad, but at least it’s countable. It’s a blackjack side bet you make after seeing your hand, on whether you’ll bust on the next hit. You get different odds, depending on your total. They’ll let you bet table limits on the side bet, regardless of the size of your main bet. So its pretty obvious that the house edge has to be horrendous to avoid it being countable. And it is. (It’s both horrendous, and countable.)
I’m pretty sure anyone can tell just by looking at the paytable, but here’s the numbers anyways.
|Total||Payout For Bust||House Edge|
Yep, it’s that bad. A true sucker bet. You might be able to fool some of the players some of the time, but you won’t be able to fool them for long. Everyone will catch on to how bad this bet is sooner or later.
Of course it has to be bad, since the first thing everyone thinks about is counting for 10′s and 9′s, and waiting until the end of the shoe to whoop out the $500 and $1000 Bust Me bets on hard-13. (The rack cards make it clear you can bet the table limits at any time, regardless of the size of your main bet.) I thought there might be frequent +EV opportunities, so I plotted the distribution of EV’s for the hard-13 bet throughout the shoe:
The Bust Me 13 sidebet gets very good rather frequently. Of course, you must have hard-13 to bet, so this +EV opportunity only occurs on about 2.6% of your hands, with an average edge of +5.4%/bet. That’s not great, but you can make a huge $500 or $1000 table limit bet, until they stop you. So you’ll get about 1.2 betting opportunities per shoe, and even if you bet $1000, you’ll only average about a $65 profit per shoe.
(Thanks to reader fivespot for pointing out my error in the first version of the post; I had one of those one-line bugs, and was shuffling after every hand. Aiyah!)
Hooray, another game that I did the math for hits the floor! House Money is a blackjack side bet created by Roger Snow of ShuffleMaster. It’s unique because it allows the player to cap his main blackjack bet with his side bet winnings. The side bet pays when your first two cards make a pair, straight, or straight flush. So, if you’re dealt a suited A-K, the side bet pays 9:1. You always have the option of taking the proceeds (10 units in this case), and adding it to your main blackjack bet. In this case, your BJ nets you a profit of (3:2)(10) + 9 = 24 units on the side bet. (If this reads too much like a paid advertisement, skip to the section on counting for this bet.)
For a 6-deck shoe game with good rules, and the correct capping strategy, the house edge for this side bet is only 2.6%. The basic strategy of when to cap your main bet with your side bet proceeds is presented below.
The rules for the House Money side bet are as follows:
- The player makes the optional side bet wager before the hand is dealt.
- The side bet pays for the initial 2-card player hands according to the paytable below.
- The player has the late (after dealer peeks for BJ) option of capping his main blackjack bet with an amount up to the entire side bet proceeds.
- The player completes the main hand following normal blackjack rules.
The table below tells you when you should cap your main bet with the winning proceeds of your side bet. “Y” means to cap the bet with the proceeds, because the EV of the hand (after the dealer peeks for BJ) is positive. “N” means not to cap the bet, but just to collect your winnings, because the post-peek EV of the hand is negative. After the capping decision, play your hand according to blackjack basic strategy.
|Straights and Straight Flushes|
|KQ, QJ, JT||Y||Y||Y||Y||Y||Y||Y||Y||Y||Y|
|98, 87, 76||N||N||N||N||N||N||N||N||N||N|
This side bet is only slightly countable, using the counting coefficients (2 => +1, 3 => +1, 4 => +1, 5 => 0, 6 => 1, 7 => 1, 8 => 1, 9 => 1, T => -1, J => -1, Q => -1, K => -2, A => -2) and a true count threshold of 3.1. From a 6-deck shoe with 1 deck behind cut card, you’ll have +EV betting opportunities about 13.4% of the time, with an average edge of +3.4%/bet. So betting $25 when the count is good will yield a profit rate (13.4%)($25)(+3.4%) = $0.11/hand. At 100 hands per hour, this yields $11/hr, which isn’t worth anyone’s time or effort.
Everybody thank Eliot Jacobson for working for you. He emailed me this morning telling me the Field of Gold blackjack side bet was crushable. And it is. For real. The count is simple, and for a 6-deck shoe game, you’ll be able to bet 19% of the time, with an average edge of +6.5%/bet. That’s a profit of ($25 bet)(19% bet/hand)(+6.5% EV/bet) = $0.31/hand. For double-deck, the numbers are even better, yielding 27% betting opportunities with an average edge of +8.2%/bet. For $25 bets, that yields a profit of $0.55 per hand dealt. That adds up pretty quickly. It’s more than $100/hr.
This is about as good as it gets, as it’s a fast blackjack game. Oh, by the way, Eliot also brought you the equally crushable Lucky Lucky bet, which I probably understated in my post. These are probably the best two countable side bets out there, and nobody but Eliot has noticed them. Oh, and he’s the one that pointed out the Dragon-7 vulnerability.
Use the following count:
|Nine, Ten, Queen, King||+1|
This side bet becomes highly profitable when the shoe is rich in aces and deuces, and lean in high cards. During some shoes, the deck can easily get really good, or really bad for the Field of Gold bet. The distribution of the side bet EV is plotted below over the course of the 6-deck shoe and the double-deck game. Note the peak of the distribution is centered about the nominal -5.66% return of the bet right after the shuffle. Then, especially towards the end of the shoe, the side bet return can vary wildly. Note all the area under the long tail of the distributions to the right of the y-axis (EV>0). This is why the game is crushable.
(5 deck penetration of 6-deck shoe; 29 cards behind cut card in double-deck.)
Well, here’s another massively countable side bet that some people might be interested in (advantage players, casino floor supervisors, and the game publisher), but that I’ll never play. I think after this one, designers will know to check their games for vulnerabilities, especially when there’s oversized items in the paytable. And we’ll remember, “It’s not a sucker bet if the count is good.”
Again, Eliot Jacobson pointed this one out to me. (But, if Barona had this side bet, I’d have already looked at it.)
The Lucky Lucky blackjack side bet is played with your first two dealt cards, and the dealer upcard. On these three cards, you get paid for various ways to make 21, and for any 20 and 19 total. The most countable version of this side bet is for the double-deck version with the paytable below. The game is also countable for the 6 deck shoe game, but it’s only 60% as profitable.
As usual, I program a function that tells me the EV for any given shoe composition. Then I simulate millions of hands, calculating the ideal EV of the side bet at the beginning of each hand. I sum up the times when the side bet is +EV, and find the average +EV bet and +EV frequency. For the double-deck Lucky Lucky, I got
double-deck, cut card @ 75th card ideal +EV frequency: 0.2769, ideal EV/bet: +0.0591
which is not a practical counting scheme, but the theoretical limit if you used a computer that took into account all info (suits, etc.).
Then I calculated the Effect-of-Removal (EORs) of a given card on the EV, in order to make counting tags. (Outside the gambling world, people would call “EORs” sensitivities, and “tags” coefficients.)
So, setting the trueCount threshold to 2.4 (bet Lucky Lucky when the trueCount is >= 2.4), you get the practical results in double deck:
practical frequency: 0.2640, average EV/bet: +0.0561
6 Deck Shoe Version
The 6 deck shoe paytable is better than the double deck version, as it pays 200:1 for a suited 777. The EORs are similar, and I came up with the same count tags as the double deck game. Using a trueCount threshold of 2.1, the practical counting scheme yields:
ideal +EV frequency: 0.2311, ideal average EV/bet: +0.0432 practical frequency: 0.2217, practical average EV/bet: +0.0409
which is only 61% of the profit rate as the double-deck game.
My local Barona Casino offers the Royal Match blackjack side bet which pays 75-to-1 when you’re dealt a suited K-Q on your first two cards, and 2-1 for any other suited hand. Normally, the house edge is 4.06% for this side bet, but as readers of this blog know by now, sucker bets are often countable. Using a simple true K-Q count, the bet yields an average 5.4% player edge.
I always play this bet for $1, and get really excited when I hit it for $75. The last time I hit it, I decided to analyze it’s countability.
I first looked at the bet’s distributions of EVs at the last hand of the shoe. This would show me if there was any potential for a counting scheme. I’d see how often and how strongly the bet went +EV. Here’s what it looks like with one deck remaining:
I could tell from the graph that the bet was exploitable. So I calculated the average profit per shoe, assuming heads-up play with the dealer. This theoretical limit comes out to a profit of +0.504 bets/shoe. That’s a really good profit rate (compare to the Dragon-7 profit rate of 0.54 bets/shoe). That means a player betting a fixed amount on the Royal Match will net an average profit equal to half his bet per shoe, when heads up with the dealer. On a per bet basis, the average Royal Match bet EV is +5.9%, assuming perfect knowledge of the dealt cards.
I then looked for a simple (practical) counting scheme that would capture most of the theoretical edge. As it worked out, the second idea that came to mind happened to be very effective. A simple true count of excess Kings and Queens yields about +0.43/shoe (85% of the theoretical edge):
trueCount = (8*decksDealt - countedKingsAndQueens)/decksRemaining
where decksDealt and decksRemaining are floating-point numbers.
Note that you should bet the Royal Match when the true count is >= 0.8.
In heads-up play, you’ll get an average of 8.0 bets/shoe, with an average bet EV of +5.4%. The scheme is very comparable with the highly profitable Dragon-7 counting scheme (EV +0.54/shoe), but it’s much faster, and has much lower variance.
So if you don’t find me at the full-exposure Mississippi Stud game, look for me in the i-Table pit counting the Royal Match.
I recently saw the Instant-18 blackjack side bet, and I thought it was funny. It’s an even-money side bet that plays against the dealer as a hand of value 18. Hence, the name “Instant-18″. You put up a bet, and it’s an 18. It has a 2.036% house edge for a 6-deck shoe, but it’s still kind of interesting. It’s an optional side bet where (typically) you can bet an amount less than or equal to your main blackjack bet. Of course, I had to see if this bet was countable.
This looked promising, so I checked out the EORs for the bet:
From the EORs, I made a simple count system, where Aces are +3, Sevens are -2, and Deuces are -1. Then I plotted the EVs of the main and side bet vs. the true count:
Unfortunately, when the count for the side bet gets good (true count >= 4), the main bet is -EV. However, for a good enough count (true count >= 7), the combination of (main bet + side bet) is +EV. Also, for a bad enough count (true count <= -3), them main bet is +EV.
So, by itself, the Instant-18 side bet gets good (true count >= 4) about 7.8% of the time, with an average return of +1.53%.
Of course, you can’t just bet the side bet when it gets good. You have to have a main bet to bet the side bet. If you bet both when the combination gets good (true count >= 7), or just the main bet for true count <= -3, and Wong all others, you'll bet 13.9% of the time with an average EV of +0.47%.
As usual, these things are interesting, but not practical.